## 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.

EVENTS

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

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,

BIRTHS

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

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

DEATHS

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

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

EVENTS

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

BIRTHS

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

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
MARKER DATABASE

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

DEATHS

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

## Sunday, 23 October 2016

### On This Day in Math - October 23

God exists since mathematics is consistent, and the devil exists since its consistency cannot be proved.
~Hermann Klaus Hugo Weyl

Remember, 1023 is the exponent for a mole, so about 6:02 (am or pm) you can set down to a Mole of molecules of your favorite brew.  Happy Mole Day.

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

And this one from * Jim Wilder @wilderlab 2973=26,198,073 and 26+198+073=297

EVENTS

4004 B.C. The date of the creation of the world according to the computation of Archbishop James Usher (1581–1656), who had a curious fascination for the integration of numerology, astronomy, and scripture. It was highly regarded for several centuries primarily because in 1701 it was inserted into the margin of the King James version of the Bible. *Sky and Telescope, vol. 62, Nov. 81, 404–405.

526 Boethius executed.Boethius translated Nicomachus's treatise on arithmetic (De institutione arithmetica libri duo) as well as Euclid and Iamblichus.
There is a long tradition, going back at least to the eighth century, regarding Boethius as having been executed for maintaining the Catholic faith against the Arian Theodoric. While Theodoric was probably paranoid about spies representing the Catholic eastern emperor-in-waiting Justinian (who would, in fact, later “reconquer” the Italian peninsula), and Boethius claims in the Consolation that he was hated for being smarter than everyone else, the truth is probably that he was caught up in the usual machinations of an imperial court.
A member of the Senate was accused of treasonably conspiring with Justinian’s predecessor Justin I against Theodoric. Boethius defended the accused (apparently the only person to do so, although the charges were surely trumped up), and in the Consolation, Boethius says he was only defending the Senate (implying that the accusations were meant to undermine the authority of the Senate by challenging its loyalty to the king).
In any event, the sources we have say that Boethius was condemned by the Senate (who appear to have thrown him under the bus) without being able to speak in his own defense. After an indeterminate time of imprisonment, he was executed.
It was while he awaited death that he wrote his most famous and arguably most influential work, The Consolation of Philosophy.” From “Executed Today” web site

1613 Kepler, in a letter to an unknown recipient goes into great detail concerning his attempts over the preceding two years to find a wife. *A Christmas Trilogy RMAT

1676 Hooke's diary records that he had “Mercator's Music” copied on 23 October . This is "Mercator's earliest thinking on music, has major sections on the consonances and on the arithmetic of proportions using ratios or using logarithms.  Descartes, Newton, and Nicolaus Mercator all worked on the problem of musical timing ( To divide the octave into tones) using logs in the mid-17th century. *Benjamin Wardhaugh, Historia Mathematica, Volume 35, Issue 1, February 2008, Pages 19–36 A longer, clearer essay on the problem, with lots of interesting notes about Mercator, and historical thought on ratios by Wardhaugh is at the Convergence web site of the MAA

In 1803, John Dalton presented an essay on the absorption of gases by water, at the conclusion of which he gave a series of atomic weights for 21 simple and compound elements. He read his paper at a meeting of the Manchester Literary and Philosophical Society. *TIS

1852 August DeMorgan reported the conjecture of his student, Francis Guthrie: Four colors suffice to color planar maps so that adjacent regions have different color. It was solved by Kenneth Appel and Wolfgang Haken in 1976. In a letter to W.R. Hamilton he recalls, “A student of mine asked me today to give him a reason for a fact which I did not know was a fact – and do not yet. He says that if a figure be anyhow divided, and the compartments differently colored so that figures with any portion of common boundary line are differently colored --- four colors may be wanted, but not more…” *Dave Richeson, Euler’s Gem, pg 132)

1892  The Duck-Rabbit double illusion was first published in Fliegende Blätter, a German humor magazine (Oct. 23, 1892, p. 147). The ambiguous figure in which the brain switches between seeing a rabbit and a duck was "originally noted" by American psychologist Joseph Jastrow (Jastrow 1899, p. 312; 1900; see also Brugger and Brugger 1993). Jastrow used the figure, together with such figures as the Necker cube and Schröder stairs, to point out that perception is not just a product of the stimulus, but also of mental activity (Kihlstrom 2002). Jastrow's cartoon was based on one originally published in Harper's Weekly (Nov. 19, 1892, p. 1114) which, in turn, was based on the earlier illustration in Fliegende Blätter,*Mathworld.Wolfram.com

