Pat'sBlog: March 2013

Sunday, 31 March 2013

On This Day in Math - March 31

God runs electromagnetics on Monday, Wednesday, and Friday by the wave theory, and the devil runs it by quantum theory on Tuesday, Thursday, and Saturday.
~Sir Lawrence Bragg

The 90th day of the year; 90 is the only number that is the sum of its digits plus the sum of the squares of its digits. (Is there any interesting distinction to the rest of the numbers for which this sum is more (or less) than the original number?)

EVENTS

In 1851, Leon Foucault demonstrated his pendulum experiment at the Pantheon of Paris at the request of Napoleon Bonaparte, who had been informed of Foucault's recent discovery on 6 Jan 1851. He had installed a pendulum in his cellar in the Arras Street of Paris. It was made from 2 m (6.5-ft) long wire supporting a 5-kg weight. He observed a small movement of the oscillation plane of the pendulum - showing that the Earth was rotating underneath the swinging pendulum. A month later, he repeated the experiment at the observatory of Paris, with a 11-m pendulum which gave longer swings and a more clearly visible deviation. His March demonstration at the Pantheon used a 28-kg sphere on a 67-m (220-ft) wire. *TIS (The first date of this demonstration seems to have been on March 28,

1854 The University of Konigsberg awarded Weierstrass an honorary doctorate. Previously he was a Gymnasium teacher without a university degree. *VFR The award was the result of the attention his 1854 paper, Zur Theorie der Abelschen Functionen, which appeared in Crelle's Journal. This paper did not give the full theory of inversion of hyperelliptic integrals that Weierstrass had developed but rather gave a preliminary description of his methods involving representing abelian functions as constantly converging power series. With this paper Weierstrass burst from obscurity.*SAU

1899 The EIFFEL TOWER, was built in 26 months and opened in Mar 1889 for the Universal Exposition. it is 320.75 m (1051 ft) high and only weighs 7000 tons – less than the air around it! The tower was inaugurated on 31 March 1889, and opened on 6 May. *VFR

1959 Sof'ja Janovskaja became the first chairperson of the newly created department of mathematical logic at the Moscow State University. *Women of Mathematics

1918 Standard time was adopted throughout the United States. 'An Act to preserve daylight and provide standard time for the United States' was enacted on March 19, 1918. It both established standard time zones and set summer DST to begin on March 31, 1918. *WebExhibits.org
I understand that at least three states are trying to repeal daylight savings in their states as of 2014.

In 1921, Professor Albert Einstein arrived in New York to give a lecture on his new theory of relativity. *TIS

1939 Harvard and IBM Agree to Build The Mark I "Giant Brain":
Harvard and IBM sign an agreement to build the Mark I, also known as the IBM Automatic Sequence Controlled Calculator (ASCC). Project leader Howard Aiken developed the original concept of the machine: a series of switches, relays, rotating shafts and clutches. The Mark I weighed about five tons and contained more than 750,000 components. It read instructions from paper tape and data from punch cards.*CHM

1981 Time (p. 51) reported that Educational Testing Service had to change the scores on 250,000 PSAT and 19,000 SAT papers because a student had successfully challenged a mathematical question about polyhedrons with no right answer. Mathematics Magazine 54 (1981), pp 152 and 277. *VFR Daniel Lowen, 17, a junior at Cocoa Beach High School in Florida was the first to call the ETS attention to their error. The problem involved putting two pyramids together and determining the number of faces on the new figure. The ETS had failed to allow for the fact that when two faces are joined, other faces meeting at the edges of the union might meld into one face.

1984 Science News reports that Persi Diaconis, a statistician at Stanford, can do a perfect riffle shuffle eight times in a row, thereby returning the 52-card deck to its original order. He has also proved that seven ordinary shuffles is enough to randomize a deck of cards. *VFR

1993 The birth of Spamming, A bug in a program written by Richard Depew sends an article to 200 newsgroups simultaneously. The term spamming is coined by Joel Furr (a writer and software trainer notable as a Usenet personality in the early and mid 1990s.) to describe the incident. *Wik

2011 The first ever "On This Day in Math"... thanks to hundreds of you for all the help.

BIRTHS

1596 René Descartes (31 March 1596 in La Haye (now Descartes),Touraine, France
- 11 Feb 1650 in Stockholm, Sweden)was a French philosopher whose work, La géométrie, includes his application of algebra to geometry from which we now have Cartesian geometry. His work had a great influence on both mathematicians and philosophers. La Géométrie is by far the most important part of this work. Scott summarises the importance of this work in four points:

He makes the first step towards a theory of invariants, which at later stages derelativises the system of reference and removes arbitrariness.
Algebra makes it possible to recognise the typical problems in geometry and to bring together problems which in geometrical dress would not appear to be related at all.
Algebra imports into geometry the most natural principles of division and the most natural hierarchy of method.
Not only can questions of solvability and geometrical possibility be decided elegantly, quickly and fully from the parallel algebra, without it they cannot be decided at all.

*SAU His lifelong habit of laying abed till noon was interrupted by Descartes’ new employer, the athletic, nineteen-year-old Queen Christiana of Sweden, who insisted he tutor her in philosophy in an unheated library early in the morning. This change of lifestyle caused the illness that killed him. [Eves, Circles, 177◦]*VFR

1730 – Étienne Bézout (31 March 1730 in Nemours, France - 27 Sept 1783 in Basses-Loges (near Fontainbleau), France) His most famous and well used book "including an incorrect proof that the quintic was solvable by radicals. In the early nineteenth century some of his in influential textbooks were translated into English. One translator, John Farrah, used
them to teach calculus at Harvard." *VFR
Bezout's theorem was essentially stated by Isaac Newton in his proof of lemma 28 of volume 1 of his principia, where he claims that two curves have a number of intersection points given by the product of their degrees. The theorem was later published in 1779 in Étienne Bézout's Théorie générale des équations algébriques. Bézout, who did not have at his disposal modern algebraic notation for equations in several variables, gave a proof based on manipulations with cumbersome algebraic expressions. From the modern point of view, Bézout's treatment was rather heuristic, since he did not formulate the precise conditions for the theorem to hold. This led to a sentiment, expressed by certain authors, that his proof was neither correct nor the first proof to be given.

1795 Louis Paul Emile Richard (31 March 1795 in Rennes, France - 11 March 1849 in Paris, France) Richard perhaps attained his greatest fame as the teacher of Galois and his report on him which stated, "This student works only in the highest realms of mathematics.... "
It is well known. However, he also taught several other mathematicians whose biographies are included in this archive including Le Verrier, Serret and Hermite. He fully realised the significance of Galois' work and so, fifteen years after he left the college, he gave Galois' student exercises to Hermite so that a record of his school-work might be preserved. It is probably fair to say that Richard chose to give them to Hermite since in many ways he saw him as being similar to Galois. Under Richard's guidance, Hermite read papers by Euler, Gauss and Lagrange rather than work for his formal examinations, and he published two mathematics papers while a student at Louis-le-Grand.
Despite being encouraged by his friends to publish books based on the material that he taught so successfully, Richard did not wish to do so and so published nothing. This is indeed rather unfortunate since it would now be very interesting to read textbooks written by the teacher of so many world-class mathematicians.*SAU

1806 Thomas Penyngton Kirkman FRS (31 March 1806 – 3 February 1895) was a British mathematician. Despite being primarily a churchman, he maintained an active interest in research-level mathematics, and was listed by Alexander Macfarlane as one of ten leading 19th-century British mathematicians. Kirkman's schoolgirl problem, an existence theorem for Steiner triple systems that founded the field of combinatorial design theory, is named after him.
Kirkman's first mathematical publication was in the Cambridge and Dublin Mathematical Journal in 1846, on a problem involving Steiner triple systems that had been published two years earlier in the Lady's and Gentleman's Diary by Wesley S. B. Woolhouse. Despite Kirkman's and Woolhouse's contributions to the problem, Steiner triple systems were named after Jakob Steiner who wrote a later paper in 1853. Kirkman's second research paper paper, in 1848, concerned hypercomplex numbers.
In 1850, Kirkman observed that his 1846 solution to Woolhouse's problem had an additional property, which he set out as a puzzle in the Lady's and Gentleman's Diary:

Fifteen young ladies in a school walk out three abreast for seven days in succession: it is required to arrange them daily, so that no two shall walk twice abreast.

This problem became known as Kirkman's schoolgirl problem, subsequently to become Kirkman's most famous result. He published several additional works on combinatorial design theory in later years. Kirkman also studied the Pascal lines determined by the intersection points of opposite sides of a hexagon inscribed within a conic section. Any six points on a conic may be joined into a hexagon in 60 different ways, forming 60 different Pascal lines. Extending previous work of Steiner, Kirkman showed that these lines intersect in triples to form 60 points (now known as the Kirkman points), so that each line contains three of the points and each point lies on three of the lines. *Wik

1847 – Yegor Ivanovich Zolotarev, (March 31, 1847, Saint Petersburg – July 19, 1878, Saint Petersburg) In 1874, Zolotarev become a member of the university staff as a lecturer and in the same year he defended his doctoral thesis “Theory of Complex Numbers with an Application to Integral Calculus”. The problem Zolotarev solved there was based on a problem Chebyshev had posed earlier. His steep career ended abruptly with his early death. He was on his way to his dacha when he was run over by a train in the Tsarskoe Selo station. On July 19, 1878 he died from blood poisoning. *Wik

1890 Sir William Lawrence Bragg (31 Mar 1890; 1 Jul 1971 at age 81) was an Australian-English physicist and X-ray crystallographer who at the early age of 25, shared the Nobel Prize for Physics in 1915 (with his father, Sir William Bragg). Lawrence Bragg formulated the Bragg law of X-ray diffraction, which is basic for the determination of crystal structure: nλ = 2dsinθ which relates the wavelength of x-rays, λ, the angle of incidence on a crystal, θ, and the spacing of crystal planes, d, for x-ray diffraction, where n is an integer (1, 2, 3, etc.). Together, the Braggs worked out the crystal structures of a number of substances. Early in this work, they showed that sodium chloride does not have individual molecules in the solid, but is an array of sodium and chloride ions. *TIS

1906 Shin'ichiro Tomonaga (31 Mar 1906; 8 Jul 1979 at age 73)Japanese physicist who shared the Nobel Prize for Physics in 1965 (with Richard P. Feynman and Julian S. Schwinger of the U.S.) for independently developing basic principles of quantum electrodynamics. He was one of the first to apply quantum theory to subatomic particles with very high energies. Tomonaga began with an analysis of intermediate coupling - the idea that interactions between two particles take place through the exchange of a third (virtual particle), like one ship affecting another by firing a cannonball. He used this concept to develop a quantum field theory (1941-43) that was consistent with the theory of special relativity. WW II delayed news of his work. Meanwhile, Feynman and Schwinger published their own independent solutions.*TIS

