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

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 an English cricket season by Tich Freeman in 1928.)

304 = 77^2 - 75^2 = 23^2 - 15^2 = 40^2 - 36^2

The complete story from a letter of Kepler about his 2 year search is told here by Thony Christie.

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.

2012 After Hurricane Sandy came ashore in New Jersey on the 29th, the huge weather system was captured with an overlay to emphasize it's Fibonacci-like structure. *HT to Bob Mrotek for sending me this image

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

- 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

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

Credits :

*CHM=Computer History Museum

*FFF=Kane, Famous First Facts

*NSEC= NASA Solar Eclipse Calendar

*RMAT= The Renaissance Mathematicus, Thony Christie

*SAU=St Andrews Univ. Math History

*TIA = Today in Astronomy

*TIS= Today in Science History

*VFR = V Frederick Rickey, USMA

*Wik = Wikipedia

*WM = Women of Mathematics, Grinstein & Campbell

**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. *WikThe complete story from a letter of Kepler about his 2 year search is told here by Thony Christie.

**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.

**1735**Benjamin Franklin’s paper “On the Usefulness of Mathematics,” appeared in the Pennsylvania Gazette. [NCTM yearbook # 32(1970), p. 20]*VFR I have also seen the date given as October 30. Some historians also question whether or not this was actually written by Franklin.**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**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**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**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, 2^{23209}-1. By April, another larger Prime had been found.)**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 1992.2012 After Hurricane Sandy came ashore in New Jersey on the 29th, the huge weather system was captured with an overlay to emphasize it's Fibonacci-like structure. *HT to Bob Mrotek for sending me this image

**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**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**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**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

**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**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**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**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

**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**1805 Ormbsy MacKnight Mitche**l (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

**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**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**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.)Credits :

*CHM=Computer History Museum

*FFF=Kane, Famous First Facts

*NSEC= NASA Solar Eclipse Calendar

*RMAT= The Renaissance Mathematicus, Thony Christie

*SAU=St Andrews Univ. Math History

*TIA = Today in Astronomy

*TIS= Today in Science History

*VFR = V Frederick Rickey, USMA

*Wik = Wikipedia

*WM = Women of Mathematics, Grinstein & Campbell