Thursday, 27 October 2016

On This Day in Math - October 27

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

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

\( 301 \equiv 1 Mod b \) for every base,b, from 2 through 6   (Sixth grade version, if you divide 301 by any number 2 through 6, you get a remainder of 1)

1725 Nicolaus II and Daniel Bernoulli arrived in St. Petersburg on October 27, 1725 (OS)

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

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

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


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

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

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

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

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

1890 Olive Clio Hazlett (October 27, 1890 - March 8, 1974) was an American mathematician who spent most of her career working for the University of Illinois. She mainly researched algebra, and wrote seventeen research papers on subjects such as nilpotent algebras, division algebras, modular invariants, and the arithmetic of algebras.*Wik She was the most prolific of the US-born women of her time who worked in pure mathematics and was recognized for her research accomplishments when, in 1927, she became the second US-born woman to be ranked as one of American’s leading mathematicians by her peers, a distinction marked by a “star” in American Men of Science. *Natl Museum of American History

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


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

1616 Johann Richter or Johannes Praetorius (1537 Jáchymov, Bohemia – 27 October 1616, Altdorf bei Nürnberg) was a Bohemian German mathematician and astronomer. From 1557 he studied at the University of Wittenberg, and from 1562 to 1569 he lived in Nuremberg. His astronomical and mathematical instruments are kept at Germanisches Nationalmuseum in Nuremberg.
In 1571 be became Professor of mathematics (astronomy) at Wittenberg where he met Valentinus Otho(Otto) and Joachim Rheticus. When Otho came to Wittenberg in 1573, he suggested to him the fraction |( \frac{355}{113}\) as an approximation to pi. Although known much earlier in the Orient, this is the first known time it was introduced in Europe.
He taught Copernicus' theory of astronomy initially as a means of eliminating the equant from Ptolemy's account, and later moving to a proto-Tychonic system.
He died in Altdorf bei Nürnberg, aged about 79. *Wik

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

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

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

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

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

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

Wednesday, 26 October 2016

On This Day in Math - October 26

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

The 300th day of the year; 300 is a triangular number, the sum of the integers from 1 to 24.

300 is also the sum of a pair of twin primes (149 + 151). And the sum of ten consecutive primes, 300 = 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47.

1639 (OS) Jeremiah Horrocks makes his first written prediction of the 1639 Transit of Venus, in a letter to William Crabtree to alert him – that Venus would pass across the Sun’s disk on 24 November. Although they notified several other acquaintances of the impending event, these two men seem to have been the only recorded astronomers to make measurements of the passage. *Allan Chapman, Jeremiah Horrocks and the transit of Venus of 1639

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

1738 Theophilus Grew, Mathematician advertises his availability for all manner of mathematical instruction in the Philadelphia Gazette.
"Forasmuch as Mathematical Learning is (and has been in all Ages) promoted in most Parts of the World especially in all great Towns, and generally pursued by the Gentry and those of the first Rank, as a necessary Qualification; it is to be hoped that this flourishing City will follow the Example and give it such Encouragement as it justly deserves.
In order to which there will be taught this Winter, over against Mr. James Steel’s in Second-Street, Philadelphia; Reading, Writing, Vulgar Arithmetick, Decimal Arithmetick, Accompts, Euclid’s Elements, Practical Geometry, Mensuration, Gauging, Surveying, Algebra, Trigonometry, Geography, Navigation, Astronomy, Dialing, Projection of the Sphere, the Use of Globes, Maps, Quadrants, Scales, sliding Rules, and all other Instruments for the Mathematical Service, by Theophilus Grew, Mathematician."
Grew would go on to become the first professor of mathematics at the Univ of Pennsylvania when it was founded. *Natl. Archives