DEATHS

1624 Joao Baptista Lavanha (1550 in Portugal - 31 March 1624 in Madrid, Spain)Lavanha is said to have studied in Rome. He was appointed by Philip II of Spain to be professor of mathematics in Madrid in 1582.
Philip had sent the Duke of Alba with an army to conquer Portugal in 1580 and soon realized that Portugal was more advanced in studies of navigation than Spain. In an attempt to correct this, Philip founded an Academy of Mathematics in Madrid with Lavanha as its first professor.
From 1587 Lavanha became chief engineer to Philip II. He was appointed cosmographer to the king in 1596 and about the same time he moved to Lisbon where he taught mathematics to sailors and navigators.
Lavanha is best known for his contributions to navigation. His book Regimento nautico gives rules for determining latitude and tables of declination of the Sun. He also worked on maps, producing some interesting new ideas. He produced a map of Aragon in about 1615. Among his publications was a translation of Euclid.
Lavanha also studied instruments used in navigation, constructing astrolabes, quadrants and compasses. *SAU

1726/7 Isaac Newton (25 December 1642 – 20 March 1727 [NS: 4 January 1643 – 31 March 1727) English physicist and mathematician, who made seminal discoveries in several areas of science, and was the leading scientist of his era. His study of optics included using a prism to show white light could be split into a spectrum of colors. The statement of his three laws of motion are fundamental in the study of mechanics. He was the first to describe the moon as falling (in a circle around the earth) under the same influence of gravity as a falling apple, embodied in his law of universal gravitation. As a mathematician, he devised infinitesimal calculus to make the calculations needed in his studies, which he published in Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy, 1687)*TIS
Newton died intestate. Immediately his relatives began to quarrel over the division of his estate, which amounted to a considerable fortune. Thomas Pellet examined Newton’s manuscript holdings in hopes of turning a quick proﬁt. His “thick clumsy annotations ‘Not ﬁt to be printed,’ now seem at once pitiful and ludicrous.” See Whiteside, Newton Works, I, xvii ﬀ for details. *VFR

1841 George Green (14 Jul 1793, 31 Mar 1841 at age 47) was an English mathematician, born near Nottingham, who was first to attempt to formulate a mathematical theory of electricity and magnetism. He was a baker while, remarkably, he became a self-taught mathematician. He became an undergraduate at Cambridge in October 1833 at the age of 40. Lord Kelvin (William Thomson) subsequently saw, was excited by the Essay. Through Thomson, Maxwell, and others, the general mathematical theory of potential developed by an obscure, self-taught miller's son heralded the beginning of modern mathematical theories of electricity.*TIS His most famous work, An Essay on the Application of Mathematical Analysis to the Theory of Electricity and Magnetism was published, by subscription, in March 1828. Most of the ﬁfty-two subscribers were friends and patrons. The work lay unnoticed until William Thomson rediscovered it and showed it to Liouville and Sturm in Paris in 1845. The Theory of Potential it developed led to the modern mathematical theory of electicity. *VFR

1877 Antoine-Augustin Cournot (28 Aug 1801; 31 Mar 1877) French economist and mathematician, who was the first economist who applied mathematics to the treatment of economic questions. In 1838, he published Recherches sur les principes mathématiques de la théorie des richesses (Researches into the Mathematical Principles of the Theory of Wealth) which was a treatment of mathematical economics. In particular, he considered the supply-and-demand functions. Further, he studied the conditions for equilibrium with monopoly, duopoly and perfect competition. He included the effect of taxes, treated as changes in production costs, and discussed problems of international trade. His definition of a market is still the basis for that presently used in economics. In other work, he applied probability to legal statistics *TIS

1997 Friedrich (Hermann) Hund (4 Feb 1896 - 31 Mar 1997) was a German physicist known for his work on the electronic structure of atoms and molecules. He introduced a method of using molecular orbitals to determine the electronic structure of molecules and chemical bond formation. His empirical Hund's Rules (1925) for atomic spectra determine the lowest energy level for two electrons having the same n and l quantum numbers in a many-electron atom. The lowest energy state has the maximum multiplicity consistent with the Pauli exclusion principle. The lowest energy state has the maximum total electron orbital angular momentum quantum number, consistent with rule. They are explained by the quantum theory of atoms by calculations involving the repulsion between two electrons. *TIS

Harold Scott MacDonald Coxeter (9 Feb 1907 in London, England - 31 March 2003 in Toronto, Canada) graduated from Cambridge and worked most of his life in Canada. His work was mainly in geometry. In particular he made contributions of major importance in the theory of polytopes, non-euclidean geometry, group theory and combinatorics. Among his most famous geometry books are The real projective plane (1955), Introduction to geometry (1961), Regular polytopes (1963), Non-euclidean geometry (1965) and, written jointly with S L Greitzer, Geometry revisited (1967). He also published a famous work on group presentations, which was written jointly with his first doctoral student W O J Moser, Generators and relations for discrete groups.
His 12 books and 167 published articles cover more than mathematical research. Coxeter met Escher in 1954 and the two became lifelong friends. Another friend, R Buckminister Fuller, used Coxeter's ideas in his architecture. In 1938 Coxeter revised and updated Rouse Ball's Mathematical recreations and essays, a book which Rouse Ball first published in 1892. *SAU

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

Saturday, 30 March 2013

On This Day in Math - March 30

Jaime Escalante *Wik

A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories. One can imagine that the ultimate mathematician is one who can see analogies between analogies.
~Stefan Banach

The 89th day of the year; 89 is the fifth Fibonacci prime and the reciprocal of 89 starts out 0.011235... (generating the first five Fibonacci numbers) *Prime Curios

If you write any integer and sum the square of the digits, and repeat, eventually you get either 1, or 89
(ex: 16; $ 1^2 + 6^2 = 37; 3^2 + 7^2 = 58; 5^2 + 8^2 = 89 $

EVENTS
In 239, B.C., was the first recorded perihelion passage of Halley's Comet by Chinese astronomers in the Shih Chi and Wen Hsien Thung Khao chronicles. Its highly elliptical, 75-year orbit carries it out well beyond the orbit of Neptune and well inside the orbits of Earth and Venus when it swings in around the Sun, travelling in the opposite direction from the revolution of the planets. It was the first comet that was recognized as being periodic. An Englishman, Edmond Halley predicted in 1705 that the comet that appeared over London in 1682 would reappear again in 1759, and that it was the same comet that appeared in 1607 and 1531. When the comet did in fact reappear again in 1759, as correctly predicted, it was named (posthumously) after Halley.*tis

1612 The Jesuit astronomer Christoph Scheiner thought he had discovered a 5th Jupiter moon He was mistaken. *Thony Christie, @rmathematicus

In 1791, after a proposal by the Académie des sciences (Borda, Lagrange, Laplace, Monge and Condorcet), the French National Assembly finally chose that a metre would be a 1/10 000 000 of the distance between the north pole and the equator. *TIS (although at the time, this distance was not known. To determine the distance from the North Pole to the equator it was assumed that a portion of a meridian could be measured accurately and the whole distance could then be estimated from this sample. The meridian chosen went from Barcelona in Spain, to Dunquerque in France; this choice was an early example of the intended international nature of the metric system. Two astronomers, Borda and Méchain, were appointed to carry out the measurement. )

1796 The nineteen year old Gauss began his scientific diary with his construction of the regular 17-gon. The Greeks had ruler-and-compass constructions for the regular polygons with 3, 4, 5 and 15 sides, and for all others obtainable from these by doubling the number of sides. Here the problem rested until Gauss completely solved it: A regular n-gon is constructable IFF n is a product of a power of 2 and one or more distinct Fermat primes, i.e., primes of the form 2^2ⁿ +1. This discovery led Gauss to devote his life to mathematics rather than philology. *VFR Gauss told his close friend Bolyai that the regular 17-gon should adorn his tombstone, but this was not done. There is a 17 pointed star on the base of a monument to him in Brunswick because the stonemason felt everyone would mistake the 17-gon for a circle. Gauss gave the tablet on which he had made the discovery to Bolyai, along with a pipe, as a souvenir. (I have been unable to find any later trace of the pipe or tablet, but if anyone has knowledge of the I would appreciate any information.)

*Genial Gauss Gottingen

1858 Pencil with attached eraser patented. It has benefited generations of mathematics students. The first patent for attaching an eraser to a pencil was issued to a man from Philadelphia named Hyman Lipman. This patent was later held to be invalid because it was merely the combination of two things, without a new use. I found a note at about.com that said that "Before rubber, breadcrumbs had been used to erase pencil marks."

1867 The U. S. purchases Alaska from Russia for $7,200,000 in gold. The most prominent American mathematician of the time, Benjamin Peirce, then superintendent of the Coast Survey, played a role in the acquisition by sending out a reconnaissance party whose reports were important aids to proponents of the purchase. *VFR

1951 UNIVAC I turned over to Census Bureau. During ENIAC project, Mauchly met with several Census Bureau officials to discuss non-military applications for electronic computing devices. In 1946, with ENIAC completed, Mauchly and Eckert were able to secure a study contract from the National Bureau of Standards (NBS) to begin work on a computer designed for use by the Census Bureau. This study, originally scheduled for six months, took about a year to complete. The final result were specifications for the Universal Automatic Computer (UNIVAC).
UNIVAC was, effectively, an updated version of ENIAC. Data could be input using magnetic computer tape (and, by the early 1950's, punch cards). It was tabulated using vacuum tubes and state-of-the-art circuits then either printed out or stored on more magnetic tape.
Mauchly and Eckert began building UNIVAC I in 1948 and delivered the completed machine to the Census Bureau in March 1951. The computer was used to tabulate part of the 1950 population census and the entire 1954 economic census. Throughout the 1950's, UNIVAC also played a key role in several monthly economic surveys. The computer excelled at working with the repetitive but intricate mathematics involved in weighting and sampling for these surveys.
UNIVAC I, as the first successful civilian computer, was a key part of the dawn of the computer age *US CENSUS Bureau Web page

In 1953, Albert Einstein announced his revised unified field theory.*TIS

1985 M.I.T. computer science graduate students Robert W. Baldwin and Alan T. Sherman successfully decode a cipher consisting of a series of numbers separated by commas. They failed to share in the $116,000 prize oﬀered by Decipher Inc. since they misread the contest rules—the contest ended the previous evening. [Burlington Free Press, 5 April 1985.]

