On This Day in Math - Oct 31

It is true that a mathematician who is not somewhat of a poet,

will never be a perfect mathematician.

~Karl Weierstrass

The 304th day of the year; 304 is the sum of six consecutive primes starting with 41, and also the sum of eight consecutive primes starting with 23. (and for those who keep up with such things, it is also the record number of wickets taken in English cricket season by Tich Freeman in 1928.)


EVENTS
In 1815, English chemist, Sir Humphrey Davy of London (Davy was actually from Penzance) patented the miner's safety lamp. Miners at work constantly met firedamp, an explosive mix of methane gas and air, during the working of coal. This was an almost insurmountable obstacle to the working of many of the collieries until the discovery of the safety lamp. The flame of the safety lamp is surrounded by a copper or iron gauze cylinder, with openings no more than 1/24-inch. Such a fine gauze prevents flame passing through, but fails if coarser. The wire absorbs or conducts away the heat of the flame contained inside the lamp so it does not explode gas outside the lamp. If firedamp is present, a pale blue flame appears around the central flame. This warns a miner to leave the area immediately! *TIS

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1839 (Sometime in October) the first teacher’s institute was held at Hartford, Connecticut, 26 men teachers attended a six week course sponsored by Henry Barnard and received the “opportunity of critically reviewing the studies which they will be called upon to teach, with a full explanation of all the principles involved.” The authority who gave instruction on higher mathematics was Charles Davies. *VFR

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1903 At a New York meeting of the AMS F. N. Cole (1861-1927) presented a paper “On the factoring of large numbers.” He spoke not a word, but carefully raised 2 to the 67th power, then subtracted one. Moving over he computed 193,707,721 times 761,838,257,287. The calculations agreed, showing that 267 − 1 was not a Mersenne prime. E. T. Bell, in Mathematics—Queen and Servant of the Sciences, wrote, with his usual exageration, “For the first and only time on record, an audience of the American Mathematical Society vigorously applauded the author or a paper delivered before it.” Later, in 1911, Bell asked Cole how long it had taken him to find this factorization and he replied “Three years of Sundays.” It is instructive to check this arithmetic on your hand held calculator. [Eves, Adieu, 297◦; BAMS 10(1903), 134] *VFR

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1915 Closing date for a prize consisting of a gold medal bearing the portrait of Weierstrass and 3000 Swedish crowns for the best essay on the theory of analytic functions. King Gustav V of Sweden founded the prize to commemorate the centenary of the birth of Weierstrass. *VFR

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1918 The wife of the Russian mathematician Lyapunov died of tuberculosis. On the same day, Lyapunov shot himself. He died three days later, on 3 November 1918. *VFR

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In 1992, the Vatican admitted erring for over 359 years in formally condemning Galileo Galilei for entertaining scientific truths such as the Earth revolves around the sun it, which the Roman Catholic Church long denounced as anti-scriptural heresy. After 13 years of inquiry, the Pope's commission of historic, scientific and theological scholars brought the pope a "not guilty" finding for Galileo. *TIS In 1822 the church lifted the ban on the works of Galileo and in 1979 Pope John Paul II selected a commission to investigate. On Mar 31 of 1984 the Vatican newspaper, L’Observatore Romano, stated, “The so-called heresy of Galileo does not seem to have any foundation, neither theologically nor under canon law.” It still took until Oct 31, 1992, before Pope John Paul II declared that the church may have been mistaken in condemning Galileo. *Wik

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BIRTHS
1711 Laura Maria Catarina Bassi (31 Oct 1711 in Bologna, Papal States, 20 Feb 1778 in Bologna, Papal States) was an Italian physicist and one of the earliest women to gain a position in an Italian university. *SAU

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1815 Karl (Theodor Wilhelm) Weierstrass (31 Oct 1815; 19 Feb 1897) was a German mathematician who is known as the "father of modern analysis" for his rigor in analysis led to the modern theory of functions, and considered one of the greatest mathematics teachers of all-time. He was doing mathematical research while a secondary school teacher, when in 1854, he published a paper on Abelian functions in the famous Crelle Journal. The paper so impressed the mathematical community that he shortly received an honorary doctorate and by 1856, he had a University appointment in Berlin. In 1871, he demonstrated that there exist continuous functions in an interval which have no derivatives nowhere in the interval. He also did outstanding work on complex variables. *TIS

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1847 Galileo Ferraris (31 Oct 1847; 7 Feb 1897) Italian physicist who studied optics, acoustics and several fields of electrotechnics, but his most important discovery was the rotating magnetic field. He produced the field with two electromagnets in perpendicular planes, and each supplied with a current that was 90º out of phase. This could induce a current in a incorporated copper rotor, producing a motor powered by alternating current. He produced his first induction motor (with 4 poles) in May-Jun 1885. Its principles are now applied in the majority of today's a.c. motors, yet he refused to patent his invention, and preferred to place it at the service of everyone. *TIS

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1890 Joseph Jean Camille Pérès (31 Oct 1890 in Clermont-Ferrand, France, 12 Feb 1962 in Paris, France) Pérès' work on analysis and mechanics was always influenced by Volterra, extending results of Volterra's on integral equations. His work in this area is now of relatively little importance since perhaps even for its day it was somewhat old fashioned.
A joint collaboration between Pérès and Volterra led to the first volume of Theorie generale des fonctionnelles published in 1936. Although the project was intended to lead to further volumes only this one was ever published. This work is discussed in [3] where the author points out that the book belongs to an older tradition, being based on ideas introduced by Volterra himself from 1887 onwards. By the time the work was published the ideas it contained were no longer in the mainstream of development of functional analysis since topological and algebraic concepts introduced by Banach, von Neumann, Stone and others were determining the direction of the subject. However, the analysis which Pérès and Volterra studied proved important in developing ideas of mathematical physics rather than analysis and Pérès made good use of them in his applications. *SAU

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1902 Abraham Wald (October 31, 1902 – December 13, 1950) was a mathematician born in Cluj, in the then Austria–Hungary (present-day Romania) who contributed to decision theory, geometry, and econometrics, and founded the field of statistical sequential analysis. He spent his researching years at Columbia University.*Wik

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1919 Father Magnus J. Wenninger OSB (born Park Falls, Wisconsin, October 31, 1919) is a mathematician who works on constructing polyhedron models, and wrote the first book on their construction. *Wik

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1925 John A. Pople (31 Oct 1925; 15 Mar 2004) British mathematician and chemist who, (with Walter Kohn), received the 1998 Nobel Prize in Chemistry for his work on computational methodology to study the quantum mechanics of molecules, their properties and how they act together in chemical reactions. Using Schrödinger's fundamental laws of quantum mechanics, he developed a computer program which, when provided with particulars of a molecule or a chemical reaction, outputs a description of the properties of that molecule or how a chemical reaction may take place - often used to illustrate or explain the results of different kinds of experiment. Pople provided his GAUSSIAN computer program to researchers (first published in 1970). Further developed, it is now used by thousands of chemists the world over. *TIS

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1927 Narinder Singh Kapany (31 Oct 1927, )Indian-American physicist who is widely acknowledged as the father of fibre optics. He coined the term fibre optics for the technology transmitting light through fine glass strands in devices from endoscopy to high-capacity telephone lines that has changed the medical, communications and business worlds. While growing up in Dehradun in northern India, a teacher informed him that light only traveled in a straight line. He took this as a challenge and made the study of light his life work, initially at Imperial College, London. On 2 Jan 1954, Nature published his report of successfully transmitting images through fiber optical bundles. The following year he went to the U.S. to teach. In 1960, Optics Technology. He holds over 100 patents.*TIS

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1935 Ronald Lewis Graham (born October 31, 1935) is a mathematician credited by the American Mathematical Society as being "one of the principal architects of the rapid development worldwide of discrete mathematics in recent years". He has done important work in scheduling theory, computational geometry, Ramsey theory, and quasi-randomness. Graham was also featured in Ripley's Believe It or Not for being not only "one of the world's foremost mathematicians", but also "a highly skilled trampolinist and juggler", and past president of the International Jugglers' Association. He is currently the Chief Scientist at the California Institute for Telecommunications and Information Technology (also known as Cal-(IT)2) and the Irwin and Joan Jacobs Professor in Computer Science and Engineering at the University of California, San Diego. *Wik My current favorite Graham quote is, "An ideal math talk should contain one proof and one joke and they should not be the same."

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DEATHS
1867 William Parsons, 3rd Earl of Rosse (17 Jun 1800, 31 Oct 1867) was an Irish astronomer who built the largest reflecting telescope of the 19th century. He learned to polish metal mirrors (1827) and spent the next few years building a 36-inch telescope. He later completed a giant 72-inch telescope (1845) which he named "Leviathan," It remained the largest ever built until decades after his death. He was the first to resolve the spiral shape of objects - previously seen as only clouds - which were much later identified as galaxies independent of our own Milky Way galaxy and millions of light-years away. His first such sighting was made in 1845, and by 1850 he had discovered 13 more. In 1848, he found and named the Crab Nebula (because he thought it resembled a crab), by which name it is still known. *TIS

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1988 George Eugene Uhlenbeck (6 Dec 1900, 31 Oct 1988) Dutch-American physicist who, with Samuel A. Goudsmit, proposed the concept of electron spin (Jan 1925) - a fourth quantum number which was a half integer. This provided Wolfgang Pauli's anticipated "fourth quantum number." In their experiment, a horizontal beam of silver atoms travelling through a vertical magnetic field was deflected in two directions according to the interaction of their spin (either "up" or "down") with the magnetic field. This was the first demonstration of this quantum effect, and an early confirmation of quantum theory. As well as fundamental work on quantum mechanics, Uhlenbeck worked on atomic structure, the kinetic theory of matter and extended Boltzmann's equation to dense gases.*TIS

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Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum

On This Day in Math - Oct 30

'Mathematics is the science that uses easy words for hard ideas.'

~ Edward Kasner

The 303rd day of the year; there are 303 different bipartite graphs with 8 vertices. *What's Special About This Number Web site.