1818 Thomas Jefferson writes Nathaniel Bowditch to offer him the Math Professorship at the newly forming University of Virginia
I have stated that where men of the 1st. order of science in their line can be found in our country, we shall give them a willing preference. we are satisfied that we can get from no country a professor of higher qualifications than yourself for our Mathematical department, and we entertain the hope and with great anxiety that you will accept of it. the house for that Professorship will be ready at midsummer next or soon after, when we should wish that school to be opened. I know the prejudices of every state against the climates of all those South of itself: but i know also that the candid traveller advancing Southwardly, to a certain degree at least, sees that they are more prejudices, and that the real advantages of climate are in the middle & temperate states, and especially when above their tide waters.
*Letters of Thomas Jefferson,

1843 John T Graves replies to Hamilton about the invention of Quaternions,
"There is something in the system which gravels me. I have not yet any clear views as to the extent to which we are at liberty arbitrarily to create imaginaries, and to endow them with supernatural properties."
"If with your alchemy you can create three pounds of gold, why should you stop there?
Graves is credited by Hamilton with being a critical inspiration in the Quaternions, and would quickly go on to liberty to create imaginaries himself and create the "Octaves", an eight dimensional normed division algebra. Why should you stop there indeed? *Joan Baez Rankin Lecture of September 17, 2008 Glascow

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

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

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

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


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

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

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

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

1902 Henrietta Hill Swope(26 October 1902; Saint Louis, Missouri - 24 November 1980; Pasadena, California)was an American astronomer. She was the eldest child of Gerard and Mary Dayton (Hill) Swope; her mother was the daughter of Thomas Hill, president of Harvard University, 1862-1868. She received her A.B. from Barnard College in 1926 and her A.M. from Radcliffe College in 1928. In 1936, while assistant at the Harvard Observatory (1928-1942), she was a member of the expedition sent jointly by the Harvard Observatory and the Massachusetts Institute of Technology to study the solar eclipse in Soviet Central Asia. During World War II she was staff member of the M.I.T. Radiation Laboratory and then served as a mathematician in the Hydrographic Office of the U.S. Department of the Navy. From 1947 to 1952 she taught astronomy at Barnard College and in 1952 was appointed assistant, later research fellow, at the Mt. Wilson and Palomar Observatories in California. After her retirement in 1968, she continued to work at the Observatories.
HHS was a member of the American Astronomical Society; she received the AAS Annie Jump Cannon Prize in 1968 for her research on photometry and variable stars. She was responsible for developing a new yardstick for measuring the universe: calibrating distance by determining the brightness of stars. She received the Distinguished Alumna Award of Barnard College in 1975 and the Barnard Medal of Distinction in 1980.
The Swope Telescope at the Las Campanas Observatory in Chile is named in her honor, as is asteroid 2168 Swope.

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

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


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

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

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

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

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

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

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

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

Tuesday, 25 October 2016

On This Day in Math - October 25

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

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

There are 299 composite numbers less than 1000 which are products of two primes.


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

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

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

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

1881 Clerk Seaton writes to the chairman of the committee on the census that he has discovered a paradox with the apportionment. Seaton had discovered the Alabama Paradox.
It seemed so easy. The 1787 US Constitution laid out simple rules for deciding how many representatives each state shall receive:
"Representatives and direct taxes shall be apportioned among the several States which may be included within this Union, according to their respective numbers, ... The number of Representatives shall not exceed one for every thirty thousand, but each State shall have at least one Representative ..."
It may have seemed easy, but for the 200+ years of US government, the question of "Who gets how many?" continues to perplex and promote controversy.
When congress discussed mathematical methods of applying this constitutional directive there were two methods of prime consideration, Jefferson's method, and Hamilton's method. Congress selected Hamilton's method and in the first use of the Presidential veto (make a note of this for extra points in History or Government class) President Washington rejected the bill. Congress submitted and passed another bill using Jefferson's method. The method used has changed frequently over the years with a method by Daniel Webster adopted in 1842, (the original 65 Representatives had grown to 223) and then replaced with Hamilton's method in 1852 (234 Representatives). In a strange "Only in America" moment in 1872, the congress reapportioned without actually adopting an official method and some analysis suggest that the difference caused Rutherford Hayes to Win instead of Samuel Tilden who would have won had Hamilton's method been used. Since 1931 the US House has had 435 Representatives with the brief exception of when Alaska and Hawaii became states. Then there was a temporary addition of one seat for each until the new apportionment after the 1960 Census. In 1941 the Huntington-Hill Method was adopted and has remained in continuous (and contentious) use ever since.
In 1880 the first of what are called the apportionment paradoxes was discovered. Here is how they state it at the Wikipedia web site:
After the 1880 census, C. W. Seaton, chief clerk of the U. S. Census Office, computed apportionment for all House sizes between 275 and 350, and discovered that Alabama would get 8 seats with a House size of 299 but only 7 with a House size of 300. In general the term Alabama paradox refers to any apportionment scenario where increasing the total number of items would decrease one of the shares. They also show a nice example (with small numbers) so you might check their site.

