## Thursday, 7 December 2017

### On This Day in Math - December 7

God made the integers, all else is Man’s work
~Leopold Kronecker

The 341st day of the year; 341 is the sum of seven consecutive primes,

and 341 is also the smallest number with seven representations as a sum of three positive squares (collect the whole set!)

341 is the smallest of the pseudoprimes base 2,  disproving a Chinese math conjecture from around 500 BC. The conjecture was that p is prime IFF it divides 2p-2.

A pseudoprime n in base b is any composite number n such that $b^{n-1} \equiv 1 Mod n$  so for this case, $2^{341-1} \equiv 1 mod (341)$
for younger students that really means if you raise two to the 340th  power, and divide by 341, you get a remainder of one.
Pseudoprimes are also called Poulet numbers, and Sarrus numbers.  "Sarrus numbers" is after Frédéric Sarrus, who, in 1819, discovered that 341 is a counterexample to the "Chinese hypothesis" mentioned above.
"Poulet numbers" appears in Monografie Matematyczne 42 from 1932, apparently because Poulet in 1928 produced a list of these numbers *OEIS

341 is also the smallest number with seven representations as a sum of three positive squares (collect the whole set!)

EVENTS

1676 The first public release of Ole Rømer's conjecture that the speed of light was finite is published in the Journal des sçavans.. He may have included a conjecture about the speed of light being finite in his presentation to the Royal Academy of Sciences in Paris on August 22 of that year, "This second inequality appears to be due to light taking some time to reach us from the satellite; light seems to take about ten to eleven minutes [to cross] a distance equal to the half-diameter of the terrestrial orbit." His final calculations of 220,000 Km/sec were presented to the Academy on 22 November, but the record of that meeting has been lost. *Wik

1725 The first meeting of the Petersburg Academy of Science was held in a meeting room of the palace of Baron Peter Pavlovich Shafirov. The meeting featured discussion of the physics theories of Wolff and Leibniz.

In 1869, the Thames Tunnel between Rotherhithe and Wapping in London, the world's first tunnel under a navigable river, was re-opened with the East London Railway line. Work had started on 2 Mar 1825. Excavation was engineered by Marc Brunel, for which he invented the tunneling shield to reduce the danger of collapse while digging through soft sediments. Beginning his own engineering career, his son Isambad Brunel assisted. They persevered through 18 years, including floods, human disasters, and delays caused by financing difficulties. Planned ramps for use by carts and freight traffic were never added due to cost, but it was opened for pedestrian use on 25 Mar 1843. It remains in use as the oldest part of the London Underground.*TIS

In 1872, the H.M.S. Challenger embarked from Portsmouth, England on the world's first scientific voyage around the world. Physicists, chemists, and biologists collaborated with expert navigators to map the sea. The Challenger was a corvette class ship, a military vessel that traveled under sail but had auxiliary steam power. The ship was fitted with a natural history laboratory where specimens were examined, identified, dissected and drawn; a chemistry laboratory; and scientific equipment. During the 4 year journey, ending on 24 May 1876, the voyage zig-zagged around the globe to visit every continent, sounded the ocean bottom to a depth of 26,850-ft, found many new species, and provided collections for scores of biologists.*TIS [First is always subject to quibbles about definitions. Thony Christie points out that Cooks 1768 voyage could claim equal status. ]

1873 Cantor wrote Dedekind that the “aggregate” of real numbers is uncountable. Five days earlier he wrote that he “had never seriously concerned himself with the problem, since it seemed to have no practical value.” *VFR
According to Dedekind's notes, Dedekind sent a new version of Cantor's proof, making its core simpler and more precise the following day . He said "this presentation was transcribed, almost word for word, in Cantor's article". When Cantor posed the problem of the denumerability of R, on November 29, Dedekind answered that he was unable to solve it, but at the same time he stated and proved the theorem on the denumerability of the set of algebraic numbers [Cantor & Dedekind 1937, 18]. Although Dedekind's letter is no longer extant, the point is confirmed by Cantor's next letter, acknowledging receipt of the proof on December 2 [Cantor & Dedekind 1937, 13]. Now, as Dedekind wrote, "after a short time, this theorem and its proof were reproduced almost literally, including the use of the technical term 'height' [HOhe], in Cantor's article" *HISTORIA MATHEMATICA 20 (1993), 343-363 On the Relations between Georg Cantor and Richard Dedekind Jos~ FERREIROS