EVENTS
1613 Kepler married his second wife (the first died of typhus). She was fifth on his slate of eleven candidates. The story that he used astrology in the choice is doubtful.*VFR Kepler married the 24-year-old Susanna Reuttinger. He wrote that she, "won me over with love, humble loyalty, economy of household, diligence, and the love she gave the stepchildren.According to Kepler's biographers, this was a much happier marriage than his first. *Wik

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1710 William Whiston, whom Newton had arranged to succeeded him as Lucasian Professor at Cambridge in 1701, was deprived of the chair and driven from Cambridge for his unorthodox religious views. Whiston was removed from his position at Cambridge, and denied membership in the Royal Society for his “heretical” views. He took the “wrong” side in the battle between Arianism (a unitarian view) and the Trinitarian view, but his brilliance still made the public attend to his proclamations. When he predicted the end of the world by a collision with a comet in October 16th of 1736 the Archbishop of Canterbury had to issue a denial to calm the panic (VFR put it this way, "it is not acceptable to be a unitarian at the College of the Whole and Undivided Trinity".
His translation of the works of Flavius Josephus may have contained a version of the famous Josephus Problem, and in 1702 Whiston's Euclid discusses the classic problem of the Rope Round the Earth, (if one foot of additional length is added, how high will the rope be). I am not sure of the dimensions in Whiston's problem, and would welcome input, I have searched the book and can not find the problem in it, but David Singmaster has said it is there, and he is not an easy source to reject. It is said that Ludwig Wittgenstein was fascinated by the problem and used to pose it to students regularly.

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1735 Ben Franklin published “On the Usefulness of Mathematics,” his only published article on mathematics. *VFR

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1826 Abel presented a paper to the French Academy of Science that was ignored by Cauchy, who was to serve as referee. The paper was published some twenty years later.*VFR

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In 1937, the closest approach to the earth by an asteroid, Hermes, was measured to be 485,000 miles, which, to an astronomer, is a mere hair's width (asteroid now lost).*TIS

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1945 The first conference on Digital Computer Technique was held at MIT. The conference was sponsored by the National Research Council, Subcommittee Z on Calculating Machines and Computation. Attended by the Whirlwind team,(The Whirlwind computer was developed at the Massachusetts Institute of Technology. It is the first computer that operated in real time, used video displays for output, and the first that was not simply an electronic replacement of older mechanical systems) it influenced the direction of this computer. *CHM

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1978 Laura Nickel and Curt Noll, eighteen year old students at California State at Hayward, show that 2^21,701 − 1 is prime. This was the largest prime known at that time. *VFR (By Feb of the next year, Noll had found another, 2²³²⁰⁹-1. By April, another larger Prime had been found.)

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1992 The Vatican announced that a 13-year investigation into the Catholic Church’s condemnation of Galileo in 1633 will come to an end and that Galileo was right: The Copernican Theory, in which the Earth moves around the Sun, is correct and they erred in condemning Galileo. *New York Times for 31 October 1992.

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BIRTHS
1840 Joseph Jean Baptiste Neuberg (30 Oct 1840 in Luxembourg City, Luxembourg - 22 March 1926 in Liège, Belgium) Neuberg worked on the geometry of the triangle, discovering many interesting new details but no large new theory. Pelseneer writes, "The considerable body of his work is scattered among a large number of articles for journals; in it the influence of A Möbius is clear." *SAU

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1844 George Henri Halphen (30 October 1844, Rouen – 23 May 1889, Versailles) was a French mathematician. He did his studies at École Polytechnique (X 1862). He was known for his work in geometry, particularly in enumerative geometry and the singularity theory of algebraic curves, in algebraic geometry. He also worked on invariant theory and projective differential geometry.*Wik

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1863 Stanislaw Zaremba (3 Oct 1863 in Romanowka, Poland - 23 Nov 1942 in Kraków, Poland) From very unpromising times up to World War I, with the recreation of the Polish nation at the end of that war, Polish mathematics entered a golden age. Zaremba played a crucial role in this transformation. Much of Zaremba's research work was in partial differential equations and potential theory. He also made major contributions to mathematical physics and to crystallography. He made important contributions to the study of viscoelastic materials around 1905. He showed how to make tensorial definitions of stress rate that were invariant to spin and thus were suitable for use in relations between the stress history and the deformation history of a material. He studied elliptic equations and in particular contributed to the Dirichlet principle.*SAU

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1906 Andrei Nikolaevich Tikhonov (30 Oct 1906 in Gzhatska, Smolensk, Russia - November 8, 1993, Moscow) Tikhonov's work led from topology to functional analysis with his famous fixed point theorem for continuous maps from convex compact subsets of locally convex topological spaces in 1935. These results are of importance in both topology and functional analysis and were applied by Tikhonov to solve problems in mathematical physics.
The extremely deep investigations of Tikhonov into a number of general problems in mathematical physics grew out of his interest in geophysics and electrodynamics. Thus, his research on the Earth's crust lead to investigations on well-posed Cauchy problems for parabolic equations and to the construction of a method for solving general functional equations of Volterra type.
Tikhonov's work on mathematical physics continued throughout the 1940s and he was awarded the State Prize for this work in 1953. However, in 1948 he began to study a new type of problem when he considered the behaviour of the solutions of systems of equations with a small parameter in the term with the highest derivative. After a series of fundamental papers introducing the topic, the work was carried on by his students.
Another area in which Tikhonov made fundamental contributions was that of computational mathematics. Under his guidance many algorithms for the solution of various problems of electrodynamics, geophysics, plasma physics, gas dynamics, ... and other branches of the natural sciences were evolved and put into practice. ... One of the most outstanding achievemnets in computational mathematics is the theory of homogeneous difference schemes, which Tikhonov developed in collaboration with Samarskii.
In the 1960s Tikhonov began to produce an important series of papers on ill-posed problems. He defined a class of regularisable ill-posed problems and introduced the concept of a regularising operator which was used in the solution of these problems. Combining his computing skills with solving problems of this type, Tikhonov gave computer implementations of algorithms to compute the operators which he used in the solution of these problems. Tikhonov was awarded the Lenin Prize for his work on ill-posed problems in 1966. In the same year he was elected to full membership of the USSR Academy of Sciences.*SAU

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1907 Harold Davenport (30 Oct 1907 in Huncoat, Lancashire, England - 9 June 1969 in Cambridge, Cambridgeshire, England) Davenport worked on number theory, in particular the geometry of numbers, Diophantine approximation and the analytic theory of numbers. He wrote a number of important textbooks and monographs including The higher arithmetic (1952)*SAU

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1946 William Paul Thurston  (October 30, 1946 – August 21, 2012) American mathematician who was awarded the Fields Medal in 1983 for his work in topology. As early as his Ph.D. thesis entitled Foliations of 3-manifolds which are circle bundles (1972) that showed the existence of compact leaves in foliations of 3-manifolds, Thurston had been working in the field of topology. In the following years, Thurston's contributions to the field of foliations were recognized to be of considerable depth, set apart by their originality. This was also true of his subsequent work on Teichmüller space. *TIS

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DEATHS
1626 Willebrord van Royen Snell (13 June 1580 in Leiden, Netherlands - 30 Oct 1626 in Leiden, Netherlands) Snell was a Dutch mathematician who is best known for the law of refraction, a basis of modern geometric optics; but this only become known after his death when Huygens published it. His father was Rudolph Snell (1546-1613), the professor of mathematics at Leiden. Snell also improved the classical method of calculating approximate values of π by polygons which he published in Cyclometricus (1621). Using his method 96 sided polygons gives π correct to 7 places while the classical method yields only 2 places. Van Ceulen's 35 places could be found with polygons of 230 sides rather than 262. In fact Van Ceulen's 35 places of π appear in print for the first time in this book by Snell. *SAU

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1631 Michael Mästin (30 Sept 1550 in Göppingen, Baden-Würtemberg, Germany
- 30 Oct 1631 in Tübingen, Baden-Würtemberg, Germany) astronomer who was Kepler's teacher and who publicized the Copernican system. Michael Mästin was a German astronomer who was Kepler's teacher and who publicised the Copernican system. Perhaps his greatest achievement (other than being Kepler's teacher) is that he was the first to compute the orbit of a comet, although his method was not sound. He found, however, a sun centered orbit for the comet of 1577 which he claimed supported Copernicus's heliocentric system. He did show that the comet was further away than the moon, which contradicted the accepted teachings of Aristotle. Although clearly believing in the system as proposed by Copernicus, he taught astronomy using his own textbook which was based on Ptolemy's system. However for the more advanced lectures he adopted the heliocentric approach - Kepler credited Mästlin with introducing him to Copernican ideas while he was a student at Tübingen (1589-94).*SAU

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1739 Leonty Filippovich Magnitsky (June 9, 1669, Ostashkov – October 30, 1739, Moscow) was a Russian mathematician and educator. From 1701 and until his death, he taught arithmetic, geometry and trigonometry at the Moscow School of Mathematics and Navigation, becoming its director in 1716. In 1703, Magnitsky wrote his famous Arithmetic (Арифметика; 2,400 copies), which was used as the principal textbook on mathematics in Russia until the middle of the 18th century. This book was more an encyclopedia of mathematics than a textbook because most of its content was communicated for the first time in Russian literature. In 1703, Magnitsky also produced a Russian edition of Adriaan Vlacq's log tables called Таблицы логарифмов и синусов, тангенсов и секансов (Tables of Logarithms, Sines, Tangents, and Secants). Legend has it that Leonty Magnitsky was nicknamed Magnitsky by Peter the Great, who considered him a "people's magnet" *Wik

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1805 Ormbsy MacKnight Mitchel (July 20, 1805 – October 30, 1862) American astronomer and major general in the American Civil War.
A multi-talented man, he was also an attorney, surveyor, and publisher. He is notable for publishing the first magazine in the United States devoted to astronomy. Known in the Union Army as "Old Stars", he is best known for ordering the raid that became famous as the Great Locomotive Chase during the Civil War. He was a classmate of Robert E. Lee and Joseph E. Johnston at West Point where he stayed as assistant professor of mathematics for three years after graduation.
The U.S. communities of Mitchell, Indiana, Mitchelville, South Carolina, and Fort Mitchell, Kentucky were named for him. A persistently bright region near the Mars south pole that was first observed by Mitchel in 1846 is also named in his honor. *TIA

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1806 Alexander (Dallas) Bache (July 19, 1806 – February 17, 1867) was Ben Franklin's great grandson. A West Point trained physicist, Bache became the second Superintendent of the Coast Survey (1844-65). He made an ingenious estimate of ocean depth in 1856. He studied records of a tidal wave that had taken 12 hours to cross the Pacific. Knowing that wave speeds depend on depth, he calculated a 2 1/5-mile average depth for the Pacific (within 15% of the right value). Bache created the National Academy of Sciences, securing greater government involvement in science. Through the Franklin Institute he instituted boiler tests to promote safety for steamboats.*TIS

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1975 Gustav Hertz (22 July 1887, 30 Oct 1975) German quantum physicist who, with James Franck, received the Nobel Prize for Physics in 1925 for the Franck-Hertz experiment, which confirmed the quantum theory that energy can be absorbed by an atom only in definite amounts and provided an important confirmation of the Bohr atomic model. He was a nephew of Heinrich Hertz. Although he fought on the German side in World War I, being of Jewish descent, he was forced to resign his professorship (1934) when Hitler took power. From 1945 he worked in the Soviet Union, and then in 1955 was a professor of physics in Leipzig, East Germany.*TIS

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2007 Juha Heinonen, (23 July 1960 in Toivakka, Finland - 30 Oct 2007 in Ann Arbor, Michigan, USA) Professor of Mathematics passed away on October 30. He arrived in the Department in 1988 as a postdoctoral assistant professor, and became a professor in 2000. He was a leading researcher in geometric function theory, having published two books and numerous articles with many collaborators. Most recently, Juha served as Associate Chair for Graduate Studies in the Department, where he mentored many young mathematicians. *Math at U of M webpage memorial (Heinonen died at the age of 47 'after a brief but courageous battle with kidney cancer'. The Department of Mathematics at the University of Michigan established the Juha Heinonen Memorial Graduate Student Fellowship in his honour. An international conference in his memory Quasiconformal Mappings and Analysis on Metric Spaces was organised at the University of Michigan, Ann Arbor in May 2008.)