1904 The first K&E Pocket watch slide rule patent was approved. Prior to this time K&E sold French made Boucher designs. The patent is in the name of Elmer A. Sperry, co-inventor of the gyrocompass. The patent covers the use of the ‘S’ and ‘L’ dials
and the geared hands and dials . *Oughtred Society

1944 Max Planck writes to Hitler to plead for the life of his son, Erwin. In the note, the discoverer of the energy quantum pleads for the life of his son, who was involved in the attempted to kill Hitler three months before. Max Planck had already lost his eldest son, who was killed in the Battle of Verdun, during World War I.
Planck writes in his letter that he is ‘confident’ that the Führer will lend his ear to ‘an imploring 87-year-old’. This plea, apparently written from the Planck family’s bombed-out home in a suburb of Berlin, was ignored by the authorities. Erwin was executed on 23 January 1945, and his death certificate recorded: ‘parents unknown’. *Graham Farmelo

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

2011   Scientists in California and Sweden have solved a 250-year-old mystery — a coded manuscript written by a secret society.  The University of Southern California announced Tuesday, Oct 25th, that researchers had broken the Copiale Cipher — the writing used in a 105-page 18th century document from Germany.
Kevin Knight, of USC, and Beata Megyesi and Christiane Schaefer, of Uppsala University, did the work.
They used a statistical computer program to decipher part of the manuscript, which was found in East Berlin after the Cold War and is now in a private collection.
The book, written in symbols and Roman letters, details complicated initiation ceremonies of a society fascinated by ophthalmology. They include making mystical signs and plucking a hair from a candidate's eyebrow. The convoluted text swears candidates to loyalty and secrecy. *Associated Press,


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

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

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

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

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

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

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


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

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

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

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

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

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

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

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

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

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

Monday, 24 October 2016

On This Day in Math - October 24

Gauss-Weber Monument in Gotttingen

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

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

298 = \( {12 \choose 1} + {12 \choose 2} + {12 \choose 3} \) This is related to the Egg Drop numbers


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

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

1826 Abel wrote Holmboe his impressions of continental mathematics and mathematicians.
Upon reaching Paris from Berlin, he worked on what would be called the Paris Treatise that he submitted to the Academy in October 1826. In this memoir, Abel obtained among other things, an important addition theorem for algebraic integrals. It is also in this treatise that we see the first occurrence of the concept of the genus of an algebraic function. Cauchy and Legendre were appointed referees of this memoir. In Paris, Abel was disappointed to find little interest in his work, which he had saved for the Academy. He wrote to Holmboe, “I showed the treatise to Mr. Cauchy, but he scarcely deigned to glance at it."
*Krishnaswami Alladi, NEILS HENRIK ABEL, Norwegian mathematical genius (paper on UFL website)

1844 Michael Faraday in a letter (his first?) to Ada Lovelace declines an invitation to be her tutor, and in response to her questions about his religion, he describes himself as, "of a small and despised sect of Christians, known, if they are known at all, as Sandemanian." Michael Brooks, in his book Free Radicals, describes the sect as resposible for Faraday's lack of much interest in the applications of his scientific discoveries; "It was his calling, as he saw it, to study nature, which was 'written by the finger of God', and make clear the eternal power and divine nature of the creator."