2010 A Blue moon - The second full moon of the month of March. The next month with a blue moon will be in 2012: August 2, August 31

BIRTHS

1862 Leonard James Rogers (30 March 1862, 12 Sept 1933) Rogers was a man of extraordinary gifts in many fields, and everything he did, he did well. Besides his mathematics and music he had many interests; he was a born linguist and phonetician, a wonderful mimic who delighted to talk broad Yorkshire, a first-class skater, and a maker of rock gardens. He did things well because he liked doing them. Music was the first necessity in his intellectual life, and after that came mathematics. He had very little ambition or desire for recognition.
Rogers is now remembered for a remarkable set of identities which are special cases of results which he had published in 1894. Such names as Rogers-Ramanujan identities, Rogers-Ramanujan continued fractions and Rogers transformations are known in the theory of partitions, combinatorics and hypergeometric series. *SAU

1864 Helen Abbot Merrill born in Llewellyn Park, Orange, New Jersey. She graduated from Wellesley College in 1886, taught school for several years and then returned to teach at Wellesley from 1893 until her retirement in 1932. She studied function theory with Heinrich Maschke at Chicago, descriptive geometry with G. F. Shilling at G¨ottingen, and function theory with James Pierpont at Yale, where she received her Ph.D. in 1903. She wrote a popular book about mathematics, Mathematical Excursions (1933), that has been reprinted by Dover.*WM

1879 Bernhard Voldemar Schmidt (30 Mar 1879, 1 Dec 1935) Astronomer and optical instrument maker who invented the telescope named for him. In 1929, he devised a new mirror system for reflecting telescopes which overcame previous problems of aberration of the image. He used a vacuum to suck the glass into a mold, polishing it flat, then allowing in to spring back into shape. The Schmidt telescope is now widely used in astronomy to photograph large sections of the sky because of its large field of view and its fine image definition. He lost his arm as a child while experimenting with explosives. Schmidt spent the last year of his life in a mental hospital.*TIS

1886 Stanisław Leśniewski (March 30, 1886, Serpukhov – May 13, 1939, Warsaw) was a Polish mathematician, philosopher and logician. Leśniewski belonged to the first generation of the Lwów-Warsaw School of logic founded by Kazimierz Twardowski. Together with Alfred Tarski and Jan Łukasiewicz, he formed the troika which made the University of Warsaw, during the Interbellum, perhaps the most important research center in the world for formal logic. *Wik

1892 Stefan Banach (30 Mar 1892, 31 Aug 1945) Polish mathematician who founded modern functional analysis and helped develop the theory of topological vector spaces. In addition, he contributed to measure theory, integration, the theory of sets, and orthogonal series. In his dissertation, written in 1920, he defined axiomatically what today is called a Banach space. The idea was introduced by others at about the same time (for example Wiener introduced the notion but did not develop the theory). The name 'Banach space' was coined by Fréchet. Banach algebras were also named after him. The importance of Banach's contribution is that he developed a systematic theory of functional analysis, where before there had only been isolated results which were later seen to fit into the new theory. *TIS
His doctoral dissertation, which was published in Fundamenta Mathematicae in 1922, marks the birth of functional analysis. *VFR

1921 Alfréd Rényi (20 March 1921 – 1 February 1970) was a Hungarian mathematician who made contributions in combinatorics, graph theory, number theory but mostly in probability theory. He proved, using the large sieve, that there is a number K such that every even number is the sum of a prime number and a number that can be written as the product of at most K primes. See also Goldbach conjecture.
In information theory, he introduced the spectrum of Rényi entropies of order α, giving an important generalisation of the Shannon entropy and the Kullback-Leibler divergence. The Rényi entropies give a spectrum of useful diversity indices, and lead to a spectrum of fractal dimensions. The Rényi–Ulam game is a guessing game where some of the answers may be wrong.
He wrote 32 joint papers with Paul Erdős, the most well-known of which are his papers introducing the Erdős–Rényi model of random graphs. Rényi, who was addicted to coffee, invented the quote: "A mathematician is a device for turning coffee into theorems.", which is generally ascribed to Erdős. The sentence was originally in German, being a wordplay on the double meaning of the word Satz (theorem or residue of coffee). *Wik

1929 Ilya Piatetski-Shapiro (30 March 1929 – 21 February 2009) During a career that spanned 60 years he made major contributions to applied science as well as theoretical mathematics. In the last forty years his research focused on pure mathematics; in particular, analytic number theory, group representations and algebraic geometry. His main contribution and impact was in the area of automorphic forms and L-functions.
For the last 30 years of his life he suffered from Parkinson's disease. However, with the help of his wife Edith, he was able to continue to work and do mathematics at the highest level, even when he was barely able to walk and speak.*Wik

DEATHS
1559 Adam Ries (23 Dec 1492 in Staffelstein (near Bamberg), Upper Franconia (now Germany) - 30 March 1559 in Annaberg, Saxony (now Annaberg-Buchholz, Germany) Ries's income came mainly from his arithmetic textbooks. The first of these was Rechnung auff der linihen written while he was in Erfurt and printed in that city in 1518 by Mathes Maler. The book was intended to teach people how to use a calculating board similar to an abacus. This type of device is described by the Money Museum,

Four horizontal and five vertical lines were painted or carved on the calculating boards to represent the decimal values in ascending order. The arithmetical sums were worked out with the help of coin-like counters. They were placed on the respective lines according to the values of the numbers and then, depending on the calculation, these were moved, removed or added to the lines until the final result could be read off. No numbers were printed on the counters; they amounted to as much as the line on which they were placed.

No copy of the first edition of this book has survived, the earliest that we have is the second of the four editions which was published in 1525.
Dirk Struik writes,

Adam Ries has remained in German memory because of his Rechenbücher -schoolbooks on arithmetic, popular for a century and a half. It is less known that he also wrote an algebra, called the Cosz, but this work has remained in manuscript form. Three of these manuscripts were bound together in 1664 by the Dresden Rechenmeister Martin Kupffer. They were thought to be lost until they were found in 1855, and are now kept at the Erzgebirgsmuseum Annaberg-Buchholz, Annaberg being the Saxonian mining town where Ries lived as a respected citizen and teacher for many years until his death. The impressive folio facsimile, published on the occasion of the 500th birthday of Ries, contains three manuscripts: Cosz I (pp. 1-325) was finished in 1524, Cosz II (pp. 329-499) was written between 1545 and 1550 ...

*SAU
Thony Christie pointed out to me that the German Wikipedia gives his date of death as April 2. He also has confirmed that the phrase "das macht nach Adam Ries" (That's according to Adam Ries) is still used in Germany to indicate something is done correctly, sort of like the American idiom, "according to Hoyle."

And here is the amazing story of how he was billed for his television license over 450 years after his death.

1832 Stephen Groombridge (7 Jan 1755; 30 Mar 1832) English astronomer and merchant, who compiled the Catalogue of Circumpolar Stars (corrected edition published 1838), often known as the Groombridge Catalog. For ten years, from 1806, he made observations using a transit circle, followed by another 10 years adjusting the data to correct for refraction, instrument error and clock error. He retired from the West Indian trade in 1815 to devote full time to the project. He was a founder of the Astronomical Society (1820). His work was continued by others when he was struck (1827) with a "severe attack of paralysis" from which he never fully recovered. The catalog eventually listed 4,243 stars situated within 50° of the North Pole and having apparent magnitudes greater than 9. Editions of the catalog were published posthumously. The 1833 edition was withdrawn due to errors, and corrected in 1838 by A Catalog of Circumpolar Stars, Reduced to January 1, 1810, edited by G. Biddell Airy. *TIS

1914 John Henry Poynting (9 Sep 1852; 30 Mar 1914)British physicist who introduced a theorem (1884-85) that assigns a value to the rate of flow of electromagnetic energy known as the Poynting vector, introduced in his paper On the Transfer of Energy in the Electromagnetic Field (1884). In this he showed that the flow of energy at a point can be expressed by a simple formula in terms of the electric and magnetic forces at that point. He determined the mean density of the Earth (1891) and made a determination of the gravitational constant (1893) using accurate torsion balances. He was also the first to suggest, in 1903, the existence of the effect of radiation from the Sun that causes smaller particles in orbit about the Sun to spiral close and eventually plunge in.*TIS

1944 Sir Charles Vernon Boys (15 Mar 1855; 30 Mar 1944 at age 88) English physicist and inventor of sensitive instruments. He graduated in mining and metallurgy, self-taught in a wide knowledge of geometrical methods. In 1881, he invented the integraph, a machine for drawing the antiderivative of a function. Boys is known particularly for his utilization of the torsion of quartz fibres in the measurement of minute forces, enabling him to elaborate (1895) on Henry Cavendish's experiment to improve the values obtained for the Newtonian gravitational constant. He also invented an improved automatic recording calorimeter for testing manufactured gas (1905) and high-speed cameras to photograph rapidly moving objects, such as bullets and lightning discharges. Upon retirement in 1939, he grew weeds.*TIS

1954 Fritz Wolfgang London (7 Mar 1900; 30 Mar 1954 at age 53) German-American physicist who, with Walter Heitler, devised the first quantum mechanical treatment of the hydrogen molecule, while working with Erwin Schrödinger at the University of Zurich. In a seminal paper (1927), they developed a wave equation for the hydrogen molecule with which it was possible to calculate approximate values of the molecule's ionization potential, heat of dissociation, and other constants. These predicted values were reasonably consistent with empirical values obtained by spectroscopic and chemical means. This theory of the chemical binding of homopolar molecules is considered one of the most important advances in modern chemistry. The approach is later called the valence-bond theory. *TIS

1995 John Lighton Synge (March 23, 1897–March 30, 1995) was an Irish mathematician and physicist. Synge made outstanding contributions to different fields of work including classical mechanics, general mechanics and geometrical optics, gas dynamics, hydrodynamics, elasticity, electrical networks, mathematical methods, differential geometry, and Einstein's theory of relativity. He studied an extensive range of mathematical physics problems, but his best known work revolved around using geometrical methods in general relativity.
He was one of the first physicists to seriously study the interior of a black hole, and is sometimes credited with anticipating the discovery of the structure of the Schwarzschild vacuum (a black hole).
He also created the game of Vish in which players compete to find circularity (vicious circles) in dictionary definitions. *Wik

2000 George Keith Batchelor FRS (8 March 1920 – 30 March 2000) was an Australian applied mathematician and fluid dynamicist. He was for many years the Professor of Applied Mathematics in the University of Cambridge, and was founding head of the Department of Applied Mathematics and Theoretical Physics (DAMTP). In 1956 he founded the influential Journal of Fluid Mechanics which he edited for some forty years. Prior to Cambridge he studied in Melbourne High School.
As an applied mathematician (and for some years at Cambridge a co-worker with Sir Geoffrey Taylor in the field of turbulent flow), he was a keen advocate of the need for physical understanding and sound experimental basis.
His An Introduction to Fluid Dynamics (CUP, 1967) is still considered a classic of the subject, and has been re-issued in the Cambridge Mathematical Library series, following strong current demand. Unusual for an 'elementary' textbook of that era, it presented a treatment in which the properties of a real viscous fluid were fully emphasized. He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1959.*Wik

2010 Jaime Alfonso Escalante Gutierrez (December 31, 1930 — March 30, 2010) was a Bolivian educator well-known for teaching students calculus from 1974 to 1991 at Garfield High School, East Los Angeles, California. Escalante was the subject of the 1988 film Stand and Deliver, in which he is portrayed by Edward James Olmos.*Wik

Friday, 29 March 2013

On This Day in Math - March 29

von Mädler Map of Moon, *www.RareMaps.com

Natural selection is a mechanism for generating an exceedingly high degree of improbability.
~R. A. Fisher

The 88th day of the year; 88² = 7744, it is one of only 5 numbers known whose square has no isolated digits. (Can you find the others?) [Thanks to Danny Whittaker @nemoyatpeace for a correction on this.]
88 is also a chance to introduce a new word (new for me). 88 is strobogrammatic, a number that is the same when it is rotated 180^o about its center... 69 is another example. If they make a different number when rotated, they are called invertible (109 becomes 601 for example). *Prime Curios

EVENTS

1796 Gauss achieved the construction of the 17-gon and a week later he would obtain his first proof of the quadratic reciprocity law. These two accomplishments mark the emergence from the ingenious manipulations of his youth, to the polished proofs of the mature mathematician. *Merzbach, An Early Version of Guass' Disquisitiones Arithmeticae, Mathematical Perspectives Academic Press 1981


first image obtained by NASA’s Dawn spacecraft	.