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Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum

On This Day in Math - Oct 29

Allez en avant, et la foi vous viendra
Push on and faith will catch up with you.

~Jean d'Alembert [advice to those who questioned the calculus](probably also great for students struggling with mathematics at any level)

The 302nd day of the year; There are 302 ways to play the first three moves in checkers.

EVENTS
1669 Newton, aged twenty-six, appointed Lucasian Professor at Cambridge. This post required Newton to lecture once each week on “some part of Geometry, Astronomy, Geography, Optics, Statics, or some other Mathematical discipline,” and to deposit ten of those lectures in the library each year. The students were required to attend, but like all other requirements they ignored this one too. We know of only three people who attended a lecture at Cambridge by Newton. [Westfall 208–210; Works, 3, xv] *VFR

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1675 Leibniz first used the integral sign. Also first used “d”. He also constructed what he calls the “triangulum characteristicum,” which had been used before him by Pascal and Barrow. [Cajori, History of Mathematical Notations, vol. 2, p. 2; Struik’s Source Book mistakenly has 26 October]

VFR Historical notes for the calculus classroom ,
In these same pages he will write examples of the integrals of x² and x³,and then illustrate that a constant multiple may be taken outside the integral as shown in the image below.

On the left is Liebniz integral sign with a vincula in place of todays parentheses to show that he is integrating the quantity (a/b) l   Then the open bottomed box is Liebniz symbol for equality,then he shows the constant (a/b) multiplied by the integral of l .

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1878 Patent issued for Odhner calculating machine. *VFR Willigot T. Odhner was granted a patent for a calculating machine that performed multiplications by repeated additions. The patent, a modified and compact version of Gottfried von Leibniz stepped wheel, was acquired and embodied in Brunsviga calculators that sold into 1950s.*CHM

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1929 "Black Tuesday", the great USA stock market crash. About 16 million shares were traded, and the Dow lost an additional 30 points, or 12%.. "Anyone who bought stocks in mid-1929 and held onto them saw most of his or her adult life pass by before getting back to even." Richard M. Salsman *Wik

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1985 On October 29th, 1985, the 329th birthday of Edmond Halley, the British threw a big party in honor of the return of Halley's Comet. The Halley's Comet Royal Gala was held at Wembley Conference Centre, London. It was a combination Variety Show and "Who's Who" in British Society, hosted by Princess Anne of the British Royal Family. *Joseph M. Laufer, Halley's Comet Society, USA

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In 1991, space probe Galileo become the first human object to fly past an asteroid, Gaspra, making its closest approach at a distance of 1,604 km, passing at a speed of 8 km/sec (5 mi/sec). The encounter provided much data, including 150 images, which showed Gaspra has numerous craters indicating it has suffered numerous collisions since its formation. Gaspra is about 20-km long and orbits the Sun in the main asteroid belt between Mars and Jupiter. Gaspra, asteroid 951, was discovered by Ukrainian astronomer Grigoriy N. Neujamin (1916) who named it after a Black Sea retreat. In the photograph (left), subtle color variations have been exaggerated by NASA to highlight changes in reflectivity, surface structure and composition. *TIS

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BIRTHS
1925 Klaus Friedrich Roth (29 Oct 1925, )German-born British mathematician who was awarded the Fields Medal in 1958. His major work has been in number theory, particularly the analytic theory of numbers. He solved in the famous Thue-Siegel problem (1955) concerning the approximation to algebraic numbers by rational numbers (for which he won the medal). Roth also proved in 1952 that a sequence with no three numbers in arithmetic progression has zero density (a conjecture of Erdös and Turán of 1935).*TIS

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DEATHS
1783 Jean le Rond D'Alembert (16 Nov 1717, 29 Oct 1783) was abandoned by his parents on the steps of Saint Jean le Rond, which was the baptistery of Notre-Dame, qv in Section 7-A-1. Foster parents were found and he was christened with the name of the saint. [Eves, vol. II, pp. 32 33. Okey, p. 297.] When he became famous, his mother attempted to reclaim him, but he rejected her. *VFR Known for his work in various fields of applied mathematics, in particular dynamics. In 1743 he published his Traité de dynamique (Treatise on Dynamics). The d'Alembert principle extends Newton's third law of motion, that Newton's law holds not only for fixed bodies but also for free moving bodies. D'Alembert also wrote on fluid dynamics, the theory of winds, the properties of vibrating strings and conducted experiments on the properties of sound . His most significant purely mathematical innovation was his invention and development of the theory of partial differential equations. He published eight volumes of mathematical studies (1761-80). He was editor of the mathematical and scientific articles for Denis Diderot's Encyclopédie.*TIS

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1917 Giovanni Battista Guccia (21 Oct 1855 in Palermo, Italy - 29 Oct 1914 in Palermo, Italy) Guccia's work was on geometry, in particular Cremona transformations, classification of curves and projective properties of curves. His results published in volume one of the Rendiconti del Circolo Matematico di Palermo were extended by Corrado Segre in 1888 and Castelnuovo in 1897. *SAU

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1921 Konstantin Alekseevich Andreev (26 March 1848 in Moscow, Russia - 29 Oct 1921 Near Sevastopol, Crimea) Andreev is best known for his work on geometry, although he also made contributions to analysis. In the area of geometry he did major pieces of work on projective geometry. Let us note one particular piece of work for which he has not received the credit he deserves. Gram determinants were introduced by J P Gram in 1879 but Andreev invented them independently in the context of problems of expansion of functions into orthogonal series and the best quadratic approximation to functions. *SAU

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1931 Gabriel Xavier Paul Koenigs (17 January 1858 Toulouse, France – 29 October 1931 Paris, France) was a French mathematician who worked on analysis and geometry. He was elected as Secretary General of the Executive Committee of the International Mathematical Union after the first world war, and used his position to exclude countries with whom France had been at war from the mathematical congresses.
He was awarded the Poncelet Prize for 1913.*Wik

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1933 Paul Painlevé worked on differential equations. He served twice as prime-minister of France. *SAU

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1951 Robert Aitken (31 Dec 1864, 29 Oct 1951) American astronomer who specialized in the study of double stars, of which he discovered more than 3,000. He worked at the Lick Observatory from 1895 to 1935, becoming director from 1930. Aitken made systematic surveys of binary stars, measuring their positions visually. His massive New General Catalogue of Double Stars within 120 degrees of the North Pole allowed orbit determinations which increased astronomers' knowledge of stellar masses. He also measured positions of comets and planetary satellites and computed orbits. He wrote an important book on binary stars, and he lectured and wrote widely for the public. *TIS

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1993 Lipman Bers (May 22, 1914 – October 29, 1993) was an American mathematician born in Riga who created the theory of pseudoanalytic functions and worked on Riemann surfaces and Kleinian groups.*Wik

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1993 Robert Palmer Dilworth (December 2, 1914 – October 29, 1993) was an American mathematician. His primary research area was lattice theory; his biography at the MacTutor History of Mathematics archive states "it would not be an exaggeration to say that he was one of the main factors in the subject moving from being merely a tool of other disciplines to an important subject in its own right". He is best known for Dilworth's theorem (Dilworth 1950) relating chains and antichains in partial orders; he was also the first to study antimatroids (Dilworth 1940). Dilworth advised 17 Ph.D. students and as of 2010 has 373 academic descendants listed at the Mathematics Genealogy Project, many through his student Juris Hartmanis, a noted complexity theorist.*Wik

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Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum

On This Day in Math - Oct 28

"Big Fleas have little fleas upon their backs to bite 'em,

and little fleas have lesser fleas,

and so ad infinitum.

~Augustus De Morgan

The 301st day of the year; 301 is the sum of three consecutive primes starting at 97


EVENTS
1386 Opening of the University of Heidelberg. It is the oldest university in Germany and was the third university established in the Holy Roman Empire. *Wik

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1462 Archbishop Adolph of Nassau captured the city of Maintz and allowed his soldiers to plunder the city. This forced Gutenberg and his printers to flee, but rather than nipping printing in the bud, it forced its spread to Strasburg, Cologne, Basel, Augsburg, Ulm, Nuremberg, Subiaco, and by 1470, Paris. [G. H. Putnam, Books and Their Makers During the Middle Ages (1896),
p. 372]. *VFR

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1636 Harvard College founded. The only mathematical master’s thesis in the U.S. before 1700 was at Harvard. This was in 1693 when the candidate took the affirmative position on “Is the quadrature of a circle possible?”. *VFR

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1886 The Statue of Liberty was dedicated on Bedloe’s Island in New York Harbor. The sculptur Bartholin was present. The statue had almost been moved to another city when there was not enough interest in New York to pay the cost of building the pedestal. Joseph Pulitzer, publisher of the World, a New York newspaper, announced a drive to raise $100,000 (the equivalent of $2.3 million today). Pulitzer pledged to print the name of every contributor, no matter how small the amount given.The drive captured the imagination of New Yorkers, especially when Pulitzer began publishing the notes he received from contributors. "A young girl alone in the world" donated "60 cents, the result of self denial." As the donations flooded in, the committee resumed work on the pedestal. After five months of daily calls to donate to the statue fund, on August 11, 1885, the World announced that $102,000 had been raised from 120,000 donors, and that 80 percent of the total had been received in sums of less than one dollar. *Wik

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1957 Only three weeks after Sputnik went into space, young Denis Cox in Victoria, Australia sent a design for a spaceship addressed, "TO A TOP SCIENTIST AT Woomera ROCKET RANGE South Australia." His design included locations for Austalian Insignia, four Rolls Royce Engines, guided missiles, etc, but advised the scientists, "YOU PUT IN OTHER DETAILS". The letter can be seen here at the Letters of Note web site Edited by Shaun Usher.
On September 24, 2009, an article on ABC Australia's web page indicated that "The Defence Science Technology Organisation is now finally organising a letter from rocket scientists in response to the letter."