In 1934, Wiley Post is credited with discovering the jet stream when he flew into the stratosphere over Bartlesville, Oklahoma. With the financial backing of Oklahoma oil pioneer Frank Phillips, Post planned flights to test the "thin air" in the stratosphere above 50,000 feet. The Winnie Mae, made of plywood, could not be pressurized so Post developed the pressurized flying suit, forerunner of the modern space suit. Made by B.F. Goodrich, it was of double ply rubberized parachute fabric, with pigskin gloves, rubber boots, and aluminium helmet, pressurized to 0.5 bar. In Mar 1935, Post flew from Burbank California to Cleveland Ohio in the stratosphere using the jet stream. At times, his ground speed exceeded 550 kph in a 290 kph aircraft.*TIS

1948 The ﬁrst transistor is developed at Bell Labs. See 10 July 1973. *VFR

1962 The Atlas computer was developed at Manchester, and the first production version of the machine ran on 7 December 1962. At the time of that switch-on, the Atlas was believed to be the most powerful machine in the world. *BBC NEWS

1972 Apollo 17, the last manned moon ﬂight was launched. *VFR Flight Commander Eugene Cernan was the last man on the moon. With him on the voyage of the command module America and the lunar module Challenger were Ronald Evans (command module pilot) and Harrison H. "Jack" Schmitt (lunar module pilot). In maneuvering Challenger to a landing at Taurus-Littrow, located on the southeast edge of Mare Serenitatis, Cernan and Schmitt activated a base of operations from which they completed three highly successful excursions to the nearby craters and the Taurus mountains, making the Moon their home for over three days. The mission returned on 19 Dec. *TIS (In 2004 President George Bush had made a pledge to return to the moon, and beyond, by 2020. But in September of 2009 the Augustine Commission, also known as the Human Space Flight committee, predicted a cost of an additional three-billion dollars a year, effectively killing the idea of manned flights beyond Earth orbit.)

BIRTHS

903 'Abd al-Rahman al-Sufi (December 7, 903 – May 25, 986) was a Persian astronomer also known as 'Abd ar-Rahman as-Sufi, or 'Abd al-Rahman Abu al-Husayn, 'Abdul Rahman Sufi, 'Abdurrahman Sufi and known in the west as Azophi; the lunar crater Azophi and the minor planet 12621 Alsufi are named after him. Al-Sufi published his famous Book of Fixed Stars in 964, describing much of his work, both in textual descriptions and pictures. He identified the Large Magellanic Cloud, which is visible from Yemen, though not from Isfahan; it was not seen by Europeans until Magellan's voyage in the 16th century. He also made the earliest recorded observation of the Andromeda Galaxy in 964 AD; describing it as a "small cloud".[3] These were the first galaxies other than the Milky Way to be observed from Earth.
He observed that the ecliptic plane is inclined with respect to the celestial equator and more accurately calculated the length of the tropical year. He observed and described the stars, their positions, their magnitudes and their colour, setting out his results constellation by constellation. For each constellation, he provided two drawings, one from the outside of a celestial globe, and the other from the inside (as seen from the earth).
Al-Sufi also wrote about the astrolabe, finding numerous additional uses for it : he described over 1000 different uses, in areas as diverse as astronomy, astrology, horoscopes, navigation, surveying, timekeeping, Qibla, Salah prayer, etc *Wik

1637 William Neile (7 Dec 1637 in Bishopsthorpe (near York), England - 24 Aug 1670 in White Waltham, Berkshire, England) Neile entered Wadham College, Oxford, in 1652 (but did not matriculate until 1655) where he was taught mathematics by John Wilkins and Seth Ward. He was a gentleman-commoner, meaning that he paid the highest fees and was ranked near the top of the social order just below the nobles. Gentleman-commoners had many privileges enjoying fine suites of rooms in College, and sat with the College Fellows at meals and in the common rooms. Certainly Neile was fortunate in being part of a family that was in the forefront of scientific work for certainly while Neile was a student, his father was observing with Christopher Wren in the observatory he had constructed on the roof of his house, the 'Hill House', at White Waltham. Paul Neile was also building a telescope for Gresham College at this time. In 1657 William Neile became a pupil of law at the Middle Temple in London. He went on to become a member of the privy council of King Charles II.
In 1657, while still a student at Oxford, he became the first person to find the arc length of an algebraic curve when he rectified the semicubical parabola. He communicated his results to William Brouncker and Christopher Wren at the Gresham College Society, the Society based at Gresham College, London, which a few years later became the Royal Society. Neile's work on this appeared in John Wallis's De Cycloide in 1659. As well as his mathematical work Neile made astronomical observations using instruments on the roof of his father's house, the 'Hill House' at White Waltham in Berkshire. He died in this house at the age of 32 and was buried in the local parish church. *SAU (The evolute of the parabola is a particular case of the semicubical parabola also called Neile's parabola or the cuspidal cubic. The "semi" is because it is a three-halves power, hence semi-cubic)(The wording of the plaque honoring Neile and his grave stone below are contained in The antiquities of Berkshire, By Elias Ashmole, which is available at Google Books