1906, Santos-Dumont won the Archdeacon prize by flying his Hargrave box kite inspired aircraft at Bagatelle in Paris. He was hailed by many in Europe as the first to fly, despite the fact that the Wright Brothers had achieved such a feat three years earlier in the United Sates. But Orville and Wilbur Wright kept their invention under wraps, avoiding any public exhibitions while they sought a patent. Most aeronauts in Europe considered them to be bluffing.
Earlier, on October 19, 1901, Santos-Dumont won the French Aero Club’s Deutsch Prize, rounding the Eiffel Tower and landing at Parc Saint Cloud in twenty-nine minutes and thirty seconds in his dirigible. *theappendix.net

2014 Today is Mole Day. Celebrated annually on October 23 from 6:02 a.m. to 6:02 p.m., Mole Day commemorates Avogadro's Number (6.02 x 10^23) (Which I recently learned from John D. Cook was approximately 24 factorial or 24!) , which is a basic measuring unit in chemistry. Mole Day was created as a way to foster interest in chemistry. Schools throughout the United States and around the world celebrate Mole Day with various activities related to chemistry and/or moles.
For a given molecule, one mole is a mass (in grams) whose number is equal to the atomic mass of the molecule. For example, the water molecule has an atomic mass of 18, therefore one mole of water weighs 18 grams. An atom of neon has an atomic mass of 20, therefore one mole of neon weighs 20 grams. In general, one mole of any substance contains Avogadro's Number of molecules or atoms of that substance. This relationship was first discovered by Amadeo Avogadro (1776-1858) and he received credit for this after his death. *Mole Day Org web page

BIRTHS

1865 Piers Bohl (23 Oct 1865 in Walka, Livonia (now Valka, Latvia) - 25 Dec 1921 in Riga, Latvia) Among Bohl's achievements was, rather remarkably, to prove Brouwer's fixed-point theorem for a continuous mapping of a sphere into itself. Clearly the world was not ready for this result since it provoked little interest.
Bohl also studied questions regarding whether the fractional parts of certain functions give a uniform distribution. His work in this area was carried forward independently by Weyl and Sierpinski. There are many seemingly simple questions in this area which still seem to be open. For example it is still unknown whether the fractional parts of (3/2)n form a uniform distribution on (0,1) or even if there is some finite subinterval of (0,1) which is avoided by the sequence. *SAU

1875 Gilbert Newton Lewis (23 Oct 1875, 23 Mar 1946 at age 70) American chemist who collaborated with Irving Langmuir in developing an atomic theory. He developed a theory of valency, which introduced the covalent bond (c. 1916), whereby a chemical combination is made between two atoms by the sharing of a pair of electrons, one contributed from each atom. This was part of his more general octet theory, published in Valence and the Structure of Atoms and Molecules (1923). Lewis visualized the electrons in an atom as being arranged in concentric cubes. The sharing of these electrons he illustrated in the Lewis dot diagrams familiar to chemistry students. He generalized the concept of acids and bases now known as Lewis acids and Lewis bases. *TIS

1893 Ernest Julius Öpik (23 Oct 1893; 10 Sep 1985) Estonian astronomer best known for his studies of meteors and meteorites, and whose life work was devoted to understanding the structure and evolution of the cosmos. When Soviet occupation of Estonia was imminent, he moved to Hamburg, then to Armagh Observatory, Northern Ireland (1948-81). Among his many pioneering discoveries were: (1) the first computation of the density of a degenerate body, namely the white dwarf 40 Eri B, in 1915; (2) the first accurate determination of the distance of an extragalactic object (Andromeda Nebula) in 1922; (3) the prediction of the existence of a cloud of cometary bodies encircling the Solar System (1932), later known as the Oort Cloud''; (4) the first composite theoretical models of dwarf stars like the Sun which showed how they evolve into giants (1938); (5) a new theory of the origin of the Ice Ages (1952). *TIS