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In 1965, the Gateway Arch (630' (190m) high) was completed in St. Louis, Missouri. This graceful sweeping tapered curve of stainless steel is the tallest memorial in the U.S. The architect of the catenary curve arch was Eero Saarinen who won the design competition in 1947. It was constructed 1961-66 in the Jefferson National Expansion Memorial Park, established on the banks of the Mississippi River, on 21 Dec 1935, to commemorate the westward growth of the United States between 1803 and 1890. Cost for the $30 million national monument was shared by the federal government and the City of St. Louis. The memorial arch has an observation room at the top for visitors reached by trams running inside the legs of the arch.*TIS

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BIRTHS
1703 Antoine Deparcieux (28 Oct 1703 in Clotet-de-Cessous, France - 2 Sept 1768 in Paris, France) was a French mathematician who is best known for an early work on annuities and mortality.*SAU

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1804 Pierre François Verhulst (28 October 1804, Brussels, Belgium – 15 February 1849, Brussels, Belgium) was a mathematician and a doctor in number theory from the University of Ghent in 1825. Verhulst published in 1838 the equation:

dN/dt = r N (1-N/k)

when N(t) represents number of individuals at time t, r the intrinsic growth rate and k is the carrying capacity, or the maximum number of individuals that the environment can support. In a paper published in 1845 he called the solution to this the logistic function, and the equation is now called the logistic equation. This model was rediscovered in 1920 by Raymond Pearl and Lowell Reed, who promoted its wide and indiscriminate use.*Wik

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1845 Ulisse Dini (14 Nov 1845 in Pisa, Italy - 28 Oct 1918 in Pisa, Italy) Dini looked at infinite series and generalised results such as a theorem of Kummer and one of Riemann, the ideas for which had first emerged in work of Dirichlet. He discovered a condition, now known as the Dini condition, ensuring the convergence of a Fourier series in terms of the convergence of a definite integral. As well as trigonometric series, Dini studied results on potential theory. *SAU

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1880 Michele Cipolla (born 28 October 1880 in Palermo; died 7 September 1947 in Palermo) was an Italian mathematician, mainly specializing in number theory.
He was a professor of Algebraic Analysis at the University of Catania and, later, the University of Palermo. He developed (among other things) a theory for sequences of sets and Cipolla's algorithm for finding square roots modulo a prime number. He also solved the problem of binomial congruence.*Wik

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1937 Dr. Marcian Edward (Ted) Hoff, Jr. was born October 28, 1937 at Rochester, New York. He received a BEE (1958) from Rensselear Polytechnic Institute in Troy, NY. During the summers away from college he worked for General Railway Signal Company in Rochester where he made developments that produced his first two patents. He attended Stanford as a National Science Foundation Fellow and received a MS (1959) and Ph.D. (1962) in electrical engineering. He joined Intel in 1962. In 1980, he was named the first Intel Fellow, the highest technical position in the company. He spent a brief time as VP for Technology with Atari in the early 1980s and is currently VP and Chief Technical Officer with Teklicon, Inc. Other honors include the Stuart Ballantine Medal from the Franklin Institute.*CHM

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1955 Bill Gates, cofounder and CEO of Microsoft Corporation, was born. Gates developed a version of BASIC for the Altair 8800 while being a student at Harvard. With the success of BASIC, he and co-developer Paul Allen​ founded Microsoft, which delivered an operating system for the IBM PC​, the Microsoft Word​ word processing program, the Window system software, and other programs. *CHM

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DEATHS
1703 John Wallis (23 Nov 1616, 28 Oct 1703) British mathematician who introduced the infinity math symbol. Wallis was skilled in cryptography and decoded Royalist messages for the Parliamentarians during the Civil War. Subsequently, he was appointed to the Savilian Chair of geometry at Oxford in 1649, a position he held until his death more than 50 years later. Wallis was part of a group interested in natural and experimental science which became the Royal Society, so Wallis is a founder member of the Royal Society and one of its first Fellows. Wallis contributed substantially to the origins of calculus and was the most influential English mathematician before Newton. *TIS

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1916 Cleveland Abbe (3 Dec 1838, 28 Oct 1916) U.S. astronomer and first meteorologist, born in New York City, the "father of the U.S. Weather Bureau," which was later renamed the National Weather Service. Abbe inaugurated a private weather reporting and warning service at Cincinnati. His weather reports or bulletins began to be issued on Sept. 1, 1869. The Weather Service of the United States was authorized by Congress on 9 Feb 1870, and placed under the direction of the Signal Service. Abbe was the only person in the country who was already experienced in drawing weather maps from telegraphic reports and forecasting from them. Naturally, he was offered an important position in this new service which he accepted, beginning 3 Jan 1871, and was often the official forecaster of the weather.*TIS

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1924 John Backus (3 Dec 1924, 28 Oct 1988) American computer scientist who invented the FORTRAN (FORmula TRANslation) programming language in the mid 1950s. He had previously developed an assembly language for IBM's 701 computer when he suggested the development of a compiler and higher level language for the IBM 704. As the first high-level computer programming language, FORTRAN was able to convert standard mathematical formulas and expressions into the binary code used by computers. Thus a non-specialist could write a program in familiar words and symbols, and different computers could use programs generated in the same language. This paved the way for other computer languages such as COBOL, ALGOL and BASIC. *TIS

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1965 Luther Pfahler Eisenhart (13 January 1876 – 28 October 1965) was an American mathematician, best known today for his contributions to semi-Riemannian geometry.*Wik

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1986 Irving Reiner was an American mathematician who (with Curtis) produced an important book on group representations.*SAU

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Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum

On This Day in Math - Oct 27

It is the duty of every true Muslim, man and woman, to strive after knowledge.
Ulugh Beg [quoting the Hadith. Inscribed on his gate in Bukhara]

The 300th day of the year; 300 is a triangular number, the sum of the integers from 1 to 24. 300 is also the sum of a pair of twin primes (149 + 151). It is also the sum of ten consecutive primes, 300 =  13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47.

EVENTS
In 1780, the first U.S. astronomical expedition to record an eclipse of the sun observed the event which lasted from 11:11 am to 1:50 pm. The observers left about three weeks earlier, on 9 Oct from Harvard College, Cambridge, Mass., for Penobscot Bay, led by Samuel Williams. A boat was supplied by the Commonwealth of Massachusetts the four professors and six students. Although the U.S. was at war with Britain, the British officer in charge of Penobscot Bay permitted the expedition to land and set up equipment to observe the predicted total eclipse of the sun. The expedition was shocked to find itself outside the path of totality. They saw a thin arc of the sun instead of its complete obscuration by the moon. *TIS

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1980 The first major network crash, the four-hour collapse of the ARPANET, occurred
The ARPANET, predecessor of the modern Internet, was set up by the Department of Defense Advanced Research Projects Agency (DARPA). Initially it had linked four sites in California and Utah, and later was expanded to cover research centers across the country.
The network failure resulted from a redundant single-error detecting code that was used for transmission but not storage, and a garbage-collection algorithm for removing old messages that was not resistant to the simultaneous existence of one message with several different time stamps. The combination of the events took the network down for four hours. *CHM 

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2011 EPL (Europhysics Letters) went beyond Earthly limits by publishing its first ever paper submitted from space: a landmark for both European and physics-based research. Concerned with the properties of complex plasma in almost zero gravity conditions, the paper represents collaborative research of 29 individual missions performed over the last 10 years by German and Russian researchers aboard the International Space Station (ISS).
The experiments detailed in the paper were performed on the ISS in July 2010 by Alexander Alexandrovich Skvortsov and were submitted on 27 October 2011 by Skvortsov’s colleague, Sergey Alexandrovich Volkov, who remains on the ISS. IOP  Blog

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BIRTHS
1678 Pierre Rémond de Montmort (27 Oct 1678 in Paris, France, 7 Oct 1719 in Paris, France) was a French mathematician who wrote an important work on probability. Montmort's reputation was made by his book on probability Essay d'analyse sur les jeux de hazard which appeared in 1708. The book, which is a collection of combinatorial problems, is a systematic study of games of chance and shows that there is important mathematics in this area.
Montmort collaborated with Nicolaus(I) Bernoulli and he was also a friend of Taylor. At a time of high feelings in the Newton-Leibniz controversy it says a lot for Montmort that he could be friends with followers of both camps.
In addition to those mentioned above, Montmort corresponded with Craig, Halley, Hermann and Poleni.
Montmort was elected to be a Fellow of the Royal Society in 1715, when he was on a trip to England. The following year he was elected to the Académie Royal des Sciences. *SAU

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1798 Heinrich Ferdinand Scherk (27 Oct 1798 in Poznań, Poland - 4 Oct 1885 in Bremen, Germany) was a mathematician born in what is now Poland who discovered an important example of a minimal surface. Scherk discovered the third non-trivial examples of a minimal surface which appeared in his paper Bemerkungen über die kleinste Fläche innerhalb gegebener Grenzen published in Crelle's Journal. The first two examples, the catenoid and the helicoid (also called the screw surface), had been found by the Frenchman Jean Baptiste Marie Meusnier in 1776. The catenoid arises from rotating the catenary curve about a horizontal line. Scherk's result was certainly seen as a major breakthough and brought him considerable fame; two surfaces, Scherk's First Surface and Scherk's Second Surface, as they are named today, are studied in the paper. Scherk's doubly periodic surface is the first example of a complete, embedded, doubly periodic minimal surface. His minimal surfaces have recently been the basis of sculptures by the American artist Brent Collins who has based many of his works on Scherk's second minimal surface.
Another contribution by Scherk is still important today, namely his work on the distribution of the prime numbers. *SAU

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1827 Pierre-Eugène-Marcellin Berthelot (27 Oct 1827, 18 Mar 1907 at age 79) was a French chemist and science historian and government official whose creative thought and work significantly influenced the development of chemistry in the late 19th century. He helped to found the study of thermochemistry, introduced a standard method for determining the latent heat of steam, measured hundreds of heats of reactions and coined the words exothermic and endothermic. Berthelot systematically synthesized organic compounds, including some not found in nature. His syntheses of many fundamental organic compounds helped to destroy the classical division between organic and inorganic compounds. *TIS

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1890 Olive Clio Hazlett born (October 27, 1890 - March 8, 1974) was an American mathematician who spent most of her career working for the University of Illinois. She mainly researched algebra, and wrote seventeen research papers on subjects such as nilpotent algebras, division algebras, modular invariants, and the arithmetic of algebras. *Wik