1823 Leopold Kronecker (7 Dec 1823; 29 Dec 1891) German mathematician who worked to unify arithmetic, algebra and analysis, with a particular interest in elliptic functions, algebraic equations, theory of numbers, theory of determinants and theory of simple and multiple integrals. However the topics he studied were restricted by the fact that he believed in the reduction of all mathematics to arguments involving only the integers and a finite number of steps. He believed that mathematics should deal only with finite numbers and with a finite number of operations. He was the first to doubt the significance of non-constructive existence proofs, and believed that transcendental numbers did not exist. The Kronecker delta function is named in his honour.*TIS

1647 Giovanni Ceva (7 Dec 1647 in Milan, Italy - 15 June 1734 in Mantua, Italy) For most of his life Giovanni Ceva worked on geometry. He discovered one of the most important results on the synthetic geometry of the triangle between Greek times and the 19th Century. The theorem states that lines from the vertices of a triangle to the opposite sides are concurrent precisely when the product of the ratio the sides are divided is 1. He published this in De lineis rectis (1678).
Ceva also rediscovered and published Menelaus's theorem. He also studied applications of mechanics and statics to geometric systems. Although he wrongly concluded that the periods of oscillation of two pendulums were in the same ratio as their lengths, he later corrected the error.
Ceva published Opuscula mathematica in 1682. In Geometria Motus (1692) he, to some extent, anticipated the infinitesimal calculus. De Re Nummeraria in 1711 is one of the first works in mathematical economics; it attempts to solve the conditions of equilibrium for the monetary system of a state like Mantua.
Ceva also did important work on hydraulics. On this topic he published Opus hydrostaticum (1728). He held official positions in Mantua and used his knowledge of hydraulics to argue successfully against a project which proposed to divert the river Reno into the river Po. *SAU (Ceva's theorem is understandable to most high school math students and (imho) should be more commonly taught.)

1830 (Antonio) Luigi (Gaudenzio Giuseppe) Cremona (7 Dec 1830; 10 Jun 1903)
was an Italian mathematician who was an originator of graphical statics (the use of graphical methods to study forces in equilibrium) and work in projective geometry. Cremona's work in statics is of great importance and he gave, in a clearer form, some theorems due to Maxwell. In a paper of 1872 Cremona took an idea of Maxwell's on forces in frame structures that had appeared in an engineering journal in 1867 and interpreted Maxwell's notion of reciprocal figures as duality in projective 3-space. These reciprocal figures, for example, have three forces in equilibrium in one figure represented by a triangle while in the reciprocal figure they are represented by three concurrent lines.*TIS

1905 Gerard Peter Kuiper (7 Dec 1905; 23 Dec 1973) Dutch-born American astronomer, who discovered Miranda, a moon of Uranus, and Nereid, a moon of Neptune. The Kuiper Belt is so-named after his original suggestion of its existence outside the orbit of Neptune before it was confirmed as a belt of small bodies. He measured the diameter of Pluto. In the Martian atmosphere Kuiper detected carbon dioxide, but the absence of oxygen (1947). In the 1960s, Kuiper pioneered airborne infrared observing using a Convair 990 aircraft and served as chief scientist for the Ranger spacecraft crash-landing probes of the moon. By analyzing Ranger photographs, he identified landing sites on the lunar surface most suitable for safe manned landings. *TIS

1910 Richard Brooke Roberts (7 Dec 1910; 4 Apr 1980) American biophysicist who contributed most to the discovery of "delayed neutrons" - that uranium fission does not release all the neutrons it produces at one time, but some come off at measurably later times. Some are emitted seconds to minutes later. This is crucial in the operation of a fission reactor. In uranium-235 fission in a thermal reactor, the proportion of delayed neutrons is about 0.65 percent. If the reactivity stays below the proportion of delayed neutrons, the reactor can be controlled. The delayed neutrons modify the rate of fission sufficiently to give time for the insertion of control rods. Without the margin of safety provided by the delayed neutrons, nuclear reactors might not be practical at all.*TIS

1924 Mary Ellen Rudin (born December 7, 1924, Hillsboro, Texas) is an American mathematician.
Born Mary Ellen Estill, she attended the University of Texas, completing her B.A. in 1944 and her Ph.D. in 1949, under Robert Lee Moore. In 1953, she married the mathematician Walter Rudin. Following her mentor Moore, her research centers on point-set topology. She was appointed as Professor of Mathematics at the University of Wisconsin in 1971, and is currently a Professor Emerita there. She served as vice-president of the American Mathematical Society, 1980–1981. In 1984 she was selected to be a Noether Lecturer. She is an honorary member of the Hungarian Academy of Sciences (1995).
Rudin is best known in topology for her constructions of counterexamples to well-known conjectures. Most famously, she was the first to construct a Dowker space, thus disproving a conjecture of Dowker's that had stood, and helped drive topological research, for more than twenty years. She also proved the first Morita conjecture and a restricted version of the second. Her latest major result is a proof of Nikiel's conjecture. Rudin's Erdős number is 1.
"Reading the articles of Mary Ellen Rudin, studying them until there is no mystery takes hours and hours; but those hours are rewarded, the student obtains power to which few have access. They are not hard to read, they are just hard mathematics, that's all." (Steve Watson)
She resides in Madison, Wisconsin, in the Rudin House, a home designed by architect Frank Lloyd Wright.*SAU

1928 Noam Chomsky is born in Philadelphia, Pennsylvania. He received his Ph.D. from the University of Pennsylvania in 1955. Since then he has taught at MIT, where he now holds the Ferrari P. Ward Chair of Modern Languages and Linguistics. Chomsky's work on the syntax of natural languages influenced the early development of programming languages. He is most famous for his work on the hierarchy of grammar that bears his name. Chomsky has been awarded an Honorary Doctorate by the University of London and the University of Chicago. In 1988 he received the Kyoto Prize in Basic Science
Chomsky has always been interested in politics. Since 1965 he has become one of the leading critics of U.S. foreign policy and divided his efforts between linguistic studies and his social concerns.*CHM

1936 Oleksandr Mikolaiovich Sharkovsky (7 Dec 1936 in Kiev, Ukraine, )attended his local university of Kiev, graduating in 1958. In 1961 he was appointed to the Institute of Mathematics of the Academy of Sciences of the Ukraine in Kiev. He also taught at the University of Kiev from 1967.
Sharkovsky's main areas of interest are the theory of dynamical systems, the theory of stability and the theory of oscillations. He also works in the theory of functional and functional differential equations, and the study of difference equations and their application.
He is perhaps best known for an important theorem on continuous functions which he proved in 1964. Although the result did not attract a great deal of interest at the time of its publication, during the 1970s other surprising results were proved which turned out to be special cases of Sharkovsky's theorem. *SAU

DEATHS

1912 Sir George Howard Darwin (9 Jul 1845, 7 Dec 1912) the second son of the famous biologist Charles Darwin, was an English astronomer who championed a theory (no longer accepted) that the Moon was once part of the Earth, in what is now the Pacific Ocean. His was the first mathematical analysis of the evolution of Earth's Moon. He suggested that since the effect of the tides has been to slow the Earth's rotation and to cause the Moon to recede from the Earth, then by extrapolating back 4.5 billion years ago the Moon and the Earth would have been very close, with a day being less than five hours. Before this time the two bodies would actually have been one, until the Moon was torn away from the Earth by powerful solar tides that would have deformed the Earth every 2.5 hours*TIS

1928 James Whitbread Lee Glaisher (5 November 1848 – 7 December 1928) son of James Glaisher, the meteorologist, was a prolific English mathematician.
He was educated at St Paul's School and Trinity College, Cambridge, where he was second wrangler in 1871.[1] Influential in his time on teaching at the University of Cambridge, he is now remembered mostly for work in number theory that anticipated later interest in the detailed properties of modular forms. He published widely over other fields of mathematics.
He was the editor-in-chief of Messenger of Mathematics. *Wik

1943 Elizabeth Ruth Naomi Belville (5 March 1854 – 7 December 1943), also known as the Greenwich Time Lady, was a businesswoman from London. She, her mother Maria Elizabeth, and her father John Henry, sold people the time. This was done by setting a watch to Greenwich Mean Time, as shown by the Greenwich clock, and then selling people the time by letting them look at the watch. *Wik A nice blog about time, and the time lady by Greg Ross at Futility Closet. and a book by David Rooney.

1952 Forest Ray Moulton (29 Apr 1872, 7 Dec 1952) American astronomer (born in the tiny town of Leroy, Michigan, population 267 in the 2000 census) who collaborated with Thomas Chamberlin in advancing the planetesimal theory of the origin of the solar system (1904). They suggested filaments of matter were ejected when a star passed close to the Sun, which cooled into tiny solid fragments, "planetesimals". Over a very long period, grains collided and stuck together. Continued accretion created pebbles, boulders, and eventually larger bodies whose gravitational force of attraction accelerated the formation of protoplanets. (This formation by accretion is still accepted, but not the stellar origin of the planetesimals.) Moulton was first to suggest that the smaller satellites of Jupiter discovered by Nicholson and others in the early 20th century were captured asteroids - now widely accepted. *TIS The crater Moulton on the Moon, the Adams-Moulton methods for solving differential equations and the Moulton plane in geometry are named after him. In incidence geometry, the Moulton plane is an example of an affine plane in which Desargues' theorem does not hold. *Wik

1970 Rube Goldberg (4 Jul 1883, 7 Dec 1970) American cartoonist who satirized the American preoccupation with technology. His name became synonymous with any simple process made outlandishly complicated because of his series of "Invention" cartoons which use a string of outlandish tools, people, plants and steps to accomplish everyday simple tasks in the most complicated way. Goldberg applied his training as a graduate engineer and used his engineering, story-telling, and drawing skills to make sure that the "Inventions" could work, even though dozens of arms, wheels, gears, handles, cups, and rods were put in motion by balls, canary cages, pails, boots, bathtubs, paddles, and even live animals for simple tasks like squeezing an orange for juice or closing a window in case it should start to rain. *TIS

1979 Cecilia Helena Payne-Gaposchkin (10 May 1900, 7 Dec 1979) was an English-born American astronomer who was the first to apply laws of atomic physics to the study of the temperature and density of stellar bodies, and the first to conclude that hydrogen and helium are the two most common elements in the universe. During the 1920s, the accepted explanation of the Sun's composition was a calculation of around 65% iron and 35% hydrogen. At Harvard University, in her doctoral thesis (1925), Payne claimed that the sun's spectrum was consistent with another solution: 99% hydrogen with helium, and just 1% iron. She had difficulty persuading her superiors to take her work seriously. It was another 20 years before Payne's original claim was confirmed, by Fred Hoyle. *TIS

1982 George Bogdanovich Kistiakowsky (November 18, 1900 – December 7, 1982) was a Ukrainian-American physical chemistry professor at Harvard who participated in the Manhattan Project and later served as President Dwight D. Eisenhower's Science Advisor.
Born in Kiev in the old Russian Empire, Kistiakowsky fled Russia during the Russian Civil War. He made his way to Germany, where he earned his PhD in physical chemistry under the supervision of Max Bodenstein at the University of Berlin. He emigrated to the United States in 1926, where he joined the faculty of Harvard University in 1930, and became a citizen in 1933.
During World War II, he was the head of the National Defense Research Committee (NDRC) section responsible for the development of explosives, and the technical director of the Explosives Research Laboratory (ERL), where he oversaw the development of new explosives, including RDX and HMX. He was involved in research into the hydrodynamic theory of explosions, and the development of shaped charges. In October 1943, he was brought into the Manhattan Project as a consultant. He was soon placed in charge of X Division, which was responsible for the development of the explosive lenses necessary for an implosion-type nuclear weapon. He watched an implosion weapon that was detonated in the Trinity test in July 1945. A few weeks later a Fat Man implosion weapon was dropped on Nagasaki.
From 1962 to 1965, he chaired the National Academy of Sciences's Committee on Science, Engineering, and Public Policy (COSEPUP), and was its vice president from 1965 to 1973.
In later years he was active in an antiwar organization, the Council for a Livable World. Kistiakowsky severed his connections with the government in protest against the US involvement in the war in Vietnam. In 1977, he assumed the chairmanship of the Council for Livable World, campaigning against nuclear proliferation. He died of cancer in Cambridge, Massachusetts, on December 17, 1982. His body was cremated, and his ashes were scattered near his summer home on Cape Cod, Massachusetts. His papers are in the Harvard University archives.*Wik

2011 Tonny Albert Springer (February 13, 1926, The Hague – December 7, 2011, Zeist) was a mathematician at Utrecht university who worked on linear algebraic groups, Hecke algebras, complex reflection groups, and who introduced Springer representations and the Springer resolution.*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