In 1851, William Lassell discovered Ariel and Umbriel, satellites of Uranus. All of Uranus's moons are named after characters from the works of William Shakespeare or Alexander Pope's The Rape of the Lock. The names of all four satellites of Uranus then known were suggested by John Herschel in 1852 at the request of Lassell. Ariel has an approx. diameter of 1160-km, an orbital period of 2.52 days, and orbital radius of 191,240-km from Uranus. The name Umbriel comes from Alexander Pope's The Rape of the Lock. Umbriel has a diameter of 1170-km, an orbital period of about 4 days and orbit radius of 266,000-km. Lassell, a British astronomer, had previously also discovered Neptune's largest satellite, Triton and (with Bond) discovered Saturn's moon Hyperion. He was a successful brewer before turning to astronomy.*TIS *Wik

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

1904 Emmy Noether matriculated at the University of Erlangen. *VFR The University was only yards from her house. Images of both are at this site from The Renaissance Mathematicus.

1927 From the 24th to 29th October 1927 in Brussels, the fifth Solvay Conference took place, Perhaps the most famous science conference in history. 17 of the 29 attendees were or became Nobel Prize winners. It is also famously remembered for it was at this conference that Einstein, who liked to invent catchy phrases, uttered his, "God does not play dice" . Bohr replied, "Einstein, stop telling God what to do".
A. Piccard, E. Henriot, P. Ehrenfest, E. Herzen, Th. de Donder, E. Schrödinger, J.E. Verschaffelt, W. Pauli, W. Heisenberg, R.H. Fowler, L. Brillouin; P. Debye, M. Knudsen, W.L. Bragg, H.A. Kramers, P.A.M. Dirac, A.H. Compton, L. de Broglie, M. Born, N. Bohr;
I. Langmuir, M. Planck, M. Skłodowska-Curie, H.A. Lorentz, A. Einstein, P. Langevin, Ch.-E. Guye, C.T.R. Wilson, O.W. Richardson

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

1994 Lynchburg College Professor Thomas Nicely, Reports a flaw in the Pentium chip by Intel that he discovered while he was trying to calculate Brun's constant,(The sum of the reciprocals of all the twin primes, 1/3+1/5+1/5+1/7+1/11+1/13.... which converges to about 1.902).
The Pentium chip occasionally gave wrong answers to a floating-point (decimal) division calculations due to errors in five entries in a lookup table on the chip. Intel spent millions of dollars replacing the faulty chips.
Nicely first noticed some inconsistencies in the calculations on June 13, 1994 shortly after adding a Pentium system to his group of computers, but was unable to eliminate other factors until October 19, 1994. On October 24, 1994 he reported the issue to Intel. According to Nicely, his contact person at Intel later admitted that Intel had been aware of the problem since May 1994, when the flaw was discovered during testing of the FPU for its new P6 core, first used in the Pentium Pro. *Wik


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

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

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

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

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

1898 Lillian Rose Vorhaus Kruskal Oppenheimer (October 24, 1898 in New York City – July 24, 1992) was an American origami pioneer. She popularized origami in the West starting in the 1950s, and is credited with popularizing the Japanese term origami in English-speaking circles, which gradually supplanted the literal translation paper folding that had been used earlier. In the 1960s she co-wrote several popular books on origami with Shari Lewis.  Lillian taught origami to Persi Diaconis when he was working as a magician;
She was the mother of three sons William Kruskal(developed the Kruskal-Wallis one-way analysis of variance), Martin David Kruskal(co-inventor of solitons and of surreal numbers), and Joseph Kruskal ( Kruskal's algorithm for computing the minimal spanning tree (MST) of a weighted graph) who all went on to be prominent mathematicians. Her grandson Clyde P. Kruskal (son of Martin) is an American computer scientist,working on parallel computing architectures, models, and algorithms. *Wik