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1728 James Cook (27 Oct 1728; 14 Feb 1779) English seaman who was the first of the really scientific navigators. Captain Cook spent several years surveying the coasts of Labrador and Newfoundland. He observed a solar eclipse on 5 Aug 1766 near Cape Ray, Newfoundland. On the first of three expeditions into the Pacific (1768) he took Joseph Banks as the ship's botanist to study the flora and fauna discovered. (This practice of carrying a naturalist took place some 75 years before Charles Darwin's famous voyage.) Cook observed the transit of Venus on this voyage from the island of Tahiti on 3 Jun 1769. This would help scientists plot the distance between the sun to the earth. His geographical discoveries made him the most famous navigator since Magellan. He was killed by cannibal natives in Hawaii.*TIS

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1856 Ernest William Hobson (27 Oct 1856 in Derby, England, 19 April 1933 in Cambridge, Cambridgeshire, England) wrote the first English book on the measure theory and integration of Baire, Borel and Lebesgue. *SAU

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1890 Olive Clio Hazlett (October 27, 1890 - March 8, 1974) was an American mathematician who spent most of her career working for the University of Illinois. She mainly researched algebra, and wrote seventeen research papers on subjects such as nilpotent algebras, division algebras, modular invariants, and the arithmetic of algebras.*Wik

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1915 Robert Alexander Rankin (27 Oct 1915 in Garlieston, Wigtownshire, Scotland, 27 Jan 2001 in Glasgow, Scotland) studied at Cambrige University. His fellowship there was interrupted by his wartime work on rockets. He became Professor of Mathematics at Birmingham before moving to the professorship at Glasgow, a post he held for 27 years. His most important work was on Number Theory. He became President of the EMS in 1957 and 1978 and an honorary member in 1990. *SAU

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DEATHS
1449 Ulugh Beg (22 Mar 1394- 27 Oct 1449) The only important Mongol scientist, mathematician, and the greatest astronomer of his time. His greatest interest was astronomy, and he built an observatory (begun in 1428) at Samarkand. In his observations he discovered a number of errors in the computations of the 2nd-century Alexandrian astronomer Ptolemy, whose figures were still being used. His star map of 994 stars was the first new one since Hipparchus. After Ulugh Beg was assassinated by his son, the observatory fell to ruins by 1500, rediscovered only in 1908. Written in Arabic, his work went unread by the world's next generation of astronomers. When his tables were translated into Latin in 1665, telescopic observations had surpassed them. *TIS

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1845 Jean-Charles-Athanase Peltier (22 Feb 1785, 27 Oct 1845) French physicist who discovered the Peltier effect (1834), that at the junction of two dissimilar metals an electric current will produce heat or cold, depending on the direction of current flow. In 1812, Peltier received an inheritance sufficient to retire from clockmaking and pursue a diverse interest in phrenology, anatomy, microscopy and meteorology. Peltier made a thermoelectric thermoscope to measure temperature distribution along a series of thermocouple circuits, from which he discovered the Peltier effect. Lenz succeeded in freezing water by this method. Its importance was not fully recognized until the later thermodynamic work of Kelvin. The effect is now used in devices for measuring temperature and non-compressor cooling units. *TIS

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1675 Gilles Personne de Roberval (8 Aug 1602- 27 Oct 1675) French mathematician who developed powerful methods in the early study of integration, writing Traité des indivisibles. He computed the definite integral of sin x, worked on the cycloid and computed the arc length of a spiral. Roberval is important for his discoveries on plane curves and for his method for drawing the tangent to a curve, already suggested by Torricelli. This method of drawing tangents makes Roberval the founder of kinematic geometry. In 1669 he invented the Roberval balance with an articulated parallelogram is now almost universally used for weighing scales of the balance type. He studied the vacuum and designed apparatus which was used by Pascal in his experiments and also worked in cartography. *TIS

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1968 Lise Meitner (7 Nov 1878, 27 Oct 1968)Austrian physicist who shared the Enrico Fermi Award (1966) with the chemists Otto Hahn and Fritz Strassmann for their joint research beginning in 1934 that led to the discovery of uranium fission. She refused to work on the atom bomb. In 1917, with Hahn, she had discovered the new radioactive element protactinium. She was the first to describe the emission of Auger electrons. In 1935, she found evidence of four other radioactive elements corresponding to atomic numbers 93-96. In 1938, she was forced to leave Nazi Germany, and went to a post in Sweden. Her other work in the field of nuclear physics includes study of beta rays, and study of the three main disintegration series. Later, she used the cyclotron as a tool. *TIS

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1980 John Hasbrouck Van Vleck (13 Mar 1899, 27 Oct 1980) was an American physicist and mathematician who shared the Nobel Prize for Physics in 1977 with Philip W. Anderson and Sir Nevill F. Mott. The prize honoured Van Vleck's contributions to the understanding of the behaviour of electrons in magnetic, noncrystalline solid materials. *TIS

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1999 Robert L. Mills (15 Apr 1927, 27 Oct 1999)American physicist who shared the 1980 Rumford Premium Prize with his colleague Chen Ning Yang for their "development of a generalized gauge invariant field theory" in 1954. They proposed a tensor equation for what are now called Yang-Mills fields. Their mathematical work was aimed at understanding the strong interaction holding together nucleons in atomic nuclei. They constructed a more generalized view of electromagnetism, thus Maxwell's Equations can be derived as a special case from their tensor equation. Quantum Yang-Mills theory is now the foundation of most of elementary particle theory, and its predictions have been tested at many experimental laboratories. *TIS

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Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum

On This Day in Math - Oct 26

There are no foolish questions and no man becomes a fool until he has stopped asking questions.
Charles P Steinmetz

The 299th day of the year; If a cubic cake was cut with 12 straight cuts, it can produce a maximum of 299 pieces.... a good day to "let 'em eat cake."

EVENTS
1676 Newton, through the intermediary of Oldenburg, wrote Leibniz concerning his work on the calculus. An anagram contained the statement of the problem of integrating differential equations. *VFR

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1847 William Whewell wrote to Aubrey De Vere expressing dismay at the influence of Carlyle's pessimism among his friends and in society. *@GalileosBalls, Twitter

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1896 Comptes Rendus publishes, "Extension of the Reimann-Roch Theorem to Algebraic Surfaces. A note by M. M. Noether, presented by M. Hermite *Mathematical Intellignecer vol 8 #4

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1893 Karl Pearson’s first statistical publication. *VFR In Pearson' s first published statistical paper of 26 October 1893, he introduced the method of moments as a means of curve fitting asymmetrical distributions. One of his aims in developing the method of moments was to provide a general method for determining the values of the parameters of a frequency distribution. *StatProb web site

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1960 Saga, a silent shoot-em-up Western playlet made on the TX-0 computer, was run on CBS' special for MIT's 100th anniversary. The TX-0 was the first general purpose transistorized computer. The program for Saga comprised 4,096 words of magnetic core storage. The 13,000 lines of code choreographed the movements of each object. A line of direction was written for each action, even if it went wrong. This led to the high point of the show where sheriff put his gun in the holster of the robber resulting in a never ending loop.
Doug Ross explained the rule-based diagram: If the robber drank from alcohol, his judgement would start to decline, but the program would remain logical.*CHM

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BIRTHS
1846 Lewis Boss (26 Oct 1846; 12 Oct 1912) American astronomer best known for his compilation of two catalogues of stars (1910, 1937). In 1882 he led an expedition to Chile to observe a transit of Venus. About 1895 Boss began to plan a general catalog of stars, giving their positions and motions. After 1906, the project had support from the Carnegie Institution, Washington, D.C. With an enlarged staff he observed the northern stars from Albany and the southern stars from Argentina. With the new data, he corrected catalogs that had been compiled in the past, and in 1910 he published the Preliminary General Catalogue of 6,188 Stars for the Epoch 1900. The work unfinished upon his death was completed by his son Benjamin in 1937 (General Catalogue of 33,342 Stars for the Epoch 1950, 5 vol.)*TIS

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1849 Georg Frobenius (26 Oct 1849; 3 Aug 1917) German mathematician who made major contributions to group theory, especially the concept of abstract groups (with Ludwig Stickleberger) and the theory of finite groups of linear substitutions (with Issai Schur), that later found important uses in the theory of finite groups as it applies to quantum mechanics. He also contributed to means of solving linear homogenous differential equations. The fact so many of Frobenius's papers read like present day text-books on the topics which he studied is a clear indication of the importance that his work, in many different areas, has had in shaping the mathematics which is studied today.*TIS

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1877 Max Mason (26 Oct 1877; 23 Mar 1961) American mathematical physicist, educator, and science administrator. During World War I he invented several devices for submarine detection - several generations of the Navy's "M," or multiple-tube, passive submarine sensors. This apparatus focused sound to ascertain its source. To determine the direction from which the sound came, the operator needed only to seek the maximum output on his earphones by turning a dial. The final device had a range of 3 miles. Mason's special interest and contributions lay in mathematics (differential equations, calculus of variations), physics (electromagnetic theory), invention (acoustical compensators, submarine-detection devices), and the administration of universities and foundations. *TIS

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1885 Niels Erik Norlund (26 Oct 1885 in Slagelse, near Soro, Sjaelland, Denmark - 4 July 1981 in Copenhagen, Denmark) In 1907 he was awarded a gold medal for an essay on continued fractions and his resulting two publications were in 1908: Sur les différences réciproques; and Sur la convergence des fractions continues both published in Comptes Rendus de l'Academie des Sciences. These publications in the most prestigious French journal earned Norlund an international reputation despite still being an undergraduate. In the summer of 1910 he earned a Master's degree in astronomy and in October of that year he successfully defended his doctoral thesis in mathematics Bidrag til de lineaere differentialligningers Theori. In the same year he published the 100-page paper Fractions continues et différences réciproques as well as Sur les fractions continues d'interpolation, a paper on Halley's comet, and an obituary of his teacher Thorvald Thiele. Norlund's sister Margrethe married Niels Bohr whose brother, Harald, was also an outstanding mathematician. In 1955 Norland reached retirement age. That mathematics was his first love now became clear, for once he gave up the responsibilities of the Geodesic Institute he returned to mathematics research. He published Hypergeometric functions in 1955 which was reviewed by Arthur Erdélyi, "This is one of those rare papers in which sound mathematics goes hand in hand with excellent exposition and style; and the reader is both instructed and delighted. It is likely to become the standard memoir on the generalized hypergeometric series ... " The paper Sur les fonctions hypergéométriques d'ordre supérieur (1956) gives a very full, rigorous and classical treatment of some integrals from generalized hypergeometric function theory.*SAU