1905 Felix Bloch (23 Oct 1905; 10 Sep 1983) Swiss-born American physicist who shared (with independent discoverer, E.M. Purcell) the Nobel Prize for Physics in 1952 for developing the nuclear magnetic resonance (NMR) method of measuring the magnetic field of atomic nuclei. He obtained his PhD under Werner Heisenberg in 1928, then taught briefly in Germany, but as a Jew, when Hitler came to power, he left Europe for the USA. Bloch's concept of magnetic neutron polarization (1934) enabled him, in conjunction with L. Alvarez, to measure the neutron's magnetic moment. During WW II he worked on the atomic bomb. Thereafter, Bloch and co-workers developed NMR, now widely used technique in chemistry, biochemistry, and medicine. In 1954 he became the first director of CERN.*TIS

1908 Ilya Mikhaylovich Frank (23 Oct 1908; 22 June 1990) Russian physicist who, with Igor Y. Tamm, theoretically explained the mechanism of Cherenkov radiation. In 1934, Cherenkov discovered that a peculiar blue light is emitted by charged particles traveling at very high speeds through water. Frank and Tamm provided the theoretical explanation of this effect, which occurs when the particles travel through an optically transparent medium at speeds greater than the speed of light in that medium. This discovery resulted in the development of new methods for detecting and measuring the velocity of high-speed particles and became of great importance for research in nuclear physics. For this, Frank received the Nobel Prize for Physics in 1958 (jointly with Pavel A. Cherenkov and Igor Y. Tamm). *TIS

1920 Tetsuya Theodore Fujita (23 Oct 1920; 19 Nov 1998) was a Japanese-American meteorologist who increased the knowledge of severe storms. In 1953, he began research in the U.S. Shortly afterwards, he immigrated and established the Severe Local Storms Project. He was known as "Mr. Tornado" as a result of the Fujita scale (F-scale, Feb 1971), which he and his wife, Sumiko, developed for measuring tornadoes on the basis of their damage. Following the crash of Eastern flight 66 on 24 Jun 1975, he reviewed weather-related aircraft disasters and verified the downburst and the microburst (small downburst) phenomena, enabling airplane pilots to be trained on how to react to them. Late in his career, he turned to the study of storm tracks and El Nino. *TIS

DEATHS

1581 Michael Neander (April 3, 1529 – October 23, 1581) German mathematician and astronomer was born in Joachimsthal, Bohemia, and was educated at the University of Wittenberg, receiving his B.A. in 1549 and M.A. in 1550.
From 1551 until 1561 he taught mathematics and astronomy in Jena, Germany. He became a professor in 1558 when the school where he taught became a university. From 1560 until his death he was a professor of medicine at the University of Jena. He died in Jena, Germany. The crater Neander on the Moon is named after him. *Wik

1944 Charles Glover Barkla (7 Jun 1877, 23 Oct 1944) was a British physicist who was awarded the Nobel Prize for Physics in 1917 for his work on X-ray scattering. This technique is applied to the investigation of atomic structures, by studying how X-rays passing through a material and are deflected by the atomic electrons. In 1903, he showed that the scattering of x-rays by gases depends on the molecular weight of the gas. His experiments on the polarization of x-rays (1904) and the direction of scattering of a beam of x-rays (1907) showed X-rays to be electromagnetic radiation like light (whereas, at the time, William Henry Bragg who held that X-rays were particles.) Barkla further discovered that each element has its own characteristic x-ray spectrum. *TIS

1985 John Semple studied at Queen's University Belfast and Cambridge. He held a post in Edinburgh for a year before becoming Professor of Pure Mathematics at Queen's College Belfast. He moved to King's College London where he spent the rest of his career. His most important work was in Algebraic geometry, in particular work on Cremona transformations and work extending results of Severi . He wrote two famous texts Algebraic projective geometry (1952) and Algebraic curves (1959) jointly with G T Kneebone. *SAU

2007 David George Kendall FRS (15 January 1918 – 23 October 2007)[2] was an English statistician, who spent much of his academic life in the University of Oxford and the University of Cambridge. He worked with M. S. Bartlett during the war, and visited Princeton University after the war. He was appointed the first Professor of Mathematical Statistics in the Statistical Laboratory, University of Cambridge in 1962, in which post he remained until his retirement in 1985. He was elected to a professorial fellowship at Churchill College, and he was a founding trustee of the Rollo Davidson Trust.
Kendall was a world expert in probability and data analysis, and pioneered statistical shape analysis including the study of ley lines. He defined Kendall's notation for queueing theory.
The Royal Statistical Society awarded him the Guy Medal in Silver in 1955, followed in 1981 by the Guy Medal in Gold. In 1980 the London Mathematical Society awarded Kendall their Senior Whitehead Prize, and in 1989 their De Morgan Medal. He was elected a fellow of the Royal Society in 1964. *Wik

2011 John McCarthy (September 4, 1927 – October 23, 2011) was an American computer scientist and cognitive scientist who received the Turing Award in 1971 for his major contributions to the field of Artificial Intelligence (AI). He was responsible for the coining of the term "Artificial Intelligence" in his 1955 proposal for the 1956 Dartmouth Conference and was the inventor of the LISP programming language.*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

## Saturday, 22 October 2016

### On This Day in Math - October 22

One of the most baneful delusions by which the minds, not only of students, but even of many teachers of mathematics in our classical colleges, have been afflicted with is, that mathematics can be mastered by the favored few, but lies beyond the grasp and power of the ordinary mind.
~Florian Cajori, The Teaching and History of Mathematics in the United States

The 296th day of the year; 296 is the number of partitions of 30 with distinct parts. (Even very young students can enjoy exploring the number of partitions of integers, and the difference in the number when the parts must be distinct. The idea can be explored for very young students with number rods, etc)

A cube with an 8x8 checker board on each fact has a total of 296 lattice points (where the squares meet)

The somewhat famous "look and say" sequence in math, 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, (the second term is 11 because the previous term has One, one; etc) has 296 digits in the 18th term.

EVENTS
1668 Leibniz writes to the German emperor to request permission to publish a "Nucleus Libareaus". This was the beginnings of the foundation of Acta Eruditorium, the first German scientific journal.

1685 Abraham De Moivre was a student of physics at the University, Collège d'Harcourt, in the 1680s. After the Revocation of the Edict of Nantes, (October 22, 1685 ) he went into seclusion in the priory of St. Martin (possibly that which became the Conservatoire National des Arts et Métiers ??) and then emigrated to England, having no contact with France until he was elected a Foreign Associate of the Academy of Sciences just before his death.*VFR

1922 M. C. ESCHER visited here(Alhambra) on 18 - 24 Oct 1922 and was impressed by the patterns, but he didn't really use them in his art until after his second visit on 22-26 May 1936 *VFR

1746 Princeton chartered as the College of New Jersey -- the name by which it was known for 150 years -- Princeton University was British North America's fourth college. Located in Elizabeth for one year and then in Newark for nine, the College of New Jersey moved to Princeton in 1756. It was housed in Nassau Hall, which was newly built on land donated by Nathaniel FitzRandolph. Nassau Hall contained the entire College for nearly half a century. *Princeton Univ web page

In 1797, the first parachute jump was made by André-Jacques Garnerin, released from a balloon 2,230-ft above the Parc Monceau, Paris. He rode in a gondola fixed to the lines of a 23-ft diameter parachute, which was supported by a wooden pole and had its 32 white canvas gores folded like a closed umbrella. Lacking any vent in the top of the parachute, Garnerin descended with violent oscillations, and suffered the first case of airsickness. For his next jump, he added a hole in the top of the parachute. He made his fifth jump on 21 Sep 1802 over London, from a height of 3,000-ft. This was the first parachute descent made in England. He landed near St. Pancras Church. Having eliminated the center vent for this jump, he again suffered a fit of vomiting. *TIS See A larger TIS article here.

1850 Fechner’s law introduced. [Springer’s 1985 Statistics Calendar] A pioneering though in many situations incorrect formulation of the relationship between the physical strength of a stimulus and its strength as perceived by humans, proposed by G. T. Fechner in 1860. Fechner postulated that sensation increases as the log of the stimulus. For example, by Fechner's law, if light A was twice as bright as light B (measured by an instrument), it would appear to the human eye to be log 2 (times a constant to allow for such factors as the units used) brighter than light B. Later experiments have shown conclusively that the Fechner's law doesn't generally apply.

1908 First meeting of the Spanish Association for the Advancement of Science was held October 22–29. Sixteen papers were read in the section of mathematics.*VFR

1938 In the back of a beauty shop in the Astoria section of Queens New York, Chester A. Carlson and his assistant Otto Kornei, conducted the ﬁrst successful experiment in electrophotography. The message, “10.-22.-38 ASTORIA,” was even less inspiring than Alexander Graham Bell’s ﬁrst phone conversation, but the effect was just as great. In 1949 Haloid Corporation marketed the Xerox Model A, a crude machine that required fourteen manual operations. Today ﬁve million copiers churn out 2,000 copies each year for every American citizen. *VFR

BIRTHS

1511 Erasmus Reinhold (October 22, 1511 – February 19, 1553) was a German astronomer and mathematician, considered to be the most influential astronomical pedagogue of his generation. He was born and died in Saalfeld, Saxony.
He was educated, under Jacob Milich, at the University of Wittenberg, where he was first elected dean and later became rector. In 1536 he was appointed professor of higher mathematics by Philipp Melanchthon. In contrast to the limited modern definition, "mathematics" at the time also included applied mathematics, especially astronomy. His colleague, Georg Joachim Rheticus, also studied at Wittenberg and was appointed professor of lower mathematics in 1536.
Reinhold catalogued a large number of stars. His publications on astronomy include a commentary (1542, 1553) on Georg Purbach's Theoricae novae planetarum. Reinhold knew about Copernicus and his heliocentric ideas prior to the publication of De revolutionibus and made a favorable reference to him in his commentary on Purbach. However, Reinhold (like other astronomers before Kepler and Galileo) translated Copernicus' mathematical methods back into a geocentric system, rejecting heliocentric cosmology on physical and theological grounds.
It was Reinhold's heavily annotated copy of De revolutionibus in the Royal Observatory, Edinburgh that started Owen Gingerich on his search for copies of the first and second editions which he describes in The Book Nobody Read.[5] In Reinhold's unpublished commentary on De revolutionibus, he calculated the distance from the Earth to the sun. He "massaged" his calculation method in order to arrive at an answer close to that of Ptolemy.*Wik

1587 Joachim Jungius (22 Oct 1587 in Lübeck, Germany - 23 Sept 1657 in Hamburg) a German mathematician who was one of the first to use exponents to represent powers and who used mathematics as a model for the natural sciences. Jungius proved that the catenary is not a parabola (Galileo assumed it was). *SAU (I can not find the first use by Jungius anywhere, but Cajori gives Descartes 1637 use in Geometrie as the first example of the common form today. A year earlier, James Hume produced a copy of Viete's Algebra in which he used exponents as powers of numbers, but his exponents were Roman Numerals.)

1792 Guillaume-Joseph-Hyacinthe-Jean-Baptiste Le Gentil de la Galaziere  (12 Sep 1725; 22 Oct 1792) was a French astronomer who attempted to observe the transit of Venus across the sun by travelling to India in 1761. He failed to arrive in time due to an outbreak of war. He stayed in India to see the next transit which came eight years later. This time, he was denied a view because of cloudy weather, and so returned to France. There, he found his heirs had assumed he was dead and taken his property.*TIS A more detailed blog about his life is at Renaissance Mathematicus

1843 John S Mackay 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

1881 Clinton Joseph Davisson (22 Oct 1881; 1 Feb 1958) American experimental physicist who shared the Nobel Prize for Physics in 1937 with George P. Thomson of England for discovering that electrons can be diffracted like light waves. Davisson studied the effect of electron bombardment on surfaces, and observed (1925) the angle of reflection could depend on crystal orientation. Following Louis de Broglie's theory of the wave nature of particles, he realized that his results could be due to diffraction of electrons by the pattern of atoms on the crystal surface. Davisson worked with Lester Germer in an experiment in which electrons bouncing off a nickel surface produced wave patterns similar to those formed by light reflected from a diffraction grating, and supporting de Broglie's electron wavelength = (h/p). *TIS

1895 Rolf Herman Nevanlinna​ (22 October 1895 – 28 May 1980) was one of the most famous Finnish mathematicians. He was particularly appreciated for his work in complex analysis.Rolf Nevanlinna's most important mathematical achievement is the value distribution theory of meromorphic functions. The roots of the theory go back to the result of Émile Picard in 1879, showing that a complex-valued function which is analytic in the entire complex plane assumes all complex values save at most one.*Wik

1905 Karl Guthe Jansky (22 Oct 1905; 14 Feb 1950) was an American electrical engineer who discovered cosmic radio emissions in 1932. At Bell Laboratories in NJ, Jansky was tracking down the crackling static noises that plagued overseas telephone reception. He found certain radio waves came from a specific region on the sky every 23 hours and 56 minutes, from the direction of Sagittarius toward the center of the Milky Way. In the publication of his results, he suggested that the radio emission was somehow connected to the Milky Way and that it originated not from stars but from ionized interstellar gas. At the age of 26, Jansky had made a historic discovery - that celestial bodies could emit radio waves as well as light waves. *TIS Image: Karl Jansky makes adjustments to his antenna *Wik

1907 Sarvadaman D. S. Chowla (22 October 1907, London–10 December 1995, Laramie, Wyoming) was a prominent Indian mathematician, specializing in number theory. Among his contributions are a number of results which bear his name. These include the Bruck–Chowla–Ryser theorem, the Ankeny–Artin–Chowla congruence, the Chowla–Mordell theorem, and the Chowla–Selberg formula, and the Mian–Chowla sequence.*Wik

1916 Nathan Jacob Fine (22 October 1916 in Philadelphia, USA - 18 Nov 1994 in Deerfield Beach, Florida, USA) He published on many different topics including number theory, logic, combinatorics, group theory, linear algebra, partitions and functional and classical analysis. He is perhaps best known for his book Basic hypergeometric series and applications published in the Mathematical Surveys and Monographs Series of the American Mathematical Society. The material which he presented in the Earle Raymond Hedrick Lectures twenty years earlier form the basis for the material in this text.*SAU

1927 Alexander Ivanovich Skopin (22 Oct 1927 in Leningrad (now St Petersburg), Russia - 15 Sept 2003 in St Petersburg, Russia) He was a Russian mathematician known for his contributions to abstract algebra. Skopin's student work was in abstract algebra, and concerned upper central series of groups and extensions of fields. In the 1970s, Skopin received a second doctorate concerning the application of computer algebra systems to group theory. From that point onward he used computational methods extensively in his research, which focused on lower central series of Burnside groups. He related this problem to problems in other areas of mathematics including linear algebra and topological sorting of graphs. *Wik

1941 Stanley Mazor was born in Chicago on October 22, 1941. He studied mathematics and programming at San Francisco State University. He joined Fairchild Semiconductor in 1964 as a programmer and then a computer designer in the Digital Research Department where he shares patents on the Symbol computer. In 1969, he joined Intel. In 1977, he began his teaching career in Intel's Technical Training group, and later taught classes at Stanford, University of Santa Clara, KTH in Stockholm and Stellenbosch, S.A. In 1984 he was at Silicon Compiler Systems. He co-authored a book on chip design language while at Synopsys 1988-1994. He was invited to present The History of the Microcomputer at the 1995 IEEE Proceedings. He is currently the Training Director at BEA Systems. *CHM

DEATHS

1950 Ada Isabel Maddison (13 April 1869 in Cumberland, England - 22 Oct 1950 in Martin's Dam, Wayne, Pennsylvania, USA) A British mathematician best known for her work on differential equations. Although Maddison passed an honors exam for the University of Cambridge, she was not given a degree there. Instead, she went to Bryn Mawr in Pennsylvania. In 1893, the University of London awarded her a bachelor's degree in mathematics with honors. After further study at the University of Göttingen, Maddison went back to Bryn Mawr, where she taught as well as doing time consuming administrative work. Her will endowed a pension fund for Bryn Mawr's administrative staff.*Wik

1977 Beniamino Segre (16 February 1903 – 2 October 1977) was an Italian mathematician who is remembered today as a major contributor to algebraic geometry and one of the founders of combinatorial geometry. Among his main contributions to algebraic geometry are studies of birational invariants of algebraic varieties, singularities and algebraic surfaces. His work was in the style of the old Italian School, although he also appreciated the greater rigor of modern algebraic geometry. Another contribution of his was the introduction of finite and non-continuous structures into geometry. In his best known paper he proved the following theorem: In a Desarguesian plane of odd order, the ovals are exactly the irreducible conics. Some critics felt that his work was no longer geometry, but today it is recognized as a separate sub-discipline: combinatorial geometry.
In 1938 he lost his professorship as a result of the anti-Jewish laws enacted under Benito Mussolini's government; he spent the next 8 years in Great Britain (mostly at the University of Manchester), then returned to Italy to resume his academic career *Wik

1979 Reinhold Baer (22 July 1902 in Berlin, Germany - 22 Oct 1979 in Zurich, Switzerland) Baer's mathematical work was wide ranging; topology, abelian groups and geometry. His most important work, however, was in group theory, on the extension problem for groups, finiteness conditions, soluble and nilpotent groups. *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