In 1807, Vesta 4, the only asteroid visible to the naked eye, thus the brightest on record, was first observed by the amateur astronomer Heinrich Wilhelm Olbers from Bremen. Vesta is a main belt asteroid with a diameter of 525-km and a rotation period of 5.34 hours. Pictures taken by the Hubble Space Telescope in 1995 show Vesta's complex surface, with a geology similar to that of terrestrial worlds - such as Earth or Mars - a surprisingly diverse world with an exposed mantle, ancient lava flows and impact basins. Though no bigger than the state of Arizona, it once had a molten interior. This contradicts conventional ideas that asteroids essentially are cold, rocky fragments left behind from the early days of planetary formation. *TIS Since the discovery of Ceres in 1801, and the asteroid Pallas in 1802, he had corresponded and became close friends with Gauss. For that reason he allowed Gauss to name the new "planet".

1933 Italy issued the world’s ﬁrst postage stamp portraying Galileo. [Scott #D16] *VFR
Galileo Galilei (1564–1642) made his first appearance on this stamp in 1933 for use in pneumatic postal systems (hence the wording “Posta Pneumatica” on the stamp). Pneumatic post involved placing letters in canisters which were then shot along pipes by compressed air from one Post Office to another. Pneumatic postal systems were set up in several European and American cities, including Rome, Naples, and Milan. Italy was the only country to issue stamps specifically for pneumatic postal use. Two of the designs showed Galileo – this one and a modified version with different face value and colour issued in 1945. The portrait is based on one by Justus Sustermans painted in 1636 when Galileo was aged 72. *Ian Ridpath, World's Oldest Astro Stamps page.

1989 Pixar Wins Academy Award for "Tin Toy":
Pixar wins an Academy Award for "Tin Toy," the first entirely computer-animated work to win in the best animated short film category. Pixar, now a division of Disney, continued its success with a string of shorts and the first entirely computer-animated feature-length film, the best-selling "Toy Story." *CHM

BIRTHS

1794 Johann Heinrich von Mädler (29 May 1794, 14 Mar 1874 at age 79) German astronomer who (with Wilhelm Beer) published the most complete map of the Moon of the time, Mappa Selenographica, 4 vol. (1834-36). It was the first lunar map to be divided into quadrants, and it remained unsurpassed in its detail until J.F. Julius Schmidt's map of 1878. Mädler and Beer also published the first systematic chart of the surface features of the planet Mars (1830). *TIS

1807 Heinrich Wilhelm Olbers discovers the Minor Planet 4 Vesta, one of the largest asteroids in the Solar System, with a mean diameter of 525 kilometres (326 mi). It is named after Vesta, the virgin goddess of home and hearth from Roman mythology. *wik

1825 Francesco Faà di Bruno (29 March 1825–27 March 1888) was an Italian mathematician and priest, born at Alessandria. He was of noble birth, and held, at one time, the rank of captain-of-staff in the Sardinian Army. He is the eponym of Faà di Bruno's formula. In 1988 he was beatified by Pope John Paul II. Today, he is best known for Faà di Bruno's formula on derivatives of composite functions, although it is now certain that the priority in its discovery and use is of Louis François Antoine Arbogast: Faà di Bruno should be only credited for the determinant form of this formula. However, his work is mainly related to elimination theory and to the theory of elliptic functions.
He was the author of about forty original articles published in the "Journal de Mathématiques" (edited by Joseph Liouville), Crelle's Journal, "American Journal of Mathematics" (Johns Hopkins University), "Annali di Tortolini", "Les Mondes", "Comptes rendus de l'Académie des sciences", etc.*Wik

1830 Thomas Bond Sprague (29 March 1830 in London, England - 29 Nov 1920 in Edinburgh, Scotland) studied at Cambridge and went on to become the most important actuary of the late 19th Century. He wrote more than 100 papers including many in the Proceedings of the EMS. *SAU

1873 Tullio Levi-Civita (29 Mar 1873, 29 Dec 1941) Italian mathematician who was one of the founders of absolute differential calculus (tensor analysis) which had applications to the theory of relativity. In 1887, he published a famous paper in which he developed the calculus of tensors. In 1900 he published, jointly with Ricci, the theory of tensors Méthodes de calcul differential absolu et leures applications in a form which was used by Einstein 15 years later. Weyl also used Levi-Civita's ideas to produce a unified theory of gravitation and electromagnetism. In addition to the important contributions his work made in the theory of relativity, Levi-Civita produced a series of papers treating elegantly the problem of a static gravitational field. *TIS

1890 Sir Harold Spencer Jones (29 Mar 1890, 3 Nov 1960) English astronomer who was 10th astronomer royal of England (1933–55). His work was devoted to fundamental positional astronomy. While HM Astronomer at the Cape of Good Hope, he worked on poper motions and parallaxes. Later he showed that small residuals in the apparent motions of the planets are due to the irregular rotation of the earth. He led in the worldwide effort to determine the distance to the sun by triangulating the distance of the asteroid Eros when it passed near the earth in 1930-31. Spencer Jones also improved timekeeping and knowledge of the Earth’s rotation. After WW II he supervised the move of the Royal Observatory to Herstmonceux, where it was renamed the Royal Greenwich Observatory.*TIS

1893 Jason John Nassau (29 March 1893 in Smyrna, (now Izmir) Turkey - 11 May 1965 in Cleveland, Ohio, USA) was an American astronomer.
He performed his doctoral studies at Syracuse, and gained his Ph.D. mathematics in 1920. (His thesis was Some Theorems in Alternants.) He then became an assistant professor at the Case Institute of Technology in 1921, teaching astronomy. He continued to instruct at that institution, becoming the University's first chair of astronomy from 1924 until 1959 and chairman of the graduate division from 1936 until 1940. After 1959 he was professor emeritus.
From 1924 until 1959 he was also the director of the Case Western Reserve University (CWRU) Warner and Swasey Observatory in Cleveland, Ohio. He was a pioneer in the study of galactic structure. He also discovered a new star cluster, co-discovered 2 novae in 1961, and developed a technique of studying the distribution of red (M-class or cooler) stars.*Wik

1896 Wilhelm Friedrich Ackermann (29 March 1896 – 24 December 1962) was a German mathematician best known for the Ackermann function, an important example in the theory of computation.*Wik

1912 Martin Eichler (29 March 1912 – 7 October 1992) was a German number theorist. He received his Ph.D. from the Martin Luther University of Halle-Wittenberg in 1936.
Eichler once stated that there were five fundamental operations of mathematics: addition, subtraction, multiplication, division, and modular forms. He is linked with Goro Shimura in the development of a method to construct elliptic curves from certain modular forms. The converse notion that every elliptic curve has a corresponding modular form would later be the key to the proof of Fermat's last theorem.*Wik

1912 Caius Jacob (29 March 1912 , Arad - 6 February 1992 , Bucharest ) was a Romanian mathematician and member of the Romanian Academy. He made contributions in the fields of fluid mechanics and mathematical analysis , in particular vigilance in plane movements of incompressible fluids, speeds of movement at subsonic and supersonic , approximate solutions in gas dynamics and the old problem of potential theory. His most important publishing was Mathematical introduction to the mechanics of fluids. *Wik

1941 Joseph Hooton Taylor, Jr. (March 29, 1941, ) is an American astrophysicist and Nobel Prize in Physics laureate for his discovery with Russell Alan Hulse of a "new type of pulsar, a discovery that has opened up new possibilities for the study of gravitation." *Wi

DEATHS

1772 Emanuel Swedenborg (29 Jan 1688; 29 Mar 1772) Swedish scientist, philosopher and theologian. While young, he studied mathematics and the natural sciences in England and Europe. From Swedenborg's inventive and mechanical genius came his method of finding terrestrial longitude by the Moon, new methods of constructing docks and even tentative suggestions for the submarine and the airplane. Back in Sweden, he started (1715) that country's first scientific journal, Daedalus Hyperboreus. His book on algebra was the first in the Swedish language, and in 1721 he published a work on chemistry and physics. Swedenborg devoted 30 years to improving Sweden's metal-mining industries, while still publishing on cosmology, corpuscular philosophy, mathematics, and human sensory perceptions. *TIS

1873 Francesco Zantedeschi (born 1797, 29 Mar 1873) Italian priest and physicist, who published papers (1829, 1830) on the production of electric currents in closed circuits by the approach and withdrawal of a magnet, preceding Faraday's classic experiment of 1831. Studying the solar spectrum, Zantedeschi was among the first to recognize the marked absorption by the atmosphere of the red, yellow, and green light. Though not confirmed, he also thought he detected a magnetic action on steel needles by ultra-violet light (1838), at least suspecting a connection between light and magnetism many years before Clerk-Maxwell's announcement (1867) of the electromagnetic theory of light. He experimented on the repulsion of flames by a strong magnetic field.*TIS

1912 Robert Falcon Scott, CVO (6 June 1868 – c. 29 March 1912) was a Royal Navy officer and explorer who led two expeditions to the Antarctic regions: the Discovery Expedition, 1901–04, and the ill-fated Terra Nova Expedition, 1910–13. During this second venture, Scott led a party of five which reached the South Pole on 17 January 1912, only to find that they had been preceded by Roald Amundsen's Norwegian expedition. On their return journey, Scott and his four comrades all died from a combination of exhaustion, starvation and extreme cold. *Wik
Such events lead to interesting exchanges, such as this reply to a British VAT (Value added tax, sort of like sales tax in US) inquiry. The response below includes a certain dry charm common to the English.

*@JonCG

1944 Grace Chisholm Young (née Chisholm; 15 March 1868 – 29 March 1944) was an English mathematician. She was educated at Girton College, Cambridge, England and continued her studies at Göttingen University in Germany. Her early writings were published under the name of her husband, William Henry Young, and they collaborated on mathematical work throughout their lives. For her work on calculus (1914–16), she was awarded the Gamble Prize.
Her son, Laurence Chisholm Young, was also a prominent mathematician. One of her living granddaughters, Sylvia Wiegand (daughter of Laurence), is also a mathematician (and a past president of the Association for Women in Mathematics.)*Wik

1980 William Gemmell Cochran (15 July 1909, Rutherglen – 29 March 1980, Orleans, Massachusetts)In 1934 R A Fisher left Rothamsted Experimental Station to accept the Galton chair at University College, London and Frank Yates became head at Rothamsted. Cochran was offered the vacant post but he had not finished his doctoral course at Cambridge. Yates later wrote:-
... it was a measure of good sense that he accepted my argument that a PhD, even from Cambridge, was little evidence of research ability, and that Cambridge had at that time little to teach him in statistics that could not be much better learnt from practical work in a research institute.
Cochran accepted the post at Rothamsted where he worked for 5 years on experimental designs and sample survey techniques. During this time he worked closely with Yates. At this time he also had the chance to work with Fisher who was a frequent visitor at Rothamsted.
Cochran visited Iowa Statistical Laboratory in 1938, then he accepted a statistics post there in 1939. His task was to develop the graduate programe in statistics within the Mathematics Department. In 1943 he joined Wilks research team at Princeton.
At Princeton he was involved in war work examining probabilities of hits in naval warfare. By 1945 he was working on bombing raid strategies.
He joined the newly created North Carolina Institute of Statistics in 1946, again to develop the graduate programe in statistics. From 1949 until 1957 he was at Johns Hopkins University in the chair of biostatistics. Here he was more involved in medical applications of statistics rather than the agricultural application he had studied earlier.
From 1957 until he retired in 1976 Cochran was at Harvard. His initial task was to help set up a statistics department, something which he had a great deal of experience with by this time. He had almost become a professional at starting statistics within universities in the USA. *SAU

1983 Sir Maurice George Kendall, FBA (6 September 1907 – 29 March 1983) was a British statistician, widely known for his contribution to statistics. The Kendall tau rank correlation is named after him.*Wik He was involved in developing one of the first mechanical devices to produce (pseudo-) random digits, eventually leading to a 100,000-random-digit set commonly used until RAND's (once well-known) "A Million Random Digits With 100,000 Normal Deviates" in 1955.
Kendall was Professor of Statistics at the London School of Economics from 1949 to 1961. His main work in statistics involved k-statistics, time series, and rank-correlation methods, including developing the Kendall's tau stat, which eventually led to a monograph on Rank Correlation in 1948. He was also involved in several large sample-survey projects. For many, what Kendall is best known for is his set of books titled The Advanced Theory of Statistics (ATS), with Volume I first appearing in 1943 and Volume II in 1946. Kendall later completed a
rewriting of ATS, which appeared in three volumes in 1966, which were updated by collaborator Alan Stuart and Keith Ord after Kendall's death, appearing now as "Kendall's Advanced Theory of Statistics". *David Bee

1999 Boris A. Kordemsky ( 23 May 1907 – 29 March, 1999) was a Russian mathematician and educator. He is best known for his popular science books and mathematical puzzles. He is the author of over 70 books and popular mathematics articles.
Kordemsky received Ph.D. in education in 1956 and taught mathematics at several Moscow colleges.
He is probably the best-selling author of math puzzle books in the history of the world. Just one of his books, Matematicheskaya Smekalka (or, Mathematical Quick-Wits), sold more than a million copies in the Soviet Union/Russia alone, and it has been translated into many languages. By exciting millions of people in mathematical problems over five decades, he influenced generations of solvers both at home and abroad. *Age of Puzzles, by Will Shortz and Serhiy Grabarchuk (mostly)

1908 John Bardeen (23 May 1908; 30 Jan 1991 at age 82) American physicist who was cowinner of the Nobel Prize for Physics in both 1956 and 1972. He shared the 1956 prize with William B. Shockley and Walter H. Brattain for their joint invention of the transistor. With Leon N. Cooper and John R. Schrieffer he was awarded the 1972 prize for development of the theory of superconductors, usually called the BCS-theory (after the initials of their names). *TIS

Thursday, 28 March 2013

On This Day in Math - March 28

*George W. Hart, Sculpture

Factoring a quadratic becomes confused with genuine mathematical talent.
~Yitz Herstein

The 87th day of the year; the sum of the squares of the first four primes is 87.

EVENTS

In 1747, the fascination with electricity upon reaching the American colonies was the subject of Benjamin Franklin's first of the famous series of letters in which he described his experiments on electricity to Peter Collinson, Esq., of London. He thanked Collison for his “kind present of an electric tube with directions for using it” with which he and others did electrical experiments. “For my own part I never was before engaged in any study that so totally engrossed my attention and my time as this has lately done; for what with making experiments when I can be alone, and repeating them to my friends and acquaintances, who, from the novelty of the thing, come continually in crowds to see them, I have, during some months past, had little leisure for anything else.”*TIS

1802 Olbers, while observing the constellation Virgo, had observed a "star" of the seventh-magnitude not found on the star charts. Over the following week he would observe the motion and determined that it was a planet. In early April he sent the data to Gauss to compute the orbit. On the 18th of April, Gauss computed the orbit in only three hours, placing the orbit between Mars and Jupitor. Olbers named the new planetoid Pallas, and predicted there would be others found in the same area. John Herschel dismissed this speculation as "dreams in which astronomers... indulge" but over 1000 such planetoids have been observed. *Dunnington, Gray, & Dohse; Carl Friedrich Gauss: Titan of Science

1809 Gauss ﬁnished work on his Theoria Motus. It explains his methods of computing planetary orbits using least squares. [Springer’s 1985 Statistics Calendar] *VFR

In 1946, the Census Bureau and the National Bureau of Standards met to discuss the purchase of a computer. The agencies agreed to buy UNIVAC, the world's first general all-purpose business computer, from Presper Eckert and John Mauchly for a mere $225,000. Unfortunately, UNIVAC cost far more than that to develop. Eckert and Mauchly's venture floundered as the company continued to build and program UNIVACs for far less than the development cost. Eventually, the company was purchased by Remington Rand. *TIS

1949 The phrase "Big Bang" is created. Shortly after 6:30 am GMT on BBC's The Third Program, Fred Hoyle used the term in describing theories that contrasted with his own "continuous creation" model for the Universe. "...based on a theory that all the matter in the universe was created in one big bang ... ". *Mario Livio, Brilliant Blunders

1959 Germany issued a stamp commemorating the 400th anniversary of the death of Adam Riese [Scott #799] *VFR I understand that the German expression "nach Adam Riese", which is still used today. It means "according to Adam Ries" and it is used in saying something is exactly correct.

In 2006, a substantial "lost" book of manuscripts by Robert Hooke in his own handwriting was bought for the Royal Society by donations of nearly £1 million. The book was just minutes before going on the auction block when a last-minute purchase agreement was made and kept the precious document in Britain. Hooke is now often overlooked, except for his law of elasticity, although in his time, he was a prolific English scientist and contributed greatly to planning the rebuilding of London after the Great Fire of 1666. The document of more than 520 pages of manuscripts included the minutes of the Royal Society from 1661-82. It had been found in a cupboard in a private house by an antiques expert there to value other items. *TIS

2012 First day of the baseball season. The exact width of home plate is irrational: 12 times the square root of two. History: The plate was originally a circle of diameter one, then a square of the same size(!), which, by mistake was a one-by-one square. Then the corners were filled in to make the current pentagonal plate. *VFR Home plate is an irregular pentagon. The front is 17 inches wide, faces the pitcher, and defines the width of the strike zone. Then parallel sides 8.5 inches long connect to the foul lines. Finally 12 inch sides run down the foul lines, connecting where the foul lines meet.
It can be thought of as a 17 inch square with the parts that would be in foul territory removed. The figure described in the official rules of MLB, as well as above, is technically impossible. One of two things must be true to make it possible:

the parallel sides of 8.5" are in reality approximately 8.5295" (the square root of 71.75)
or
the 12" sides that run along the foul lines are approximately 12.0208" (square root of 144.5)

The latter is more likely the case, as it would produce the angle measurements of 90º at the base and rear point and 135º at the sides.

BIRTHS

1847 Gyula Farkas (28 March 1847 in Sárosd, Fejér County, Hungary - 27 Dec 1930 in Pestszentlorinc, Hungary) He is remembered for Farkas theorem which is used in linear programming and also for his work on linear inequalities. In 1881 Gyula Farkas published a paper on Farkas Bolyai's iterative solution to the trinomial equation, making a careful study of the convergence of the algorithm. In a paper published three years later, Farkas examined the convergence of more general iterative methods. He also made major contributions to applied mathematics and physics, particularly in the areas of mechanical equilibrium, thermodynamics, and electrodynamics.*SAU

1923 Israel Nathan Herstein (March 28, 1923, Lublin, Poland – February 9, 1988, Chicago, Illinois) was a mathematician, appointed as professor at the University of Chicago in 1951. He worked on a variety of areas of algebra, including ring theory, with over 100 research papers and over a dozen books.
He is known for his lucid style of writing, as exemplified by the classic and widely influential Topics in Algebra, an undergraduate introduction to abstract algebra that was published in 1964, which dominated the field for 20 years. A more advanced classic text is his Noncommutative Rings in the Carus Mathematical Monographs series. His primary interest was in noncommutative ring theory, but he also wrote papers on finite groups, linear algebra, and mathematical economics.*Wik

1928 Alexander Grothendieck (28 Mar 1928) In 1966 he won a Fields Medal for his work in algebraic geometry. He introduced the idea of K-theory and revolutionized homological algebra. *VFR

DEATHS

1678 Claude François Milliet Dechales (1621 in Chambéry, France - 28 March 1678 in Turin, Italy) Dechales is best remembered for Cursus seu mundus mathematicus published in Lyons in 1674, a complete course of mathematics. Topics covered in this wide ranging work included practical geometry, mechanics, statics, magnetism and optics as well as topics outwith the usual topics of mathematics such as geography, architecture, astronomy, natural philosophy and music. In 1678 he published in Lausanne his edition of Euclid, The Elements of Euclid Explained in a New but Most Easy Method: Together with the Use of Every Proposition through All Parts of the Mathematics, written in French by That Most Excellent Mathematician, F Claude Francis Milliet Dechales of the Society of Jesus. This work covers Books 1 to 6, together with Books 11 and 12, of Euclid's Elements. A second edition was published in 1683, then an edition revised by Ozanam was published in Paris in 1753. An English translation was published in London by M Gillyflower and W Freeman, the translation being by Reeve Williams. A second edition of this English translation appeared in 1696. Schaap writes, "Dechales's separate edition of Euclid, long a favourite in France and elsewhere on the Continent, never became popular in England." *SAU

1794 Marie Jean Antoine Nicolas de Caritat, marquis de Condorcet (17 September 1743 – 28 March 1794), known as Nicolas de Condorcet, was a French philosopher, mathematician, and early political scientist whose Condorcet method in voting tally selects the candidate who would beat each of the other candidates in a run-off election. Unlike many of his contemporaries, he advocated a liberal economy, free and equal public education, constitutionalism, and equal rights for women and people of all races. His ideas and writings were said to embody the ideals of the Age of Enlightenment and rationalism, and remain influential to this day. He died a mysterious death in prison after a period of being a fugitive from French Revolutionary authorities.*Wik
Condorcet committed suicide by poisoning while in jail so that the republican terrorists could not take him to Paris. *VFR (The St Andrews site has the date of his death one day later.)

1840 Simon Antoine Jean Lhuilier (24 April 1750 in Geneva, Switzerland - 28 March 1840 in Geneva, Switzerland) His work on Euler's polyhedra formula, and exceptions to that formula, were important in the development of topology. Lhuilier also corrected Euler's solution of the Königsberg bridge problem. He also wrote four important articles on probability during the years 1796 and 1797. His most famous pupil was Charles-François Sturm who studied under Lhuilier during the last few years of his career in Geneva. *SAU

1850 Bernt Michael Holmboe (23 March 1795 – 28 March 1850) was a Norwegian mathematician. Holmboe was hired as a mathematics teacher at the Christiania Cathedral School in 1818, where he met the future renowned mathematician Niels Henrik Abel. Holmboe's lasting impact on mathematics worldwide has been said to be his tutoring of Abel, both in school and privately. The two became friends and remained so until Abel's early death. Holmboe moved to the Royal Frederick University in 1826, where he worked until his own death in 1850.
Holmboe's significant impact on mathematics in the fledgling Norway was his textbook in two volumes for secondary schools. It was widely used, but faced competition from Christopher Hansteen's alternative offering, sparking what may have been Norway's first debate about school textbooks. *Wik

1874 Peter Andreas Hansen (8 Dec 1795; 28 Mar 1874) Danish astronomer whose most important work was the improvement of the theories and tables of the orbits of the principal bodies in the solar system. At Altona observatory he assisted in measuring the arc of meridian (1821). He became the director (1825) of Seeberg observatory, which was removed to Gotha in a new observatory built for him (1857). He worked on theoretical geodesy, optics, and the theory of probability. The work in celestial mechanics for which he is best known are his theories of motion for comets, minor planets, moon and his lunar tables (1857) which were in use until 1923. He published his lunar theory in Fundamenta ("Foundation") in 1838, and Darlegung ("Explanation") in 1862-64.*TIS

1950 Ernst David Hellinger (0 Sept 1883 in Striegau, Silesia, Germany (now Strzegom, Poland) - 28 March 1950 in Chicago, Illinois, USA) introduced a new type of integral: the Hellinger integral . Jointly with Hilbert he produced an important theory of forms. From 1907 to 1909 he was an assistant at Göttingen and, during this time, he ".. edited Hilbert's lecture notes and Felix Klein's influential Elementarmathematik vom höheren Standpunkte aus (Berlin, 1925) which was translated into English (New York, 1932). Years later the story is told that,

Shortly after his arrival at Northwestern, one of the professors in describing Northwest's mathematics program to him remarked that in the honours course Felix Klein's 'Elementary mathematics from an advanced standpoint' was used as a text and "perhaps Hellinger was familiar with it". At this Hellinger ... replied "familiar with it, I wrote it!".

*SAU

Wednesday, 27 March 2013

On This Day in Math - March 27

Charles Minard's Napoleon's March,

Modern science, as training the mind to an exact and impartial analysis of facts, is an education specially fitted to promote citizenship.
~Karl Pearson

The 86th day of the year; 86 is conjectured to be the largest number n such that 2ⁿ (in decimal) doesn't contain a 0. *Tanya Khovanova, Number Gossip

EVENTS

In 1827, Charles Darwin, aged 18, submitted his first report of an original scientific discovery to the Plinian Society in Edinburgh, Scotland. Darwin had discovered several things about the biology of tiny marine organisms found along the Scottish coast. *TIS

1958 The ﬁrst national high-school mathematics competition in the U.S. was held. Since 1983 it has been known as the American High School Mathematics Examination (AHSME). [The College Mathematics Journal, 16 (1985), p. 331] *VFR

1976 20-Year Old Bill Gates Gives Opening Address to Hobbyists:
Bill Gates gives the opening address at the First Annual World Altair Computer Convention in Albuquerque, N.M. MITS, the company that developed the Altair, had set up shop in the southwestern city to develop its kit computer, which was a hit among hobbyists after it graced the cover of "Popular Mechanics" magazine. Gates, then a 20-year-old erstwhile Harvard student, had helped develop the form of BASIC sold with the Altair. *CHM

BIRTHS

1781 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

1824 Johann Wilhelm Hittorf (27 Mar 1824, 28 Nov 1914) German physicist who was a pioneer in electrochemical research. His early investigations were on the allotropes (different physical forms) of phosphorus and selenium. He was the first to compute the electricity- carrying capacity of charged atoms and molecules (ions), an important factor in understanding electrochemical reactions. He investigated the migration of ions during electrolysis (1853-59), developed expressions for and measured transport numbers. In 1869, he published his laws governing the migration of ions. For his studies of electrical phenomena in rarefied gases, the Hittorf tube has been named for him. Hittorf determined a number of properties of cathode rays, including (before Crookes) the deflection of the rays by a magnet. *TIS

1845 Wilhelm Conrad Röntgen (27 Mar 1845 - 10 Feb 1923 at age 77) was a German physicist who discovered the highly penetrating form of radiation that became known as X-rays on 8 Nov 1895. He received the first Nobel Prize for Physics (1901), “in recognition of the extraordinary services he has rendered by the discovery of the remarkable rays subsequently named after him.” This high-energy radiation, though first called Röngen rays, became known as X-rays. His discovery initiated revolutionary improvements in making medical diagnoses and enabled many new advances in modern physics. *TIS "In 1901 he became the ﬁrst physicist to receive a Nobel prize." *VFR

1855 Sir Alfred Ewing (27 Mar 1855, 7 Jan 1935) was a Scottish physicist who discovered and named hysteresis (1881), the resistance of magnetic materials to change in magnetic force. Ewing was born and educated in Dundee and studied engineering on a scholarship at Edinburgh University. He helped Sir William Thomson, later Lord Kelvin in a cable laying project. In 1878 he became professor of Mechanical Engineering and Physics at Tokyo University, where he devised instruments for measuring earthquakes. In 1903 he moved to the Admiralty as head of education and training, where during WW I, he and his staff took on the task of deciphering coded messages. *TIS

1857 Karl Pearson (27 Mar 1857; 27 Apr 1936 at age 79) English mathematician who was one of the founders of modern statistics. His lectures as professor of geometry evolved into The Grammar of Science (1892), his most widely read book and a classic in the philosophy of science. Stimulated by the evolutionary writings of Francis Galton and a personal friendship with Walter F.R. Weldon, Pearson became immersed in the problem of applying statistics to biological problems of heredity and evolution. The methods he developed are essential to every serious application of statistics. From 1893 to 1912 he wrote a series of 18 papers entitled Mathematical Contributions to the Theory of Evolution, which contained much of his most valuable work, including the chi-square test of statistical significance. *TIS

1897 Douglas Rayner Hartree PhD, FRS (27 March 1897 – 12 February 1958) was an English mathematician and physicist most famous for the development of numerical analysis and its application to the Hartree-Fock equations of atomic physics and the construction of the meccano differential analyser. *Wik

1905 László Kalmár (27 March 1905 in Edde (N of Kaposvar), Hungary - 2 Aug 1976 in Mátraháza, Hungary) worked on mathematical logic and theoretical computer science. He was ackowledged as the leader of Hungarian mathematical logic. *SAU

1928 Alexander Grothendieck In 1966 he won a Fields Medal for his work in algebraic geometry. He introduced the idea of K-theory and revolutionized homological algebra. *VFR

DEATHS

1850 Wilhelm Beer (4 Jan 1797, 27 Mar 1850 at age 53) German banker and amateur astronomer who owned a fine Fraunhofer refractor which he used in his own a private observatory. He worked jointly with Johann Heinrich von Mädler, to produce the first large-scale moon map to be based on precise micrometric measurements. Their four-year effort was published as Mappa Selenographica (1836). This fine lithographed map provided the most complete details of the Moon's surface in the first half of the 19th century. It was the first lunar map divided in quadrants, and recorded the Moon's face in great detail detail. It was drawn to a scale of scale of just over 38 inches to the moon's diameter. Mädler originated a convention for naming minor craters with Roman letters appended to the name of the nearest large crater (ex. Egede A,B, and C).

1888 Francesco Faà di Bruno (29 March 1825–27 March 1888) was an Italian mathematician and priest, born at Alessandria. He was of noble birth,[1] and held, at one time, the rank of captain-of-staff in the Sardinian Army. He is the eponym of Faà di Bruno's formula. In 1988 he was beatified by Pope John Paul II. Today, he is best known for Faà di Bruno's formula on derivatives of composite functions, although it is now certain that the priority in its discovery and use is of Louis François Antoine Arbogast: Faà di Bruno should be only credited for the determinant form of this formula. However, his work is mainly related to elimination theory and to the theory of elliptic functions.
He was the author of about forty original articles published in the "Journal de Mathématiques" (edited by Joseph Liouville), Crelle's Journal, "American Journal of Mathematics" (Johns Hopkins University), "Annali di Tortolini", "Les Mondes", "Comptes rendus de l'Académie des sciences", etc.*Wik

1923 Sir James Dewar (20 Sep 1842; 27 Mar 1923) British chemist and physicist. Blurring the line between physics and chemistry, he advanced the research frontier in several fields at the turn of the century, and gave dazzling lectures. His study of low-temperature phenomena entailed making an insulating double-walled flask of his own design by creating a vacuum between the two silvered layers of steel or glass (1892). This Dewar flask that has been named for him led to the domestic Thermos bottle. In June 1897, The Scientific American reported that "Dewar has just succeeded in liquefying fluorine gas at a temperature of -185 degrees C." He obtained liquid hydrogen in 1898. Dewar also invented cordite, the first smokeless powder.*TIS

1925 Carl Gottfried Neumann,(7 May 1832 in Königsberg, Germany (now Kaliningrad, Russia) - 27 March 1925 in Leipzig, Germany) He worked on a wide range of topics in applied mathematics such as mathematical physics, potential theory and electrodynamics. He also made important pure mathematical contributions. He studied the order of connectivity of Riemann surfaces.
During the 1860s Neumann wrote papers on the Dirichlet principle and the 'logarithmic potential', a term he coined. In 1890 Émile Picard used Neumann's results to develop his method of successive approximation which he used to give existence proofs for the solutions of partial differential equations.*SAU

1929 Samuil Shatunovsky (25 March 1859 – 27 March 1929) was a Russian mathematician. focused on several topics in mathematical analysis and algebra, such as group theory, number theory and geometry. Independently from Hilbert, he developed a similar axiomatic theory and applied it in geometry, algebra, Galois theory and analysis.[1] However, most of his activity was devoted to teaching at Odessa University and writing associated books and study materials.*Wik

1972

Maurits Cornelius Escher (17 June 1898 in Leeuwarden, Netherlands - 27 March 1972 in Laren, Netherlands) an artist whose works have included a considerable mathematical content. He is known for his often mathematically inspired woodcuts, lithographs, and mezzotints. These feature impossible constructions, explorations of infinity, architecture, and tessellations. *Wik

Tuesday, 26 March 2013

On This Day in Math - March 26

“Have you seen the world go around?"

Every human activity, good or bad, except mathematics, must come to an end.
~Paul Erdos

The 85th day of the year; 85 is the largest number for which the sum of 1² + 2²+3²+4²+...+n²= 1+2+3+4+.... +M for some M, can you find that M? 85 is the largest such n, but can you find some solutions n,M that are smaller?
and a bonus I found at the Prime Curios web site, (85¹¹ - 85)/11 ± 1 are twin primes. (too cool)

85 is the second smallest n such that n, n+1 and n+2 are products of two primes. *Don S McDonald

EVENTS

1619 Descartes reported (to Beekman) his ﬁrst glimpse of “an entirely new science,” which was to become his analytic geometry (published 1637). [DSB 4, 51]*VFR

1760 Guillaume le Gentil sailed from France planning to view the transit of Venus the following year from the east coast of India. Monsoons blew his ship off course, and on the day of the transit, he was becalmed in the Indian Ocean, unable to make any useful observations. Determined to redeem his expedition he books passage to India and builds an observatory to await the 1769 transit in Pondecherry. "The sky remained marvelously clear throughout May, only to cloud over on June 4, the morning of the transit, then clear again as soon as the transit was over."
His ordeal of a decade was not yet over. Stricken with dysentary he had to stay nine months more in India, and then booked passage on a Spanish warship. The ship lost its mast in a hurricane off the Cape of Good Hope, and finally limped into Cadiz. Le Gentil set out across the Pyranees and returned to Paris after a total absence of eleven years, six months, and thirteen days, only to find that he had been presumed dead and his estate divided among his heirs. *Timothy Ferris, Coming of Age in the Milky Way (Thony Christie, The Renaissance Mathematicus, has a more detailed, and perhaps somewhat more accurate, version of Guillame's great adventure. See it here

1851 French Science reporter Terrien wrote in “le National, “Have you seen the world go around? Would you like to see it rotate? Go to the Parthenon on Thursday…the experiment devised by M. Leon Foucault is carried out there, in the presence of the public, under the finest conditions in the world.” *Amir D Aczel, Pendulum, pg 152
Foucault’s most famous pendulum . He suspended a 28 kg brass-coated lead bob with a 67 meter long wire from the dome of the Panthéon, Paris. The plane of the pendulum's swing rotated clockwise 11° per hour, making a full circle in 32.7 hours. *Wik

In 1859, Lescarbault, a French medical doctor and amateur astronomer reported sighting a new planet in an orbit inside that of Mercury which he named Vulcan. He had seen a round black spot on the Sun with a transit time across the solar disk 4 hours 30 minutes. He sent this information and his calculations on the planet's movements to Jean LeVerrier, France's most famous astronomer. Le Verrier had already noticed that Mercury had deviated from its orbit. A gravitational pull from Vulcan would fit in nicely with what he was looking for. However, it was not consistently seen again and it is now believed to have been a "rogue asteroid" making a one-time pass close to the sun.*TIS (It was just pointed out to me by @Astroguyz,David Dickinson, that Leonard Nimoy, the actor who is best remembered for his role as the half-Vulcan character of Dr. Spock in the Star Trek series and films was also born on this day in 1931.)

1900 In 1900, the Roentgen Society of the United States was organised a meeting of doctors from nine states held in Dr. Herber Robarts' office in St. Louis. Dr. Robarts was founder and editor of the American X-Ray Journal, and had been active in radiology since exposing his first X-ray plates in Feb 1896. Robarts was elected as president of the new society and and Dr. J. Rudis-Jicinsky as secretary. They arranged to hold the first annual meeting at the Grand Central Palace in New York City on 13-14 Dec 1900. In 1901, it was renamed as the Roentgen Society of America to include Canadians. It was reorganised at the next annual meeting on 10-11 Dec 1902 as the American Roentgen Ray Society.*TIS

1936 The 200" Hale mirror was SHIPPED, it had been cast in 1934. Still a great video: *David Dickinson ‏@Astroguyz
The 200-inch (5.1 m) Hale Telescope (f/3.3) was the world's largest effective telescope for 45 years (1948 - 1993). It is still a workhorse of modern astronomy. It is used nightly for a wide range of astronomical studies. On average the weather allows for at least some data collection about 290 nights a year. *Caltech Astronomy

1985 Alexander's Star is a puzzle similar to the Rubik's Cube, in the shape of a great dodecahedron.
Alexander's Star was invented by Adam Alexander, an American mathematician, in 1982. It was patented on 26 March 1985, with US patent number 4,506,891, and sold by the Ideal Toy Company. It came in two varieties: painted surfaces or stickers. Since the design of the puzzle practically forces the stickers to peel with continual use, the painted variety is likely a later edition.

*Wik

1994, A picture was released showing the first moon discovered to be in orbit around an asteroid. The potato-shaped asteroid Ida and its newly-discovered moon, Dactyl was imaged by NASA's Galileo spacecraft, about 14 minutes before its closest approach to the asteroid on 28 Aug 1993. Ida appears to be about about 36 miles long and 14 miles wide. It shows numerous craters, including many degraded craters, indicating Ida's surface is older than previously thought. The tiny moon is about one mile (1.5-km) across. The names are derived from the Dactyli, a group of mythological beings who lived on Mount Ida, where the infant Zeus was hidden (and raised, in some accounts) by the nymph Ida and protected by the Dactyli.
2010 Crocheting Adventures with Hyperbolic Planes by Dr Daina Taimina has won the 2009 Diagram Prize, having received the majority of the public vote for the oddest titled book of the year at thebookseller.com. The first award was given in 1978 for Proceedings of the Second International Workshop on Nude Mice

BIRTHS

1753 Count Benjamin Thompson Rumford (26 Mar 1753, 21 Aug 1814) American-born British physicist, government administrator, and a founder of the Royal Institution of Great Britain, London. Because he was a Redcoat officer and an English spy during the American revolution, he moved into exile in England. Through his investigations of heat he became one of the first scientists to declare that heat is a form of motion rather than a material substance, as was popularly believed until the mid-19th century. Among his numerous scientific contributions are the development of a calorimeter and a photometer. He invented a double boiler, a kitchen stove and a drip coffee pot. *TIS
1773 Nathaniel Bowditch (26 Mar 1773, 16 Mar 1838 at age 65) Self-educated American mathematician and astronomer. He learned Latin to study Newton's Principia and later other languages to study mathematics in these languages. Between 1795 and 1799 he made four sea voyages and in 1802 he was in command of a merchant ship. He was author of the best book on navigation of his time, New American Practical Navigator (1802), and his translation (assisted by Benjamin Peirce) of Laplace's Mécanique céleste gave him an international reputation. Bowditch was the discoverer of the Bowditch curves (more often called Lisajous figures for their co-discoverer), which have important applications in astronomy and physics.*TIS Bowditch was a navigator on the Wilkes Expedition and an island in the Stork Archipelago in the South Pacific is named for him (and sometimes called Fakaofu) *TIS Nathaniel Bowditch acquired his knowledge of mathematics through self-study while apprenticed to a ship’s chandler. He is most noted for his translation of Laplace’s M´ecanique c´eleste. [DSB 2, 368] *VFR

1789 William C. Redfield (26 Mar 1789, 12 Feb 1857 at age 67) American meteorologist who observed the whirlwind character of tropical storms. Following a hurricane that struck New England on 3 Sep 1821, he noted that in central Connecticut trees had toppled toward the northwest, but in the opposite direction 80-km further west. He found that hurricanes are generated in a belt between the Equator and the tropics, then veer eastward when meeting westerly winds at about latitude 30ºN. In 1831, he published his evidence that storm winds whirl counterclockwise about a centre that moves in the normal direction of the prevailing winds. He also promoted railroads and steamships. He co-founded the American Association for the Advancement of Sciences and was president at its first meeting (Sep 1848).*TIS

1803 Sir John William Lubbock, (London, England, 26 March 1803 - Downe, Kent, England, 20 June 1865 )English astronomer and mathematician. He made a special study of tides and of the lunar theory and developed a method for calculating the orbits of comets and planets. In mathematics he applied the theory of probability to life insurance problems. He was a strong proponent of Continental mathematics and astronomy.
Lubbock, third Baron Lubbock, was born into a London banking family. After attending Eton, he moved to Trinity College, Cambridge, where he became a student of William Whewell.(it was at the request of Lubbock that Whewell created the term "biometry".) He excelled in mathematics and traveled to France and Italy to deepen his knowledge of the works of Pierre-Simon de Laplace and Joseph Lagrange. Entering his father’s banking firm as a junior partner, he devoted his free time to science.
Lubbock strongly supported Lord Brougham’s Society for the Diffusion of Useful Knowledge [SDUK], which produced scientific and technical works designed for the working class. His articles on tides for the Society’s publications resulted in a book, *An Elementary Treatise on the Tides, in 1839. *Biographical Encyclopedia of Astronomers

1821 Ernst Engel (26 Mar 1821, 8 Dec 1896) German statistician, the head of the Prussian Statistical Bureau (1860-82), known for the "Engel curve," or Engel's law, which states that the proportion of expenditure on food will fall as income rises, i.e. food is a necessary good. Engel's law applies to goods as a whole. Demand for food, clothing and shelter - and for most manufactured products - doesn't keep pace with increases in incomes. Engel curves are useful for separating the effect of income on demand from the effects of changes in relative prices. Engel also examined the relationship between the size of the Prussian rye harvest and the average price of rye over a number of years prior to 1860, probably the first empirical study of the relationship between price and supply. *TIS

1848 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

1862 Philbert Maurice d'Ocagne (26 March 1862 in Paris, France - 23 Sept 1938 in Le Havre, France) In 1891 he began publishing papers on nomography, the topic for which he is most remembered today. Nomography consists in the construction of graduated graphic tables, nomograms, or charts, representing formulas or equations to be solved, the solutions of which were provided by inspection of the tables. An advertisement for a colloquium at the Edinburgh Mathematical Society gave the following description of d'Ocagne's course:

It is now generally recognised that for most purposes the nomographic methods are superior to the older graphical methods of calculation. The introduction of some nomographic teaching in British Universities (and schools, for much of it is not too hard for schoolboys) is much to be desired.

*SAU
Nomographs are still used in wide areas of science and technology. The book below is an excellent coverage of the history and modern usage.

1875 Max Abraham (26 Mar 1875, 16 Nov 1922) German physicist whose life work was almost all related to Maxwell's theory. The text he wrote was the standard work on electrodynamics in Germany for a long time. Throughout his life, he remained strongly opposed to Einstein's Theory of Relativity, objecting to its postulates which he felt were contrary to classical common sense. He further held that the experimental evidence did not support that theory. In 1902, he had developed a theory of the electron in which he held that an electron was a perfectly rigid sphere with a charge distributed evenly over its surface. He also believed in the ether theory, thought that future astronomical data would validate it, and thus relativity was not in fact a good description of the real world. *TIS

1902 Marion Gray (26 March 1902, 16 Sept 1979) graduated from Edinburgh University and then went to Bryn Mawr College in the USA. She completed her doctorate there and returned to posts at Edinburgh and Imperial College London. She returned to the USA and worked for AT&T for the rest of her career. The Gray graph is named after her.*SAU The Gray graph is an undirected bipartite graph with 54 vertices and 81 edges. It is a cubic graph: every vertex touches exactly three edges. The Gray graph is interesting as the first known example of a cubic graph having the algebraic property of being edge but not vertex transitive *Wik

1903 Patrick du Val (March 26, 1903–January 22, 1987) was a British mathematician, known for his work on algebraic geometry, differential geometry, and general relativity. The concept of Du Val singularity of an algebraic surface is named after him. Du Val's early work before becoming a research student was on relativity, including a paper on the De Sitter model of the universe and Grassmann's tensor calculus. His doctorate was on algebraic geometry and in his thesis he generalised a result of Schoute. He worked on algebraic surfaces and later in his career became interested in elliptic functions.*Wik

1908 Theodore Samuel Motzkin (26 March 1908–15 December 1970) was an Israeli-American mathematician. Motzkin received his Ph.D. in 1934 from the University of Basel under the supervision of Alexander Ostrowski.
He was appointed at UCLA in 1950 and worked there until retirement.
The Motzkin transposition theorem, Motzkin numbers and the Fourier–Motzkin elimination are named after him. Motzkin first developed the "double description" algorithm of polyhedral combinatorics and computational geometry.[3] He was the first to prove the existence of principal ideal domains that are not Euclidean domains.
The quote "complete disorder is impossible," describing Ramsey theory is attributed to him. *Wik

1913 Paul Erdös (26 Mar 1913; 20 Sep 1996 at age 83) Hungarian mathematician, who was one of the century's top math experts and pioneered the fields of number theory and combinatorics. The type of mathematics he worked on were beautiful problems that were simple to understand, but notoriously difficult to solve. At age 20, he discovered a proof for a classic theorem of number theory that states that there is always at least one prime number between any positive integer and its double. In the 1930s, he studied in England and moved to the USA by the late 1930s when his Jewish origins made a return to Hungary impossible. Affected by McCarthyism in the 1950s, he spent much of the next ten years in Israel. Writing his many hundreds of papers made him one of history's most prolific mathematicians. *TIS His forte is posing and solving problems. One of his customs is to offer cash prizes for problems he poses. These awards range from $5 to $10,000 depending on how difficult he judges them to be. Erdos has written over 1,000 research papers, more than any other mathematician. The previous record was held by Arthur Cayley, who wrote 927. [Gallian, Contemporary Abstract Algebra, p 378]*VFR
McGill University Professor Willy Moser, a friend and collaborator of Erdos, tells of the "trial" of hosting Erdos. Once when Erdos was staying with him, Moser set up five dinners for him with five of erdos' old friends. Moser's wife pointed out that after the many times he had visited these homes and never brought a gift, perhaps Moser should remind him to bring candy or flowers. When he suggested the idea to Erdos, he thought it was a great idea and asked Moser, "Would you pick me up five boxes of chocolates?"

1922 Guido Stampacchia (March 26, 1922 - April 27, 1978) was a 20th century mathematician. Stampacchia was active in research and teaching throughout his career. He made key contributions to a number of fields, including calculus of variation and differential equations. In 1967 Stampacchia was elected President of the Unione Matematica Italiana. It was about this time that his research efforts shifted toward the emerging field of variational inequalities, which he modeled after boundary value problems for partial differential equations.
Stampacchia accepted the position of Professor Mathematical Analysis at the University of Rome in 1968 and returned to Pisa in 1970. He suffered a serious heart attack in early 1978 and died of heart arrest on April 27 of that year *Wik

1938 Sir Anthony James (Tony) Leggett (26 March 1938, ), has been a Professor of Physics at the University of Illinois at Urbana-Champaign since 1983.
Professor Leggett is widely recognized as a world leader in the theory of low-temperature physics, and his pioneering work on superfluidity was recognized by the 2003 Nobel Prize in Physics. He has shaped the theoretical understanding of normal and superfluid helium liquids and strongly coupled superfluids. He set directions for research in the quantum physics of macroscopic dissipative systems and use of condensed systems to test the foundations of quantum mechanics. *Wik

DEATHS

1609 John Dee (13 July 1527– *SAU gives 26 March 1609 in Mortlake, London, England) was an English mathematician, astronomer, astrologer, occultist, navigator, imperialist[4] and consultant to Queen Elizabeth I. He devoted much of his life to the study of alchemy, divination and Hermetic philosophy.
Dee straddled the worlds of science and magic just as they were becoming distinguishable. One of the most learned men of his age, he had been invited to lecture on advanced algebra at the University of Paris while still in his early twenties. Dee was an ardent promoter of mathematics and a respected astronomer, as well as a leading expert in navigation, having trained many of those who would conduct England's voyages of discovery.
Simultaneously with these efforts, Dee immersed himself in the worlds of magic, astrology and Hermetic philosophy. He devoted much time and effort in the last thirty years or so of his life to attempting to commune with angels in order to learn the universal language of creation and bring about the pre-apocalyptic unity of mankind. A student of the Renaissance Neo-Platonism of Marsilio Ficino, Dee did not draw distinctions between his mathematical research and his investigations into Hermetic magic, angel summoning and divination. Instead he considered all of his activities to constitute different facets of the same quest: the search for a transcendent understanding of the divine forms which underlie the visible world, which Dee called "pure verities".
In his lifetime Dee amassed one of the largest libraries in England. His high status as a scholar also allowed him to play a role in Elizabethan politics. He served as an occasional adviser and tutor to Elizabeth I and nurtured relationships with her ministers Francis Walsingham and William Cecil. Dee also tutored and enjoyed patronage relationships with Sir Philip Sidney, his uncle Robert Dudley, 1st Earl of Leicester, and Edward Dyer. He also enjoyed patronage from Sir Christopher Hatton.*Wik
I have Woolley's book, and enjoyed it.

1797 James Hutton (3 June 1726 in Edinburgh, Scotland - 26 March 1797 in Edinburgh, Scotland) geologist who initiated the principle of uniformitarianism with his Theory of the Earth (1785). He asserted that geological processes examined in the present time explain the formation of older rocks. John Playfair effectively championed Hutton's theory. Hutton, in effect, was the founder of modern geology, replacing a belief in the role of a biblical flood forming the Earth's crust. He introduced an understanding of the action of great heat beneath the Earth's crust in fusing sedimentary rocks, and the elevation of land forms from levels below the ocean to high land in a cyclical process. He established the igneous origin of granite (1788). He also had early thoughts on the evolution of animal forms and meterology. *TIS

1914 John S Mackay (22 Oct 1843 in Auchencairn near Kirkudbright, Kirkcudbrightshire, Scotland - 26 March 1914 in Edinburgh, Scotland)graduated from St Andrews University and taught at Perth Academy and Edinburgh Academy. He was a founder member of the EMS and became the first President in 1883 and an honorary member in 1894. He published numerous papers on Geometry in the EMS Proceedings.*SAU

1933 József Kürschák (14 March 1864 – 26 March 1933) was a Hungarian mathematician noted for his work on trigonometry and for his creation of the theory of valuations. He proved that every valued field can be embedded into a complete valued field which is algebraically closed. In 1918 he proved that the sum of reciprocals of consecutive natural numbers is never an integer. Extending Hilbert's argument, he proved that everything that can be constructed using a ruler and a compass, can be constructed by using a ruler and the ability of copying a fixed segment. He was elected a member of the Hungarian Academy of Sciences in 1897. *Wik

1974 Edward Uhler Condon (March 2, 1902 – March 26, 1974) was a distinguished American nuclear physicist, a pioneer in quantum mechanics, and a participant in the development of radar and nuclear weapons during World War II as part of the Manhattan Project. The Franck–Condon principle and the Slater–Condon rules are named after him.
He was the director of the National Bureau of Standards (now NIST) from 1945 to 1951. In 1946, Condon was president of the American Physical Society, and in 1953 was president of the American Association for the Advancement of Science.
During the McCarthy period, when efforts were being made to root out communist sympathizers in the United States, Edward Condon was a target of the House Un-American Activities Committee on the grounds that he was a 'follower' of a 'new revolutionary movement', quantum mechanics; Condon defended himself with a famous commitment to physics and science.
Condon became widely known in 1968 as principal author of the Condon Report, an official review funded by the United States Air Force that concluded that unidentified flying objects (UFOs) have prosaic explanations. The lunar crater Condon is named for him.
Years later, Carl Sagan reported how Condon described one encounter with a loyalty review board. A board member stated his concern: "Dr. Condon, it says here that you have been at the forefront of a revolutionary movement in physics called...quantum mechanics. It strikes this hearing that if you could be at the forefront of one revolutionary movement...you could be at the forefront of another". Condon said he replied: "I believe in Archimedes' Principle, formulated in the third century B.C. I believe in Kepler's laws of planetary motion, discovered in the seventeenth century. I believe in Newton's laws...." and continued with a catalog of scientists from earlier centuries, including the Bernoulli, Fourier, Ampère, Boltzmann, and Maxwell.[35] He once said privately: "I join every organization that seems to have noble goals. I don't ask whether it contains Communists".*Wik

1996 Hewlett-Packard Co-Founder David Packard Dies:
Hewlett-Packard Company co-founder David Packard dies after several weeks of illness. With fellow Stanford graduate Bill Hewlett, Packard founded Hewlett-Packard in a Palo Alto garage in 1938, spurring the development of what has come to be known as Silicon Valley. The company's first product was an oscillator, eight of which Disney used in its groundbreaking film ""Fantasia."" Since then, HP has made a name in personal computers, laser printers, calculators, accessories, and test equipment.*CHM

1966 Anna Johnson Pell Wheeler (5 May 1883 in Calliope (now Hawarden), Iowa, USA - 26 March 1966 in Bryn Mawr, Pennsylvania, USA) In 1899 she entered the University of South Dakota where she showed great promise in mathematics. The professor of mathematics, Alexander Pell, recognised her talents and helped persuade Anna Johnson that she should follow a career in mathematics. She received an A.B. degree in 1903.
After winning a scholarship to study for her master's degrees at the University of Iowa, she was awarded the degree for a thesis The extension of Galois theory to linear differential equations in 1904. A second master's degree from Radcliffe was awarded in 1905 and she remained there to study under Bôcher and Osgood.
Anna Johnson was awarded the Alice Freeman Palmer Fellowship from Wellesley College to study for a year at Göttingen University. There she attended lectures by Hilbert, Klein, Minkowski, Herglotz and Schwarzschild. She worked for her doctorate at Göttingen. While there Alexander Pell, her former mathematics professor came to Göttingen so that they could marry.
After returning to the United States, where her husband was by now Dean of Engineering, she taught courses in the theory of functions and differential equations. In 1908 Anna Pell returned to Göttingen where she completed the work for her doctorate but, after a disagreement with Hilbert, she returned to Chicago, where her husband was now on the university staff, without the degree being awarded.
At Chicago she became a student of Eliakim Moore and received her Ph.D. in 1909, her thesis Biorthogonal Systems of Functions with Applications to the Theory of Integral Equations being the one written originally at Göttingen. From 1911 Anna Pell taught at Mount Holyoke College and then at Bryn Mawr from 1918. Anna Pell's husband Alexander, who was 25 years older than she was, died in 1920. In 1924 Anna Pell became head of mathematics when Scott retired, becoming a full professor in 1925.
After a short second marriage to Arthur Wheeler, during which time they lived at Princeton and she taught only part-time, her second husband died in 1932. After this Anna Wheeler returned to full time work at Bryn Mawr where Emmy Noether joined her in 1933. However Emmy Noether died in 1935. The period from 1920 until 1935 certainly must have been one with much unhappiness for Anna Wheeler since during those years her father, mother, two husbands and close friend and colleague Emmy Noether died. Anna Wheeler remained at Bryn Mawr until her retirement in 1948.
The direction of Anna Wheeler's work was much influenced by Hilbert. Under his guidance she worked on integral equations studying infinite dimensional linear spaces. This work was done in the days when functional analysis was in its infancy and much of her work has lessened in importance as it became part of the more general theory.
Perhaps the most important honour she received was becoming the first woman to give the Colloquium Lectures at the American Mathematical Society meetings in 1927.
*SAU

Pat'sBlog

Sunday, 31 March 2013

On This Day in Math - March 31

Saturday, 30 March 2013

On This Day in Math - March 30

Friday, 29 March 2013

On This Day in Math - March 29

Thursday, 28 March 2013

On This Day in Math - March 28

Wednesday, 27 March 2013

On This Day in Math - March 27

Tuesday, 26 March 2013

On This Day in Math - March 26

Blog Archive

Stat Counter