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1911 Shiing-shen Chern (26 Oct 1911; 3 Dec 2004) Chinese-American mathematician and educator whose researches in differential geometry include the development of the Chern characteristic classes in fibre spaces, which play a major role in mathematics and in mathematical physics. "When Chern was working on differential geometry in the 1940s, this area of mathematics was at a low point. Global differential geometry was only beginning, even Morse theory was understood and used by a very small number of people. Today, differential geometry is a major subject in mathematics and a large share of the credit for this transformation goes to Professor Chern." *TIS

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1930 Walter Feit (26 Oct 1930 in Vienna, Austria - 29 July 2004 in Branford, Connecticut, USA) was an Austrian mathematician who (with John Thompson) proved one of the most important theorems about finite simple groups. In 1990 his 60th birthday was celebrated with an 'International Symposium on the Inverse Galois Problem' held in Oxford. His retirement from Yale in October 2003 was marked with the holding of a 'Conference on Groups, Representations and Galois Theory' in his honour. Feit died after a long illness at the Connecticut Hospice in Branford, Connecticut, USA. A memorial service was held on Sunday 10 October 2004 at the New Haven Lawn Club, New Haven, Connecticut. *SAU

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DEATHS
1817 Aida Yasuaki was a Japanese mathematician who published about 2000 works. Aida compiled Sampo tensi shinan which appeared in 1788. It is a book of geometry problems, developing formulae for ellipses, spheres, circles etc. Aida explained the use of algebraic expressions and the construction of equations. He also worked on number theory and simplified continued fraction methods due to Seki. *SAU

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1923 Charles Proteus Steinmetz (9 Apr 1865- 26 Oct 1923) German-born American inventor and electrical engineer whose theories and mathematical analysis of alternating current systems helped establish them as the preferred form of electrical energy in the United States, and throughout the world. In 1893, Steinmetz joined the newly organized General Electric Company where he was an engineer then consultant until his death. His early research on hysteresis (loss of power due to magnetic resistance) led him to study alternating current, which could eliminate hysteresis loss in motors. He did extensive new work on the theory of a.c. for electrical engineers to use. His last research was on lightning, and its threat to the new AC power lines. He was responsible for the expansion of the electric power industry in the U.S. *TIS

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1968 Sergei Natanovich Bernstein (March 5, 1880 – October 26, 1968) was a Russian and Soviet mathematician. His doctoral dissertation, submitted in 1904 to the Sorbonne, solved Hilbert's nineteenth problem on the analytic solution of elliptic differential equations. Later, he published numerous works on Probability theory, Constructive function theory, and mathematical foundations of genetics. From 1906 until 1933, Bernstein was a member of the Kharkov Mathematical Society. *Wik

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1970 Marcel Gilles Jozef Minnaert (12 Feb 1893; 26 Oct 1970 at age 77)
Flemish astronomer and solar physicist who was one of the pioneering solar researchers during the first half of the 20th century. Applying solar spectrophotometry, he was one of the first to make quantitative measurements of the intensity distribution inside Fraunhofer lines, and interpret from them information about the outer solar layers. His range of study also included comets, nebulae and lunar photometry. During the time he was director of the observatory at the University of Utrecht, (1937-1963) he created a modern astronomical institute to study solar and stellar spectra with resources including a solar telescope, spectrograph, photometer, and mechanical workshop. Minnaert also maintained a strong interest in the education of physics teachers, and as a univeristy professor gave clear, enthusiastic and well-prepared lectures. *TIS

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1983 Alfred Tarski (14 Jan 1902, 26 Oct 1983) Polish-born American mathematician and logician who made important studies of general algebra, measure theory, mathematical logic, set theory, and metamathematics. Formal scientific languages can be subjected to more thorough study by the semantic method that he developed. He worked on model theory, mathematical decision problems and with universal algebra. He produced axioms for "logical consequence", worked on deductive systems, the algebra of logic and the theory of definability. Group theorists study 'Tarski monsters', infinite groups whose existence seems intuitively impossible. *TIS

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1984 Mark Kac (3 Aug 1914 in Krzemieniec, Poland, Russian Empire - 26 Oct 1984 in California, USA) pioneered the modern development of mathematical probability, in particular its applications to statistical physics. The method of quantization now in use involves the Feynman-Kac path integral, named after Richard Feynman and Mark Kac. He published a classic text Statistical Independence in Probability, Analysis and Number Theory in 1959. To many Kac will be remembered best for a paper he wrote for the American Mathematical Monthly in 1966. This is the famous paper Can One Hear the Shape of a Drum? and Kac received the Chauvenet Prize from the Mathematical Association of America in 1968 for the, "most outstanding expository article on a mathematical topic by a member of the Association." *SAU

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1998 Kenkichi Iwasawa (11 Sept 1917 in Shinshuku-mura (near Kiryu), Gumma Prefecture, Japan - 26 Oct 1998 in Tokyo, Japan ) In the late 1960s Iwasawa made a conjecture for algebraic number fields which, in some sense, was the analogue of the relationship which Weil had found between the zeta function and the divisor class group of an algebraic function field. This conjecture became known as "the main conjecture on cyclotomic fields" and it remained one of the most outstanding conjectures in algebraic number theory until it was solved by Mazur and Wiles in 1984 using modular curves. "it is no exaggeration to say that Iwasawa's ideas have played a pivotal role in many of the finest achievements of modern arithmetical algebraic geometry on such questions as the conjecture of B Birch and H Swinnerton-Dyer on elliptic curve; the conjecture of B Birch, J Tate, and S Lichtenbaum on the orders of the K-groups of the rings of integers of number fields; and the work of A Wiles on the modularity of elliptic curves and Fermat's Last Theorem." *SAU

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Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum

On This Day in Math - Oct 25

Unfortunately what is little recognized is that the most worthwhile scientific books are those in which the author clearly indicates what he does not know; for an author most hurts his readers by concealing difficulties.t.
E. Torricelli

The 298th day of the year; If you multiply 298 by (298 + 3) you get a palindromic number, 89,698. Can every number be similarly adjusted to make a palindrome?

EVENTS
1666 William Lilly, astrologer, was called before the House of Commons to explain the embarrassing success of his 1651 prediction of the plague (of 1665) and “exorbitant fire” of 1666. The House ultimately attributed the fire to the papists. *W W Rouse Ball, Mathematical Recreations and Essays,6th edition, p. 390 Lilly caused much controversy in 1652 for allegedly predicting the Great Fire of London some 14 years before it happened. For this reason many people believed that he might have started the fire, but there is no evidence to support these claims. He was tried for the offence in Parliament but was found to be innocent.*Wik

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In 1671, Giovanni Cassini discovered Iapetus, one of Saturn's moons. Iapetus is the third largest and one of the stranger of the 18 moons of Saturn. Its leading side is dark with a slight reddish color while its trailing side is bright. The dark surface might be composed of matter that was either swept up from space or oozed from the moon's interior. This difference is so striking that Cassini noted that he could see Iapetus only on one side of Saturn and not on the other. In Greek mythology Iapetus was a Titan, the son of Uranus, the father of Prometheus and Atlas and an ancestor of the human race. Cassini (1625-1712), first director of the Paris Royal Observatory, also discovered other moons of Saturn (Tethys, Dione, Rhea) and the major gap in its rings. *TIS

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1713 Leibniz, in a letter to Johann Bernoulli, observed that an alternating series whose terms monotonically decrease to zero in absolute value is convergent. In a letter of January 10, 1714, he gave an incorrect proof (Big Kline, p. 461). Examination of the proof reveales that it is the one we give today, except he fails to say anything about the completeness of the reals. *VFR

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1846 William Thompson (Lord Kelvin) writes to Sir George Stokes regarding the "recent proceedings about Oceanus, or Neptune, or Le Verrier. " commenting that "Cambridge is behind the rest of the world on scientific subjects.". John C. Adams, later became a fellow at Pembroke College, and he and Stokes became close friends. *The correspondence between Sir George Gabriel Stokes and Sir William Thompson, pg 2

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1881 Clerk Seaton writes to the chairman of the committee on the census that he has discovered a paradox with the apportionment. Seaton had discovered the Alabama Paradox.

It seemed so easy. The 1787 US Constitution laid out simple rules for deciding how many representatives each state shall receive:
"Representatives and direct taxes shall be apportioned among the several States which may be included within this Union, according to their respective numbers, ... The number of Representatives shall not exceed one for every thirty thousand, but each State shall have at least one Representative ..."
It may have seemed easy, but for the 200+ years of US government, the question of "Who gets how many?" continues to perplex and promote controversy.
When congress discussed mathematical methods of applying this constitutional directive there were two methods of prime consideration, Jefferson's method, and Hamilton's method. Congress selected Hamilton's method and in the first use of the Presidential veto (make a note of this for extra points in History or Government class) President Washington rejected the bill. Congress submitted and passed another bill using Jefferson's method. The method used has changed frequently over the years with a method by Daniel Webster adopted in 1842, (the original 65 Representatives had grown to 223) and then replaced with Hamilton's method in 1852 (234 Representatives). In a strange "Only in America" moment in 1872, the congress reapportioned without actually adopting an official method and some analysis suggest that the difference caused Rutherford Hayes to Win instead of Samuel Tilden who would have won had Hamilton's method been used. Since 1931 the US House has had 435 Representatives with the brief exception of when Alaska and Hawaii became states. Then there was a temporary addition of one seat for each until the new apportionment after the 1960 Census. In 1941 the Huntington-Hill Method was adopted and has remained in continuous (and contentious) use ever since.
In 1880 the first of what are called the apportionment paradoxes was discovered. Here is how they state it at the Wikipedia web site:
After the 1880 census, C. W. Seaton, chief clerk of the U. S. Census Office, computed apportionments for all House sizes between 275 and 350, and discovered that Alabama would get 8 seats with a House size of 299 but only 7 with a House size of 300. In general the term Alabama paradox refers to any apportionment scenario where increasing the total number of items would decrease one of the shares. They also show a nice example (with small numbers) so you might check their site.

*pballew.net

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2001 Microsoft Releases Windows XP​, the family of 32-bit and 64-bit operating systems produced by Microsoft for use on personal computers. The name "XP" stands for “Experience.” The successor to both Windows 2000 Professional​ and Windows ME, Windows XP was the first consumer-oriented operating system Microsoft built on the Windows NT​ kernel and architecture. Over 400 million copies were in use by January 2006, according to an International Data Corporation​ analyst. It was succeeded by Windows Vista, which was released to the general public in January 2007*CHM

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2011   Scientists in California and Sweden have solved a 250-year-old mystery — a coded manuscript written by a secret society.  The University of Southern California announced Tuesday, Oct 25th, that researchers had broken the Copiale Cipher — the writing used in a 105-page 18th century document from Germany.

Kevin Knight, of USC, and Beata Megyesi and Christiane Schaefer, of Uppsala University, did the work.