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

1908 John Tuzo Wilson, CC, OBE, FRS, FRSC, FRSE (October 24, 1908 – April 15, 1993) the world-renowned Canadian geophysicist, served as Director General of the Ontario Science Centre from 1974 to 1985. He was instrumental in developing the theory of Plate Tetonics in the 1960s. This theory describes the formation, motion and destruction of the Earth's crust, the origin of volcanic eruptions and earthquakes, and the growth of mountains. Dr. Wilson's signficant contributions to this theory revolutionized Earth Sciences. He proposed the existence of transform faults to explain the numerous narrow fracture zones and earthquakes along oceanic ridges. He also showed that rising magma plumes beneath the Earth's crust could create stationary hot spots, leading to the formation of mid-plate volcanic chains like the Hawaiian Islands.
The first graduate of geophysics from the University of Toronto in 1930, Dr. Wilson went on to study at Cambridge and Princeton, earning his doctorate in 1936. After spending two years with the Geological Survey of Canada and almost a decade with the Canadian Military Engineers, he accepted the position of Professor of Geophysics at the University of Toronto in 1946. Internationally recognized for his major contributions as a research scientist, educator and visionary, Dr. Wilson received many prestigious
awards, including the Vetlesen Prize, the Earth Sciences equivalent of the Nobel Prize.*THE HISTORICAL

1922 Werner Buchholz​  (October 24, 1922 in Detmold, Germany - ). He was a member of the teams that designed the IBM 701​ and Stretch models. Buchholz used term byte to describe eight bits—although in the 1950s, when the term first was used, equipment used six-bit chunks of information, and a byte equaled six bits. Buchholz described a byte as a group of bits to encode a character, or the numbers of bits transmitted in parallel to and from input-output. *CHM

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


1601 Tycho Brahe (14 December 1546 – 24 October 1601) Kepler inherited his vast accurate collection of astronomical data. He used this to derive his laws of planetary motion. *VFR In 1901, on the three hundredth anniversary of his death, the bodies of Tycho Brahe and his wife Kirstine were exhumed in Prague. They had been embalmed and were in remarkably good condition, but the astronomer’s artificial nose was missing, apparently filched by someone after his death. It had been made for him in gold and silver when his original nose was sliced off in a duel he fought in his youth at Rostock University after a quarrel over some obscure mathematical point. He always carried a small box of glue in his pocket for use when the new nose became wobbly. Tycho Brahe was famous for the most accurate and precise observations achieved by any astronomer before the invention of the telescope. Born to an aristocratic family in Denmark in 1546, he was one of twin boys – the other twin was still-born – and while still a baby Tycho was stolen from his parents by a rich, childless uncle, who paid for his education and sent him to Leipzig University to study law. His imagination had been fired, however, by a total eclipse of the sun in 1560 and he was determined to be an astronomer. He found that the existing tables recording the positions of planets and stars were wildly inaccurate and dedicated himself to correcting them. *History Today Was Tycho Murdered? Read an excellent blog on "The crazy life and crazier death of Tycho Brahe, history’s strangest astronomer".

1635 Wilhelm Shickard  (22 April 1592 – 24 October 1635) He invented and built a working model of the first modern mechanical calculator. *VFR 
Schickard's machine could perform basic arithmetic operations on integer inputs. His letters to Kepler explain the application of his "calculating clock" to the computation of astronomical tables.
In 1935 while researching a book on Kepler, a scholar found a letter from Schickard and a sketch of his calculator, but did not immediately recognize the designs or their great importance. Another twenty years passed before the book's editor, Franz Hammer, found additional drawings and instructions for Schickard's second machine and released them to the scientific community in 1955.A professor at Schickard's old university, Tübingen, reconstructed the calculator based upon Schickard's original plans; it is still on display there today. 
He was a friend of Kepler and did copperplate engravings for Kepler's Harmonice Mundi. He built the first calculating machine in 1623, but it was destroyed in a fire in the workshop in 1624.

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

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

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

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

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