They used a statistical computer program to decipher part of the manuscript, which was found in East Berlin after the Cold War and is now in a private collection.

The book, written in symbols and Roman letters, details complicated initiation ceremonies of a society fascinated by ophthalmology. They include making mystical signs and plucking a hair from a candidate's eyebrow. The convoluted text swears candidates to loyalty and secrecy. *Associated Press,

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BIRTHS
1789 Samuel Heinrich Schwabe (25 Oct 1789; 11 Apr 1875) Amateur German astronomer who discovered the 10-year sunspot activity cycle. Schwabe had been looking for possible intramercurial planets. From 11 Oct 1825, for 42 years, he observed the Sun virtually every day that the weather allowed. In doing so he accumulated volumes of sunspot drawings, the idea being to detect his hypothetical planet as it passed across the solar disk, without confusion with small sunspots. Schwabe did not discover any new planet. Instead, he published his results in 1842 that his 17 years of nearly continuous sunspot observations revealed a 10-year periodicity in the number of sunspots visible on the solar disk. Schwabe also made (1831) the first known detailed drawing of the Great Red Spot on Jupiter.*TIS

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1796 James Curley (Irish: Séamus MacThoirealaigh (26 October 1796 – 24 July 1889) was an Irish-American astronomer. He was born at Athleague, County Roscommon, Ireland. His early education was limited, though his talent for mathematics was discovered, and to some extent developed, by a teacher in his native town. He left Ireland in his youth, arriving in Philadelphia on 10 October 1817. Here he worked for two years as a bookkeeper and then taught mathematics at Frederick, Maryland. In 1826 he became a student at the old seminary in Washington, DC, intending to prepare himself for the Catholic priesthood, and at the same time taught one of its classes. The seminary, however, which had been established in 1820, was closed in the following year and he joined the Society of Jesus on 29 September 1827. After completing his novitiate he again taught in Frederick and was sent in 1831 to teach natural philosophy at Georgetown University. He also studied theology and was ordained priest on 1 June 1833. His first Mass was said at the Visitation Convent, Georgetown, where he afterwards acted as chaplain for fifty years.He spent the remainder of his life at Georgetown, where he taught natural philosophy and mathematics for forty-eight years. He planned and superintended the building of the Georgetown Observatory in 1844 and was its first director, filling this position for many years. One of his earliest achievements was the determination of the latitude and longitude of Washington, D.C. in 1846. His results did not agree with those obtained at the Naval Observatory, and it was not until after the laying of the first transatlantic cable in 1858 that his determination was found to be near the truth. *Wik

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1811 Evariste Galois born in the little village of Bourg-la-Reine, near Paris, France. *VFR (25 Oct 1811; 31 May 1832) famous for his contributions to the part of higher algebra known as group theory. His theory solved many long-standing unanswered questions, including the impossibility of trisecting the angle and squaring the circle. Galois fought a duel with Perscheux d'Herbinville on 30 May 1832, the reason for the duel not being clear but certainly linked with a love affair. Galois was wounded in the duel, and died in hospital the following day, at age 20. His funeral was held on 2 June. It was the focus for a Republican rally and riots followed which lasted for several days. He was commemorated as a revolutionary and geometrician on a French postal stamp issued on 10 Nov 1984.*TIS

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1877 Henry Norris Russell (25 Oct 1877; 18 Feb 1957) American astronomer and astrophysicist who showed the relationship between a star's brightness and its spectral type, in what is usually called the Hertzsprung-Russell diagram, and who also devised a means of computing the distances of binary stars. As student, professor, observatory director, and active professor emeritus, Russell spent six decades at Princeton University. From 1921, he visited Mt. Wilson Observatory annually. He analyzed light from eclipsing binary stars to determine stellar masses. Russell measured parallaxes and popularized the distinction between giant stars and "dwarfs" while developing an early theory of stellar evolution. Russell was a dominant force in American astronomy as a teacher, writer, and advisor. *TIS

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1886 Lester Randolph Ford (25 Oct 1886 in Missouri, USA - 11 Nov 1967 in Charlottesville, Virginia, USA) was an American mathematician who lectured for several years in Edinburgh before moving back to the USA. He wrote some important text-books and is best known for his contributions to the Mathematical Association of America and the American Mathematical Monthly. *SAU (Ford circles are named after him. If you have never explored this idea, and the related idea of mediants, do it today)

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1910 William Higinbotham (Oct 1910; 10 Nov 1994) American physicist who invented the first video game, Tennis for Two, as entertainment for the 1958 visitor day at Brookhaven National Laboratory, where he worked (1947-84) then as head of the Instrumentation Division. It used a small analogue computer with ten direct-connected operational amplifiers and output a side view of the curved flight of the tennis ball on an oscilloscope only five inches in diameter. Each player had a control knob and a button. Late in WW II he became electronics group leader at Los Alamos, New Mexico, where the nuclear bomb was developed. After the war, he became active with other nuclear scientists in establishing the Federation of American Scientists to promote nuclear n)on-proliferation.*TIS (raise your hand if you are old enough to remember "Pong")

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1945 David N. Schramm (25 Oct 1945; 19 Dec 1997) American theoretical astrophysicist who was an authority on the particle-physics aspects of the Big Bang theory of the origin of the universe. He considered the nuclear physics involved in the synthesis of the light elements created during the Big Bang comprising mainly hydrogen, with lesser quantities of deuterium, helium, lithium, beryllium and boron. He predicted, from cosmological considerations, that a third family of neutrinos existed - which was later proven in particle accelerator experiments (1989). Schramm worked to evaluate undetected dark matter that contributed to the mass of the universe, and which would determine whether the universe would ultimately continue to expand. He died in the crash of the small airplane he was piloting. *TIS

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DEATHS
1400 Geoffrey Chaucer died. Although rightly famous for his Canterbury Tales, he also wrote two astronomical works. [DSB 3, 217] *VFR In his lifetime he was far more known for his “Treatise on the Astrolabe”

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1647 Evangelista Torricelli (15 Oct 1608- 25 Oct 1647)Born in Faenza, Italy, Torricelli was an Italian physicist and mathematician who invented the barometer and whose work in geometry aided in the eventual development of integral calculus. Inspired by Galileo's writings, he wrote a treatise on mechanics, De Motu ("Concerning Movement"), which impressed Galileo. He also developed techniques for producing telescope lenses. The barometer experiment using "quicksilver" filling a tube then inverted into a dish of mercury, carried out in Spring 1644, made Torricelli's name famous. The Italian scientists merit was, above all, to admit that the effective cause of the resistance presented by nature to the creation of a vacuum (in the inverted tube above the mercury) was probably due to the weight of air*TIS

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1733 Girolamo Saccheri (5 Sep 1667, 25 Oct 1733) Italian mathematician who worked to prove the fifth postulate of Euclid, which can be stated as, "Through any point not on a given line, one and only one line can be drawn that is parallel to the given line." Euclid saw the proof was not self-evident, yet neither did he provide one; instead he accepted it as an assumption. Subsequently many mathematicians tried to prove this fifth postulate from the remained axioms - and failed. Saccheri took the novel approach of first assuming that the postulate was wrong, then followed the all consequences seeking any one contradiction that then leaves the only original postulate as the only possible solution. In the process, he came close to discovering non-Euclidian geometry, but gave up too early.*TIS

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1884 Carlo Alberto Castigliano (9 November 1847, Asti – 25 October 1884, Milan) was an Italian mathematician and physicist known for Castigliano's method for determining displacements in a linear-elastic system based on the partial derivatives of strain energy.*Wik

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1905 Otto Stolz (3 May 1842 in Hall (now Solbad Hall in Tirol), Austria - 25 Oct 1905 in Innsbruck, Austria) Stolz's earliest papers were concerned with analytic or algebraic geometry, including spherical trigonometry. He later dedicated an increasing part of his research to real analysis, in particular to convergence problems in the theory of series, including double series; to the discussion of the limits of indeterminate ratios; and to integration.*SAU

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1914 Wilhelm Lexis studied data presented as a series over time thus initiating the study of time series.*SAU

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1933 Albert Wangerin worked on potential theory, spherical functions and differential geometry. *SAU

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1996 Ennio de Giorgi (Lecce, February 8, 1928 – Pisa, October 25, 1996) was an Italian mathematician who worked on partial differential equations and the foundations of mathematics.*SAU

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2002 René Frédéric Thom (September 2, 1923 – October 25, 2002) was a French mathematician. He made his reputation as a topologist, moving on to aspects of what would be called singularity theory; he became world-famous among the wider academic community and the educated general public for one aspect of this latter interest, his work as founder of catastrophe theory (later developed by Erik Christopher Zeeman). He received the Fields Medal in 1958.*Wik

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Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum

On This Day in Math - Oct 24

Monument to Gauss and Weber in Gottingen

Now it is quite clear to me that there are no solid spheres in the heavens, and those that have been devised by authors to save the appearances, exist only in their imagination, for the purpose of permitting the mind to conceive the motion which the heavenly bodies trace in their courses.
~Tycho Brahe

The 297th day of the year; 297² = 88209 and 88+209 = 297. (Numbers that have this property are a type of Kaprekar number; there are only three such numbers of three digits, now you know one of them.)


EVENTS
1676 Newton summarized the stage of development of his method in the “Epistola posterior,” which he sent to Oldenburg to transmit to Leibniz. *VFR (see Oct 26, 1676) This may be the first time Newton used irrational exponents in communication to others. It is one of the earlier uses by anyone. In the letter to Oldenburg, Newton he remarks that Leibniz had developed a number of methods, one of which was new to him.

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1729 Euler mentioned the gamma function in a letter to Goldbach. In 1826 Legendre gave the function its symbol and name. * F. Cajori, History of Mathematical Notations, vol. 2, p. 271 (the Oct 13 date is for the Julian Calendar still used in Russia when Euler wrote from there. It was the 24th in most of the rest of the world using the Gregorian Calendar.)

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1826 Abel wrote Holmboe his impressions of continental mathematics and mathematicians.

Upon reaching Paris from Berlin, he worked on what would be called the Paris Treatise that he submitted to the Academy in October 1826. In this memoir, Abel obtained among other things, an important addition theorem for algebraic integrals. It is also in this treatise that we see the first occurence of the concept of the genus of an algebraic function. Cauchy and Legendre were appointed referees of this memoir. In Paris, Abel was disappointed to find little interest in his work, which he had saved for the Academy. He wrote to Holmboe, “I showed the treatise to Mr. Cauchy, but he scarcely deigned to glance at it."

*Krishnaswami Alladi, NEILS HENRIK ABEL, Norwegian mathematical genius (paper on UFL website)

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In 1851, William Lassell discovered Ariel and Umbriel, satellites of Uranus. Like most of the other Uranian moons Ariel is named after a Shakespearean character (Ariel is the captive spirit in The Tempest, also featured in Alexander Pope's Rape of the Lock). Ariel has an approx. diameter of 1160-km, an orbital period of 2.52 days, and orbital radius of 191,240-km from Uranus. The name Umbriel comes from Alexander Pope's The Rape of the Lock. Umbriel has a diameter of 1170-km, an orbital period of about 4 days and orbit radius of 266,000-km. Lassell, a British astronomer, had previously also discovered Neptune's largest satellite, Triton and (with Bond) discovered Saturn's moon Hyperion. He was a successful brewer before turning to astronomy.*TIS

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1902 In Science, George Bruce Halsted wrote that his student R. L. Moore, who had proved that one of Hilbert’s betweenness axioms was redundant, “was displaced in favor of a local schoolmarm,” Miss Mary E. Decherd. *VFR Halstead was contentious in many ways, and Moore's rejection may have been a response to the fact that Halstead had suggested him. Halstead would be fired himself on December 11 of the same year. *D. Reginald Traylor , Creative Teaching: The Heritage of R. L. Moore, pg 35-37

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1904 Emmy Noether matriculated at the University of Erlangen. *VFR

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1989 “Welcome to the White House on this glorious fall day. I’m sorry if I’m just a little bit late. I was sitting in there trying to solve a few quadratic equations. [Laughter] Somewhat more difficult than balancing the budget, I might say. And then I thought it might be appropriate to have a moment of silence in memory of those substitute teachers back home. [Laughter].” Remarks by President George Bush (the elder) at the Presentation Ceremony for the Presidential Awards for Excellence in Science and Math Teaching.

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BIRTHS
1632 Antonie van Leeuwenhoek (24 Oct 1632; 26 Aug 1723.) Dutch microscopist who was the first to observe bacteria and protozoa. His researches on lower animals refuted the doctrine of spontaneous generation, and his observations helped lay the foundations for the sciences of bacteriology and protozoology.*TIS "The 31th of May, I perceived in the same water more of those Animals, as also some that were somewhat bigger. And I imagine, that [ten hundred thousand] of these little Creatures do not equal an ordinary grain of Sand in bigness: And comparing them with a Cheese-mite (which may be seen to move with the naked eye) I make the proportion of one of these small Water-creatures to a Cheese-mite, to be like that of a Bee to a Horse: For, the circumference of one of these little Animals in water, is not so big as the thickness of a hair in a Cheese-mite. "

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1804 Wilhelm Eduard Weber (24 Oct 1804; 23 Jun 1891)German physicist who investigated terrestrial magnetism. For six years, from 1831, Weber worked in close collaboration with Gauss. Weber developed sensitive magnetometers, an electromagnetic telegraph (1833) and other magnetic instruments during this time. His later work (1855) on the ratio between the electrodynamic and electrostatic units of charge proved extremely important and was crucial to Maxwell in his electromagnetic theory of light. (Weber found the ratio was 3.1074 x 108 m/sec but failed to take any notice of the fact that this was close to the speed of light.) Weber's later years were devoted to work in electrodynamics and the electrical structure of matter. The magnetic unit, weber, is named after him.*TIS

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1821 Philipp Ludwig von Seidel (23 October 1821, Zweibrücken, Germany – 13 August 1896, Munich) born. He formulated the notion of uniform convergence.*VFR 
was a German mathematician. His mother was Julie Reinhold and his father was Justus Christian Felix Seidel.
Lakatos credits von Seidel with discovering, in 1847, the crucial analytic concept of uniform convergence, while analyzing an incorrect proof of Cauchy's. In 1857, von Seidel decomposed the first order monochromatic aberrations into five constituent aberrations. They are now commonly referred to as the five Seidel Aberrations.   The Gauss–Seidel method is a useful numerical iterative method for solving linear systems. *Wik

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1853 Heinrich Maschke (24 October 1853 in Breslau, Germany (now Wrocław, Poland) – 1 March 1908 Chicago, Illinois, USA) was a German mathematician who proved Maschke's theorem.*Wik

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1873 Sir Edmund Taylor Whittaker (24 Oct 1873; 24 Mar 1956) English mathematician who made pioneering contributions to the area of the special functions, which is of particular interest in mathematical physics. Whittaker is best known work is in analysis, in particular numerical analysis, but he also worked on celestial mechanics and the history of applied mathematics and physics. He wrote papers on algebraic functions and automorphic functions. His results in partial differential equations (described as most sensational by Watson) included a general solution of the Laplace equation in three dimensions in a particular form and the solution of the wave equation. On the applied side of mathematics he was interested in relativity theory and he also worked on electromagnetic theory. *TIS

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1906 Aleksandr Osipovich Gelfond (24 Oct 1906; 7 Nov 1968) Russian mathematician who originated basic techniques in the study of transcendental numbers (numbers that cannot be expressed as the root or solution of an algebraic equation with rational coefficients). He profoundly advanced transcendental-number theory, and the theory of interpolation and approximation of complex-variable functions. He established the transcendental character of any number of the form ab, where a is an algebraic number different from 0 or 1 and b is any irrational algebraic number, which is now known as Gelfond's theorem. This statement solved the seventh of 23 famous problems that had been posed by the German mathematician David Hilbert in 1900. *TIS

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1922 Werner Buchholz​ was born. He was a member of the teams that designed the IBM 701​ and Stretch models. Buchholz used term byte to describe eight bits—although in the 1950s, when the term first was used, equipment used six-bit chunks of information, and a byte equaled six bits. Buchholz described a byte as a group of bits to encode a character, or the numbers of bits transmitted in parallel to and from input-output. *CHM

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1932 Pierre-Gilles de Gennes (24 Oct 1932; 18 May 2007) French physicist who was awarded the 1991 Nobel Prize for Physics for "discovering that methods developed for studying order phenomena in simple systems can be generalized to more complex forms of matter, in particular to liquid crystals and polymers." He described mathematically how, for example, magnetic dipoles, long molecules or molecule chains can under certain conditions form ordered states, and what happens when they pass from an ordered to a disordered state. Such changes of order occur when, for example, a heated magnet changes from a state in which all the small atomic magnets are lined up in parallel to a disordered state in which the magnets are randomly oriented. Recently, he has been concerned with the physical chemistry of adhesion. *TIS

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DEATHS
1601 Tycho Brahe died. Kepler inherited his vast accurate collection of astronomical data. He used this to derive his laws of planetary motion. *VFR In 1901, on the three hundredth anniversary of his death, the bodies of Tycho Brahe and his wife Kirstine were exhumed in Prague. They had been embalmed and were in remarkably good condition, but the astronomer’s artificial nose was missing, apparently filched by someone after his death. It had been made for him in gold and silver when his original nose was sliced off in a duel he fought in his youth at Rostock University after a quarrel over some obscure mathematical point. He always carried a small box of glue in his pocket for use when the new nose became wobbly. Tycho Brahe was famous for the most accurate and precise observations achieved by any astronomer before the invention of the telescope. Born to an aristocratic family in Denmark in 1546, he was one of twin boys – the other twin was still-born – and while still a baby Tycho was stolen from his parents by a rich, childless uncle, who paid for his education and sent him to Leipzig University to study law. His imagination had been fired, however, by a total eclipse of the sun in 1560 and he was determined to be an astronomer. He found that the existing tables recording the positions of planets and stars were wildly inaccurate and dedicated himself to correcting them. *History Today Was Tycho Murdered? Read an excellent blog on "The crazy life and crazier death of Tycho Brahe, history’s strangest astronomer".

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1635 Wilhelm Shickard He invented and built a working model of the first modern mechanical calculator. *VFR 

Schickard's machine could perform basic arithmetic operations on integer inputs. His letters to Kepler explain the application of his "calculating clock" to the computation of astronomical tables.
In 1935 while researching a book on Kepler, a scholar found a letter from Schickard and a sketch of his calculator, but did not immediately recognize thedesigns or their great importance. Another twenty years passed before the book's editor, Franz Hammer, found additional drawings and instructions for Schickard's second machine and released them to the scientific community in 1955.A professor at Schickard's old university, Tübingen, reconstructed thecalculator based upon Schickard's original plans; it is still on display there today. 
He was a friend of Kepler and did copperplate engravings for Kepler's Harmonice Mundi. He built the first calculating machine in 1623, but it was destroyed in a fire in the workshop in 1624.

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1655 Pierre Gassendi (22 Jan 1592, 24 Oct 1655) French scientist, mathematician, and philosopher who revived Epicureanism as a substitute for Aristotelianism, attempting in the process to reconcile Atomism's mechanistic explanation of nature with Christian belief in immortality, free will, an infinite God, and creation. Johannes Kepler had predicted a transit of Mercury would occur in 1631. Gassendi used a Galilean telescope to observed the transit, by projecting the sun's image on a screen of paper. He wrote on astronomy, his own astronomical observations and on falling bodies. *TIS

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1870 Charles Joseph Minard (27 Mar 1781; 24 Oct 1870 at age 89) French civil engineer who made significant contributions to the graphical representations of data. His best-known work, Carte figurative des pertes successives en hommes de l'Armee Français dans la campagne de Russe 1812-1813, dramatically displays the number of Napoleon's soldiers by the width of an ever-reducing band drawn across a map from France to Moscow. At its origin, a wide band shows 442,000 soldiers left France, narrowing across several hundred miles to 100,000 men reaching Moscow. With a parallel temperature graph displaying deadly frigid Russian winter temperatures along the way, the band shrinks during the retreat to a pathetic thin trickle of 10,000 survivors returning to their homeland. *TIS

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1930 Paul Emile Appell (27 Sept 1855 in Strasbourg, France - 24 Oct 1930) Appell's first paper in 1876 was based on projective geometry continuing work of Chasles. He then wrote on algebraic functions, differential equations and complex analysis. In 1878 he noted the physical significance of the imaginary period of elliptic functions in the solution of the pendulum which had been though to be purely a mathematical curiosity. He showed that the double periodicity follows from physical considerations. *SAU

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1940 Pierre-Ernest Weiss (25 Mar 1865, 24 Oct 1940) French physicist who investigated magnetism and determined the Weiss magneton unit of magnetic moment. Weiss's chief work was on ferromagnetism. Hypothesizing a molecular magnetic field acting on individual atomic magnetic moments, he was able to construct mathematical descriptions of ferromagnetic behaviour, including an explanation of such magnetocaloric phenomena as the Curie point. His theory succeeded also in predicting a discontinuity in the specific heat of a ferromagnetic substance at the Curie point and suggested that spontaneous magnetization could occur in such materials; the latter phenomenon was later found to occur in very small regions known as Weiss domains. His major published work was Le magnetisme ( 1926).*TIS

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Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum