Wednesday, 7 December 2022

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

1669  Christopher Wren, architect of St Paul's London & 'rebuilder' of London marries Faith Coghil. *jdmccafferty

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 .  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

1905 One of Alfred North Whitehead's early developmental papers on philosophy, "On Mathematical concepts of the Material World" was read before the Royal Society in London, and published in the Philosophical Transactions in 1906.

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.)


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- – March 18, 2013)) was 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 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 resided until her death 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


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

Tuesday, 6 December 2022

On This Day in Math - December 6

"I have finally found a subject where I do not need to memorize, but can think things out myself – mathematics."
~Herta Taussig Freitag (from her diary, age 12)

The 340th day of the year; 340 is the sum of the first four powers of four.

340 can also be written as the sum of consecutive primes in three different ways.

340! +1 is prime. There are only thirteen day numbers of the year for which n! +1 is prime, and 340 is the last of these.

Jim Wilder@wilderlab pointed out that 340 = 41 + 42 + 43 + 44. Just think, tomorrow will be even a longer string of consecutive powers of four!


1586 Jesuit astronomer, Niccolò Zucchi, the first to attempt to build a reflecting telescope was born 6 December 1586.  In his Optica philosophia experimentis et ratione a fundamentis constituta published in 1652 he describes his attempt to create a reflecting telescope.*Thony Christie  

1592, Galileo was appointed Professor of Mathematics at the University of Padua (the University of the Republic of Venice) at a salary of three times that he had received at Pisa. On 7 December 1592 he gave his inaugural lecture and began a period of 18 years at the University, years which he later described as the happiest of his life. *British Journal of Sports Medicine (honest) 

In 1631, the transit of Venus occurred as first predicted by Kepler. He correctly predicted that an ascending node transit of Venus would occur in Dec 1631, but no-one observed it - due to the fact that it occurred after sunset for most of Europe. Kepler himself died in 1630. He not only predicted this particular transit but also worked out that transits of Venus involve a cyclical period of approximately 120 years. When such a transit is observed, Venus appears as a small black circle moving across the face of the Sun.*TIS  Kepler had predicted transits in 1631 and 1761 and a near miss in 1639. Horrocks corrected Kepler's calculation for the orbit of Venus, realized that transits of Venus would occur in pairs 8 years apart, and so predicted the transit of 1639. *Wik 

1710 An advertisement in the Old Bailey Proceedings for a book on mathematics, and more
*** The Marrow of the Mathematicks, made Plain and Easie to the Understanding of any ordinary Capacity. Containing the Doctrines of Arithmetick, Geometry, Astronomy, Gauging, the Use of the Sector, Surveying, Dyaling, and the Art of Navigation, &c. Illustrated with several Cuts, for the better Explanation of the whole Matter. After a New, Compendious, Easy Method By W. Pickering, Merchant-Adventurer.
To which is added,
Measuring Surfaces and Solids, such as Plank, Timber, Stone, &c. Joiners, Carpenters, Bricklayers, Glasiers, Painters and Paviers Work: Each Proposition being wrought Vulgarly, Decimally, Practically and Instrumentally. With a small Tract of Gauging Wine, Ale, or Malt, without Inches, or Division; by which any one may Gauge ten Backs or Floors of Malt, in the same time another shall Guage one, by the Way now used. Altogether New, and submitted to the Censure of the Honourable Commissioners of Excise. By J. L. P. M.
Both Printed for Eben. Tracy, at the Three Bibles on London-Bridge. 1710
Pedro Nunes Nonius original model
(They just don't make titles like they used to) Available on line for free here

1763 From Charles Mason's Journal of the Mason Dixon survey, "Set up a Sector brought by the Commissioners from Maryland and found that the nonius would not touch the middle part of the arch" A nonius is a device, named in honor to its author and inventor Pedro Nunes (Latin: Petrus Nonius), created in 1542 as a system for taking fine measurements on the astrolabe which could largely improve its accuracy. Later on, it was adapted in 1631 by the French mathematician Pierre Vernier, to create the vernier scale. *Wik

1830 First national observatory established at Washington, D.C. Established by the order of the Secretary of the Navy, John Branch, on 6 December 1830 as the Depot of Charts and Instruments, the Observatory rose from humble beginnings. Placed under the command of Lieutenant Louis M. Goldsborough, with an annual budget of 330 US Dollars, its primary function was the restoration, repair, and rating of navigational instruments. It was made into a national observatory in 1842 via a federal law and a Congressional appropriation of 25,000 dollars. Lieutenant James Melville Gilliss was put in charge of "obtaining the instruments needed and books." *Wik (Interestingly, Goldsborough was appointed to the Naval Academy at the age of seven, although he did not enter for several years. He rose to the rank of Admiral during the U S Civil War and three naval ships were named for him.)

1882 Venus crossed the disc of the Sun. The most recent transit of Venus when observed from Earth took place on June 8, 2004. The event received significant attention, since it was the first Venus transit to take place after the invention of broadcast media. No human alive at the time had witnessed a previous Venus transit. The next transit of Venus will occur on June 5–June 6 in 2012,. After 2012, the next transits of Venus will be in December 2117 and December 2125.*Wik
The transit of Venus across the sun was photgraphed on a series of glass plate negatives made by Amherst College astronomer David Peck Todd. He used a solar photographic telescope (made by the renowned optical firm Alvan Clark & Sons) stationed on the summit of Mount Hamilton, California, where the Lick Observatory was under construction. Of the photos, 147 survived, having been archived in the mountain vault. A century later, they were retrieved and an animation made from them premiered at the International Astronomical Union's general assembly in Sydney in Jul 2003. This is perhaps the most complete surviving record of a historical transit of Venus, dating from the time when Chester Arthur was president of the United States.*TIS

1917 Kazimierz Kuratowski gave a talk “On the definitions in mathematics,” which became his first published paper. This work grew out of Jan LLukasiewicz’s crushing criticism of the foundations of StanisLlaw Zaremba’s Theoretical Arithmetic (1912). Kuratowski’s now famous 1921 definition of ordered pair (a nice note for Alg classes) also grew out of LLukasiewicz’s critique. [Kuratowski, A Half Century of Polish Mathematics, p. 24] *VFR

1946 Birthdate of Nicolette Weil, younger daughter of the mathematician Andre Weil. She was born on St. Nicholas’ day, as he planned, or so he jokingly claimed, but she is named after Nicolas Bourbaki. Professor Weil was one of the founders of the Bourbaki group. See Joong Fang, Bourbaki, Paideia Press, 1970, p. 40. His older daughter is named Sylvie and was born 12 September 1942. *VFR

1956 The knapsack problem was first named and discussed by George B. Dantzig, the father of linear programming. *VFR (The part about naming it may be an error; the problem existed long before and *Wik has this note:) "The knapsack problem has been studied for more than a century, with early works dating as far back as 1897. It is not known how the name "knapsack problem" originated,(they should read my blog?) though the problem was referred to as such in the early works of mathematician Tobias Dantzig (1884–1956)(This was George's Father), suggesting that the name could have existed in folklore before a mathematical problem had been fully defined."


In 1957
, America's first attempt at putting a satellite into orbit failed when the Vanguard rocket carrying it blew up on the launch pad at Cape Canaveral, Florida. With a series of rumbles audible for miles around, the vehicle, having risen about four feet into the air, suddenly sank. Falling against the firing structure, fuel tanks rupturing as it did so, the rocket toppled to the ground on the northeast or ocean side of the structure in a roaring, rolling, ball-shaped volcano of flame. *TIS

1963 Time magazine published a copy of Salvador Dali’s “Fifty abstract pictures which as seen from two yards change into three Lenines masquerading as Chinese and as seen from six yards appear as the head of a royal tiger.” It is based on the semi-regular tessellation 4–3–4–3–3 made up of squares and triangles.*VFR

1987 Florida rapist Tommy Lee Andrews is the first person to be convicted as a result of DNA fingerprinting. *Wik

2005 At a book signing after a mathematics professor at West Point was asked what he taught, former president Jimmy Carter commented “In retrospect, I possibly received the best insight into human nature by studying differential equations and systems of differential equations. That subject seemed to interrelate rates of change between interconnected entities.” *VFR


1586 Niccolò Zucchi (6 Dec 1586; 21 May 1670) Italian astronomer who, in approximately 1616, designed one of the earliest reflecting telescopes, antedating those of James Gregory and Sir Isaac Newton. A professor at the Jesuit College in Rome, Zucchi developed an interest in astronomy from a meeting with Johannes Kepler. With this telescope Zucchi discovered the belts of the planet Jupiter (1630) and examined the spots on Mars (1640). He also demonstrated (in 1652) that phosphors generate rather than store light. His book Optica philosophia experimentalis et ratione a fundamentis constituta (1652-56) inspired Gregory and Newton to build improved telescopes.*TIS(I belive the observations he made were NOT with his reflecting telescope, which never seemed to work, but with the more common refracting telescope. See more on reflecting telescopes at this blog where Thony Christie takes me to task for giving (too much) credit to one of the  early developers.)

1682 Giulio Carlo Fagnano dei Toschi (December 6, 1682 – September 26, 1766) who was born in Sinigaglia, Italy. He was the founder of the geometry of the triangle, studied the lemniscate, and coined the term “elliptic integral.” *VFR
Fagnano is best known for investigations on the length and division of arcs of certain curves, especially the lemniscate; this seems also to have been in his own estimation his most important work, since he had the figure of the lemniscate with the inscription: "Multifariam divisa atque dimensa Deo veritatis gloria", engraved on the title-page of his Produzioni Matematiche, which he published in two volumes (Pesaro, 1750), and dedicated to Pope Benedict XIV. The same figure and words "Deo veritatis gloria" also appear on his tomb.
Failing to rectify the ellipse or hyperbola, Fagnano attempted to determine arcs whose difference should be rectifiable. He also pointed out the remarkable analogy existing between the integrals which represent the arc of a circle and the arc of a lemniscate. Finally he proved the formula π = 2i log((1-i)/(1+i)
One of his sons, Giovanni, is the namesake of the optimization problem called Fagnano's Problem in geometry :
For a given acute triangle determine the inscribed triangle of minimal perimeter.
The solution is the orthic triangle.

1848 Johann Palisa (6 Dec 1848; 2 May 1925) Silesian astronomer who was a prolific discoverer of asteroids, 122 in all, beginning with Asteroid 136 Austria (on 18 Mar 1874, using a 6” refractor) to Asteroid 1073 Gellivara in 1923 - all by visual observation, without the aid of photography. In 1883, he joined the expedition of the French academy to observe the total solar eclipse on May 6 of that year. During the eclipse, he searched for the putative planet Vulcan, which was supposed to circle the sun within the orbit of Mercury. In addition to observing the eclipse, Palisa collected insects for the Natural History Museum in Vienna. He also prepared two catalogs containing the positions of almost 4,700 stars. He remains the most successful visual discoverer in the history of minor planet research.*TIS

1856 Walther Franz Anton von Dyck (6 Dec 1856 in Munich, Germany - 5 Nov 1934 in Munich, Germany) Von Dyck made important contributions to function theory, group theory (where a fundamental result on group presentations is named after him) topology and potential theory. *SAU

1880 Pierre Léon Boutroux (6 December 1880 – 15 August 1922) was a French mathematician and historian of science. Boutroux is chiefly known for his work in the history and philosophy of mathematics.
He was born in Paris on 6 December 1880 into a well connected family of the French intelligentsia. His father was the philosopher Émile Boutroux. His mother was Aline Catherine Eugénie Poincaré, sister of the scientist and mathematician Henri Poincaré. A cousin, Raymond Poincaré was to be President of France.
He occupied the mathematics chair at Princeton University from 1913 until 1914. He occupied the History of sciences chair from 1920 to 1922.
Boutroux published his major work Les principes de l'analyse mathématique in two volumes; Volume 1 in 1914 and Volume 2 in 1919. This is a comprehensive view of the whole field of mathematics at the time.*Wik

1900 George Eugene Uhlenbeck (6 Dec 1900; 31 Oct 1988) Dutch-American physicist who, with Samuel A. Goudsmit, proposed the concept of electron spin (Jan 1925) - a fourth quantum number which was a half integer. This provided Wolfgang Pauli's anticipated "fourth quantum number." In their experiment, a horizontal beam of silver atoms travelling through a vertical magnetic field was deflected in two directions according to the interaction of their spin (either "up" or "down") with the magnetic field. This was the first demonstration of this quantum effect, and an early confirmation of quantum theory. As well as fundamental work on quantum mechanics, Uhlenbeck worked on atomic structure, the kinetic theory of matter and extended Boltzmann's equation to dense gases.*TIS

1907 Mathematical Logician Rosser is Born, J. Barkley Rosser is born in Jaksonville, FL. In 1934 Rosser received a Ph.D. in logic from Princeton under the supervision of Alonso Church. Rosser was able to anticipate the potential of early computers in many areas of mathematics as well as the ultimate impact of logic on the future of computing. He contributed to the Church-Rosser theorem that identifies the outer limit of what is achievable in automated theorem proving and, therefore, plays the same role in computing science as the second law of thermodynamics in engineering.
Rosser taught at Cornell and the University of Wisconsin, served as a president of the Association of Symbolic Logic and SIAM. He died on September 5, 1989. *CHM

1908 Herta Taussig Freitag (December 6, 1908 - January 25, 2000) Herta obtained a job at a private high school, the Greer School, in upstate New York. There she met Arthur H. Freitag and they were married in 1950. Herta started teaching at Hollins College (now University) in Roanoke, VA in 1948. She received a Ph.D. degree from Columbia University in 1953 and the title of her dissertation was "The Use of the History of Mathematics in its Teaching and Learning on the Secondary Level."
During Herta's years at Hollins she was a frequent guest speaker at local schools and gave lectures at both Virginia and North Carolina Governor's Schools. She published numerous articles in The Mathematics Teacher, The Arithmetic Teacher, and The Mathematics Magazine. At the request of the National Council of Teachers of Mathematics, Professor Freitag wrote the monograph, The Number Story, with her husband. In 1962 she was the first woman to be President of the Maryland-District of Columbia-Virginia Section of the Mathematical Association of America (MAA). Professor Freitag received the Hollins' Algernon Sydney Sullivan Award, which is awarded for recognition of "extraordinary humane and scholarly achievement." She officially retired from Hollins in 1971 to spend time with her husband, who was ill. After his death in 1978, Hollins welcomed her back to the classroom as a leave replacement in 1979-1980 and as a teacher in the Master of Arts in Liberal Studies (MALS) program for several years. Professor Herta Freitag was the first faculty member to receive the Hollins Medal (1979) and the first recipient of the Virginia College Mathematics Teacher of the Year award (1980).
Professor Freitag was very proud of her perfect attendance at the International Conferences of the Fibonacci Association. Most of her work with Fibonacci numbers occurred after she retired, which demonstrates the fallacy of a commonly held belief that mathematicians complete their best work before the age of 40. Professor Freitag published more than thirty articles in the Fibonacci Quarterly after 1985. The November 1996 issue of the Fibonacci Quarterly was dedicated to "Herta Taussig Freitag as she enters her 89th year, in recognition of her years of outstanding service and achievement in the mathematics community through excellence in teaching, problem solving, lecturing and research." This award was given to celebrate her 89th birthday, since 89 is a Fibonacci number. *Biographies of Women Mathematicians, Agnes Scott College web site

1941 Filep László (6 Dec 1941 in Csaszlo, Szabolcs-Szatmar-Bereg, Hungary - 19 Nov 2004 in Budapest, Hungary) He worked for the degree of dr. univ. submitting his thesis Life and work of Gyula Farkas (1847-1930) to the Kossuth University in Debrecen in 1978. But this was not László's first publication, for he had published a number of articles in the prestigious Hungarian popular scientific magazine, Termeszet Vilaga (The World of Nature). The first of these articles was Farkas Gyula (1847-1930) published in 1976, was followed by A matematika nagy nöalakjai (1977) and Helyunk a tudomany vilagaban (1979). He published many other articles on the history of mathematics such as Lajos David (1881-1962), historian of Hungarian mathematics (1981), Great female figures of Hungarian mathematics in 19th-20th centuries (1983), The development, and the developing of the concept of a , fraction (2001), The genesis of Eudoxus's infinity lemma and proportion theory (2001), From Fejer's disciples to Erdős's epsilons - change over from analysis to combinatorics in Hungarian mathematics (2002), and Irrationality and approximation of √2 and √3 in Greek mathematics (2004). He also published biographies of many mathematicians including Janos Bolyai, John C Harsanyi, John von Neumann, and Paul Erdős. László's research interest was not only in the history of mathematics for he also published a long series of papers on fuzzy groups, some written with his collaborator Iulius Gyula Maurer, beginning in 1987. *SAU


1788 Nicole-Reine Lepaute (5 Jan 1723 in Paris, France - 6 Dec 1788 in Saint-Cloud, France) was a French noblewoman who helped Lalande with astronomical calculations. In June 1757 Lalande decided that he would like to attempt to calculate a precise date for the return of Halley's comet. It was known to have been seen in 1305, 1380, 1456, 1531, 1607 and 1682 and Halley, taking into account perturbations to the orbit caused by the gravitational effects of Jupiter, had predicted that the comet would return reaching perihelion in December 1758. However the only way to get a more accurate prediction of its date of return was to calculate the perturbations to the orbit caused by the gravitational effects of both Jupiter and Saturn. Lalande approached Alexis Clairaut for help and Clairaut provided a basic programme of work requiring an extraordinary amount of computation. Lalande then asked Nicole-Reine Lepaute to assist him in the computations. Lalande wrote, "During six months we calculated from morning to night, sometimes even at meals. ... The assistance of Mme Lepaute was such that, without her I should never have been able to undertake the enormous labour, in which it was necessary to calculate the distance of each of the two planets Jupiter and Saturn from the comet, separately for each successive degree for 150 years. *SAU

1893 Rudolf Wolf (7 Jul 1816, 6 Dec 1893) Swiss astronomer and astronomical historian. Wolf's main contribution was the discovery of the 11 year sunspot cycle and he was the codiscoverer of its connection with geomagnetic activity on Earth. In 1849 he devised a system now known as Wolf's sunspot numbers. This system is still in use for studying solar activity by counting sunspots and sunspot groups. In mathematics, Wolf wrote on prime number theory and geometry, then later on probability and statistics - a long paper discussed Buffon's needle experiment. He estimated by Monte Carlo methods.*TIS

1959 Erhard Schmidt (13 Jan 1876 in Dorpat, Estonia (Russian Empire) (now Tartu, Estonia)- 16 Dec 1959 in Berlin, Germany) 1876 Erhard Schmidt (13 January 1876 – 6 December 1959) was a German mathematician whose work significantly influenced the direction of mathematics in the twentieth century. He was born in Tartu, Governorate of Livonia (now Estonia). His advisor was David Hilbert and he was awarded his doctorate from Georg-August University of Göttingen in 1905. His doctoral dissertation was entitled Entwickelung willkürlicher Funktionen nach Systemen vorgeschriebener and was a work on integral equations.
Together with David Hilbert he made important contributions to functional analysis. He is best known for the Gram-Schmidt orthogonalisation process, which constructs an orthogonal base from any vector space. *Wik

1973 Joseph Leonard Walsh, (September 21, 1895 – December 6, 1973) was an American mathematician. His work was mainly in the field of analysis.
For most of his professional career he studied and worked at Harvard University.*Wik

1990 Lev Arkad'evich Kaluznin (31 Jan 1914 in Moscow, Russia - 6 Dec 1990 in Moscow, Russia) Kaluznin is best known for his work in group theory and in particular permutation groups. He studied the Sylow p-subgroups of symmetric groups and their generalisations. In the case of symmetric groups of degree pn, these subgroups were constructed from cyclic groups of order p by taking their wreath product. His work allowed computations in groups to be replaced by computations in certain polynomial algebras over the field of p elements. Despite the fact that the earliest applications of wreath products of permutation groups was due to C Jordan, W Specht and G Polya, it was Kaluznin who first developed special computational tools for this purpose. Using his techniques, he was able to describe the characteristic subgroups of the Sylow p-subgroups, their derived series, their upper and lower central series, and more. These results have been included in many textbooks on group theory. *SAU

1993 Wolfgang Paul (10 Aug 1913, 6 Dec 1993) German physicist who developed the Paul trap, an electromagnetic device that captures ions and holds them long enough for study and precise measurement of their properties. During the 1950s he developed the so-called Paul trap as a means of confining and studying electrons. The device consists of three electrodes - two end caps and an encircling ring. The ring is connected to an oscillating potential. The direction of the electric field alternates; for half the time the electron is pushed from the caps to the ring and for the other half it is pulled from the ring and pushed towards the caps. For his work he shared the 1989 Nobel Prize for Physics with Hans G. Dehmelt and Norman F. Ramsey.*TIS

1996 Stefan Schwarz (18 May 1914 in Nové Mesto nad Váhom, Austria-Hungarian Empire (now Slovakia) - 6 Dec 1996 in Bratislava, Slovak Republic) In addition to his work on semigroups, number theory and finite fields, Schwarz contributed to the theory of non-negative and Boolean matrices.
Schwarz organized the first International Conference on Semigroups in 1968. At this conference setting up the journal Semigroup Forum was discussed and Schwarz became an editor from Volume 1 which appeared in 1970, continuing as editor until 1982. This was not his first editorial role since he had been an editor of the Czechoslovak Mathematical Journal from 1945 and continued to edit this journal until he was nearly 80 years old. He also founded the Mathematico-Physical Journal of the Slovak Academy of Sciences in 1950 and continued as an editor of the mathematics part of the journal when it split from the physics part to become Mathematica Slovaca until 1990. *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

Monday, 5 December 2022

On This Day in Math - December 5


The Knot gate at Cambridge Math Dept

…separation of the observer from the phenomenon to be observed is no longer possible.
~Werner Heisenberg

The 339th day of the year; the plane can be divided into 339 regions with 13 hyperbolae.

There are also 339 possible 2x2 matrices with integer entries between zero and 13.

I just discovered the term emirprimes (semiprime reversed) for numbers like 339 and 933 which are semiprimes that are reversals of each other.  339 = 3 x 113 and 933 is 311 x 3, even the factors are reversals of each other.

339 is the fourth, and last, day of the year which can be expressed as the sum of the squares of three consecutive primes.
Be amazed, someone checked and found that 339 (repeated 339 times) x 2339 - 1 is prime. (What! You don't believe it, well factor it and prove they're wrong.)


1610 Benedetto Castelli, a former student of Galileo, wrote him, that if Copernicus was correct, Venus should sometimes appear “horned” and sometimes not. *VFR (Venus is at its brightest as it approaches Earth, when it appears as a crescent. Many cultures around the world describe it as the 'horned star', which suggests that early astronomers, although lacking telescopes, could somehow make out its crescent shape.)
Castelli wrote to Galileo
If the position of Copernicus, that Venus revolves around the sun, is true (as I believe), it is clear that it would necessarily sometimes be seen by us horned and sometimes not, even though the planet maintains the same position relative to the sun. ... Now I want to know from you if you, with the help of your marvellous glasses, have observed such a phenomenon, which will be, beyond doubt, a sure means to convince even the most obstinate mind. I also suspect a similar thing with Mars near the quadrature with the sun; I don't mean a horned or non-horned shape, but only a semicircular and a more full one.
It is now impossible to prove whether this idea occurred to both Galileo and Castelli at the same time, or whether this letter of Castelli made Galileo turn his telescope on Venus to see if it showed phases. Certainly by 11 December Galileo had discovered that Venus did indeed appear as a crescent for on that day he wrote to Giuliano d'Medici expressing the discovery in code. It is of little consequence which scenario is correct, for in either case Castelli came up with one of the most important ideas of the time. *SAU

1658 Simon Douw wins court judgement against Christian Huygen.
“Today, no clock by Simon Douw is known; I find that most curious, it is as if he has been excised from history, deliberately. Dutch Court papers described Douw as "City clockmaker of Rotterdam... a master in the art of great tower, domestic or office clocks", ("en meester in de kunst van groote Toorn, Camer ofte Comptoirwerken"). Yet his mechanical insights. his escapement, also his drive mechanisms, are best, and now only, revealed by his Patent Grant on
August 9th, 1658, and by the evidence and judgement in a claim and counterclaim
started in the Provinces of Holland and West Friesland, but then
referred to the Court of The Netherlands in October 1658, with a Judgement
by Consent on December 5th, 1658. And that case went entirely in Douw's
favour, against the highly favoured joint Complainants of Huygens and Coster.
In itself, that is remarkable. Huygens, the Noble patrician, the most famous
Dutch scientist, and the self-professed inventor of the pendulum clock, who
had in the course of this trial published "Horologium", was forced by the
judges to settle the case rather than face unfavourable verdict; also to concede
Consent; also one-third Royalties to Douw. It would have been a crushing
humiliation for Huygens, the seed of his libels. Subsequently, the Lower
Court of Holland, Zeeland and Friesland confirmed to Douw, on December
16th and 19th 1658, their Upper Court's judgement by consent”.
* Keith Piggottm, antique Horology

1735 Euler presents his paper on “The sums of Series of reciprocals” to the St Petersburg Academy. Regarding the series 1+1/4 + 1/9 …. he writes, “I have shown the sum of the series to be approximately 1.644934066842264364 (“Euler calculates as other men breath”); multiplying the number by six, and then taking the square root.. “ and he shows that it is equal to pi, again expressed to nineteen digits accuracy. He then found the sum of the series of powers of the harmonic sequence for n= 4,6,8, 10 and 12

1776 The first scholastic fraternity in America, Phi Beta Kappa, was organized at William and Mary College in Virginia. *VFR

1825 Abel wrote how delighted he was that Crelle was starting a new mathematics journal, for it meant he would now have a place to publish his researches. The first volume contained seven papers by Abel*VFR

1851 J. J. Sylvester Receives a letter from Arthur Cayley that "amounted to a birth certificate" of their theory of invariants. Giving a relationship between invariants and differential equations, Cayley states that "This will constitute the foundation of a new theory of invariants." *Karen Hunger Parshall, James Joseph Sylvester: Jewish Mathematician in a Victorian World

1883 Sylvester, in Baltimore, received a cable containing the single word “Elected,” informing him of his appointment as Savilian Professor of Geometry at Oxford. This ended his seven year stay at Johns Hopkins. *Osiris, 1(1936), 150

1890 Harold Jacoby, later head of the Department of Astronomy at Columbia University, proposed at a meeting of the New York Mathematical Society that they publish a bulletin. In October 1891, the first issue of the Bulletin of the New York Mathematical Society, A Historical and Critical Review of Mathematical Science appeared. *VFR

1979 Iran issued a stamp commemorating the 600th anniversary of the death of the mathematician Ghyath-al-din Jamshid Kashani. He is pictured with an astrolabe in the background.*VFR

1941 Zuse Completes Z3 Machine: Konrad Zuse completes his Z3 computer, the first program-controlled electromechanical digital computer. It followed in the footsteps of the Z1 - the world’s first binary digital computer - which Zuse had developed in 1938. Much of Zuse’s work was destroyed in World War II, although the Z4, the most sophisticated of his creations, survives. *CHM Thony C. at The Renaissance Mathematicus has a nice post about Zuse and Computing

1965 The First Ph.D. Dissertation in Computer Science is Presented;
Richard L.Wexelblat was the first candidate in a computer science program to complete a dissertation. Many doctorate candidates had performed computer-related work, but Wexelblat’s diploma, presented by the University of Pennsylvania - the home of the ENIAC - was the first one to carry the designation computer science.*CHM

2012 The Atlas computer was developed at Manchester, and the first production version of the machine ran almost 50 years ago, on 7 December 1962.
At the time of that switch-on, the Atlas was believed to be the most powerful machine in the world.
On 4 and 5 December, scientists and engineers who created Atlas as well as former students who learned to code on the machine will attend events to commemorate the achievement at Manchester's Museum of Science and Industry. *BBC


1863 Paul Painlevé (5 Dec 1863; 29 Oct 1933) French politician, mathematician, and patron of aviation. Painlevé received a doctorate in mathematics from Paris in 1887. In his work on differential equations and mechanics, he solved, using Painlevé functions, differential equations which Poincaré and Picard had failed to solve. He took a special interest in aviation, applying his theoretical skills to study the theory of flight. He was Wilbur Wright's first passenger making a record 1 hr 10 min flight, then within a year he created the first university course in aeronautical mechanics. Although less skilled in politics than mathematics he began a political career in 1906 leading to two periods as French Prime Minister at a crucial period of World War I and again during the 1925 financial crisis. *TIS

1868 Arnold Johannes Wilhelm Sommerfeld (5 December 1868 – 26 April 1951) was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and groomed a large number of students for the new era of theoretical physics. He was nominated a record 81 times for the Nobel Prize, and served as PhD supervisor for more Nobel prize winners in physics than any other supervisor before or since. He introduced the 2nd quantum number (azimuthal quantum number) and the 4th quantum number (spin quantum number). He also introduced the fine-structure constant, and pioneered X-ray wave theory.*Wik

1895 Elbert Frank Cox (December 5, 1895–November 28, 1969) was an American mathematician who became the first black person in the world to receive a Ph.D. in mathematics. He spent most of his life as a professor at Howard University in Washington, D.C., where he was known as an excellent teacher. During his life, he overcame various difficulties which arose because of his race. In his honor, the National Association of Mathematicians established the Cox-Talbot Address, which is annually delivered at the NAM's national meetings. The Elbert F. Cox Scholarship Fund, which is used to help black students pursue studies, is named in his honor as well.*Wik

1901 Werner Karl Heisenberg (5 Dec 1901; 1 Feb 1976) was the German physicist and philosopher who discovered a way to formulate quantum mechanics in terms of matrices (1925). For that discovery, he was awarded the Nobel Prize for Physics for 1932. In 1927 he published his indeterminacy, or uncertainty, principle, upon which he built his philosophy and for which he is best known. He also made important contributions to the theories of the hydrodynamics of turbulence, the atomic nucleus, ferromagnetism, cosmic rays, and elementary particles, and he planned the first post-World War II German nuclear reactor, at Karlsruhe, then in West Germany. *TIS

1903 Cecil Frank Powell (5 Dec 1903; 9 Aug 1969) British physicist and winner of the Nobel Prize for Physics in 1950 for his development of the photographic method of studying nuclear processes and for the resulting discovery of the pion (pi-meson), a heavy subatomic particle. The pion proved to be the hypothetical particle proposed in 1935 by Yukawa Hideki of Japan in his theory. *TIS

1932 Sheldon Lee Glashow (5 Dec 1932, ) American theoretical physicist who, with Steven Weinberg and Abdus Salam, received the Nobel Prize for Physics in 1979 for their complementary efforts in formulating the electroweak theory, which explains the unity of electromagnetism and the weak force.*TIS

1943 Robin James Wilson (5 December, 1943 - ) is an emeritus professor in the Department of Mathematics at the Open University, having previously been Head of the Pure Mathematics Department and Dean of the Faculty. He was a Stipendiary Lecturer at Pembroke College, Oxford and, as of 2006, Professor of Geometry at Gresham College, London, where he has also been a visiting professor. On occasion, he guest teaches at Colorado College.
From January 1999 to September 2003, Robin Wilson was editor-in-chief of the European Mathematical Society Newsletter.[4]
He is the son of Harold Wilson, former Prime Minister of the United Kingdom. He is married with two daughters.
Professor Wilson's academic interests lie in graph theory, particularly in colouring problems, e.g. the four colour problem, and algebraic properties of graphs.
He also researches the history of mathematics, particularly British mathematics and mathematics in the 17th century and the period 1860 to 1940 and the history of graph theory and combinatorics.
Due to his collaboration on a 1977 paper[6] with the noted Hungarian mathematician Paul Erdős, Wilson has an Erdős number of 1. *Wik


1708 Takakazu Seki Kawa (1642 in Fujioka, Kozuke, Japan
- 5 Dec 1708 in Edo (now Tokyo), Japan) a Japanese mathematician in the Edo period.
Seki laid foundations for the subsequent development of Japanese mathematics known as wasan; and he has been described as "Japan's Newton".
He created a new algebraic notation system and, motivated by astronomical computations, did work on infinitesimal calculus and Diophantine equations. A contemporary of Gottfried Leibniz and Isaac Newton, Seki's work was independent. His successors later developed a school dominant in Japanese mathematics until the end of the Edo period.
While it is not clear how much of the achievements of wasan are Seki's, since many of them appear only in writings of his pupils, some of the results parallel or anticipate those discovered in Europe. For example, he is credited with the discovery of Bernoulli numbers. The resultant and determinant (the first in 1683, the complete version no later than 1710) are attributed to him. This work was a substantial advance on, for example, the comprehensive introduction of 13th-century Chinese algebra made as late as 1671, by Kazuyuki Sawaguchi. *Wik

1770 James Stirling (1692, 5 Dec 1770) Scottish mathematician who contributed important advances to the theory of infinite series and infinitesimal calculus. His most important book, Methodus Differentialis (1730), was written while in London. It is a treatise on infinite series, summation, interpolation and quadrature, and the text includes the asymptotic formula for n! for which Stirling is best known. In 1735 he returned to Scotland where he became manager of the 'Scotch mining company, Leadhills'. In 1745 Stirling published a paper on the ventilation of mine shafts. *TIS

1859 Louis Poinsot was the inventor of geometrical mechanics, investigating how a system of forces acting on a rigid body could be resolved into a single force and a couple.*SAU

1973 Sir Robert Alexander Watson-Watt (13 Apr 1892, 5 Dec 1973) Scottish physicist who is credited with the development of radar location of aircraft, in England. He studied at St Andrews University, taught at Dundee University, and in 1917 worked in the Meteorological Office, designing devices to locate thunderstorms, and investigating the ionosphere (a term he invented in 1926). He became head of the radio section of the National Physical Laboratory (1935), where he began work on locating aircraft. His work led to the development of radar (RAdio Detection And Ranging) which played a vital role in the defence of Britain against German air raids in 1940. He was knighted in 1942. *TIS

1999 Nathan Jacobson (October 5, 1910, Warsaw, Congress Poland, Russian Empire — December 5, 1999, Hamden, Connecticut) was an American mathematician.
Born in Warsaw, Jacobson emigrated to America with his Jewish family in 1918. Recognized as one of the leading algebraists of his generation, he was also famous for writing more than a dozen standard textbooks. *Wik

2001 Franco Dino Rasetti (August 10, 1901 – December 5, 2001) was an Italian scientist. Together with Enrico Fermi, he discovered key processes leading to nuclear fission. Rasetti refused to work on the Manhattan Project, however, on moral grounds.*Wik

2005 Claude Ambrose Rogers (1 Nov 1920, 5 Dec 2005) wrote extensively on Number Theory and on Sphere-packing problems.Roger's continues to produce a remarkable mathematical output having published to date over 170 papers. His early work was on number theory and he wrote on Diophantine inequalities and the geometry of numbers. Jointly with Erdős, he wrote The covering of n-dimensional space by spheres (1953) and Covering space with convex bodies (1961), writing many other articles on coverings and packings including Covering space with equal spheres with Coxeter. His later work covered a wide range of different topics in geometry and analysis including Borel functions, Hausdorff measure and local measure, topological properties of Banach spaces and upper semicontinuous functions. Rogers has written two important books, Packing and Covering in 1964 and Hausdorff Measures in 1970. *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

Sunday, 4 December 2022

On This Day in Math - December 4


Taking him for all and all, I think it will be conceded that Michael Faraday was the greatest experimental philosopher the world has ever seen.
~John Tyndall

The 338th day of the year; the last day of the year which will be twice a perfect square.

338 is the arithmetic mean of two triangular numbers.

338 is the smallest number for which the number of divisors (6) and the sum of its prime factors (28) are both perfect numbers. Are there others?


1639 "On this day in 1639 Jeremiah Horrocks and William Crabtree were the first human beings to have recorded a transit of Venus. ...  Moreover, Horrocks predicted the event from his own calculations, improving on Kepler’s ephemeris of Venus and the sun. Horrocks still used the old Julian calendar, which differed then by 10 days with the Gregorian calendar we use today. That is, to Horrocks the transit took place on November 24, (see my blog for that date) while in the rest of Europe it was already December 4."  The image is from the same site . " It’s a mosaic showing Horrocks observing the transit of Venus, and a line from one of his own poems: His mortal eyes to scan the furthest heavens."  *Transit of Venus 
 image by Mark Phillips

1679 Philosopher Thomas Hobbes died, thus ending his 25 year feud with John Wallis over Hobbes’s attempt to square the circle in 1655. It began when Hobbes called Wallis’s Arithmetica Infinitorum a “scab of symbols”. *VFR

1930 Wolfgang Pauli writes to propose the existence of what would come to be called the neutrino
--in it he thinks very widely of missing stuff, of some of the basic bits of the universe, in a rather open and guarded way, about the ghost of the neutron. He didn't feel very comfortable with his ideas yet, at least for professional consumption--that would have to wait another three years when it was discussed at the 7th Solvay Conference (1933) and another three when it first came into print (1936). The name "neutron" would also be changed to the familiar "neutrino" ("little one") by Enrico Fermi in 1933 to differentiate it from the much larger nuclear particle discovered the year earlier by James Chadwick--Chadwick's paper was published in Nature, which would reject Fermi's paper in 1934 as too radical a leap.
A translation appears here "Dear Radioactive Ladies and Gentlemen" ,*Ptak Science Books

1965 Gemini 7 (officially Gemini VII) lifted off, the fourth crewed spaceflight in NASA's Gemini program. The crew of Frank Borman and Jim Lovell spent nearly 14 days in space, making a total of 206 orbits. Their spacecraft was the passive target for the first crewed space rendezvous performed by the crew of Gemini 6A.

1980 Ireland issued a stamp picturing Robert Boyle (1627-1691) and his 1659 Air Pump. [Scott #492]. *VFR

1985 Cray X-MP Supercomputer Begins Operation. The Cray X-MP/48 started operation at the San Diego Supercomputer Center. The X-MP was popular for generating computer graphics, especially for movies. It nearly doubled the operating speed of competing machines with its parallel processing system, which ran at 420 million floating-point operations per second, or megaflops. An even faster speed could be achieved by arranging two Crays to work together on different parts of the same problem. Other applications included the defense industry and scientific research.*CHM

In 1998, the space shuttle Endeavour and a crew of six blasted off on the first mission to begin assembling the international space station.*TIS


1795 Thomas Carlyle (4 Dec 1795 in Ecclefechan, Dumfriesshire, Scotland - 5 Feb 1881 in Chelsea, London, England) was a Scottish writer who was also interested in mathematics. He translated Legendre's work.*SAU

1806 John Thomas Graves (4 December 1806, Dublin, Ireland–29 March 1870, Cheltenham, England) was an Irish jurist and mathematician. He was a friend of William Rowan Hamilton, and is credited both with inspiring Hamilton to discover the quaternions and with personally discovering the octonions, which he called the octaves. He was the brother of both the mathematician Charles Graves and the writer and clergyman Robert Perceval Graves.
In his twentieth year (1826) Graves engaged in researches on the exponential function and the complex logarithm; they were printed in the Philosophical Transactions for 1829 under the title An Attempt to Rectify the Inaccuracy of some Logarithmic Formulæ. M. Vincent of Lille claimed to have arrived in 1825 at similar results, which, however, were not published by him till 1832. The conclusions announced by Graves were not at first accepted by George Peacock, who referred to them in his Report on Algebra, nor by Sir John Herschel. Graves communicated to the British Association in 1834 (Report for that year) on his discovery, and in the same report is a supporting paper by Hamilton, On Conjugate Functions or Algebraic Couples, as tending to illustrate generally the Doctrine of Imaginary Quantities, and as confirming the Results of Mr. Graves respecting the existence of Two independent Integers in the complete expression of an Imaginary Logarithm. It was an anticipation, as far as publication was concerned, of an extended memoir, which had been read by Hamilton before the Royal Irish Academy on 24 November 1833, On Conjugate Functions or Algebraic Couples, and subsequently published in the seventeenth volume of the Transactions of the Royal Irish Academy. To this memoir were prefixed A Preliminary and Elementary Essay on Algebra as the Science of Pure Time, and some General Introductory Remarks. In the concluding paragraphs of each of these three papers Hamilton acknowledges that it was "in reflecting on the important symbolical results of Mr. Graves respecting imaginary logarithms, and in attempting to explain to himself the theoretical meaning of those remarkable symbolisms", that he was conducted to "the theory of conjugate functions, which, leading on to a theory of triplets and sets of moments, steps, and numbers" were foundational for his own work, culminating in the discovery of quaternions.
For many years Graves and Hamilton maintained a correspondence on the interpretation of imaginaries. In 1843 Hamilton discovered the quaternions, and it was to Graves that he made on 17 October his first written communication of the discovery. In his preface to the Lectures on Quaternions and in a prefatory letter to a communication to the Philosophical Magazine for December 1844 are acknowledgments of his indebtedness to Graves for stimulus and suggestion. After the discovery of quaternions, Graves employed himself in extending to eight squares Euler's four-square identity, and went on to conceive a theory of "octaves" (now called octonions) analogous to Hamilton's theory of quaternions, introducing four imaginaries additional to Hamilton's i, j and k, and conforming to "the law of the modulus".
Graves devised also a pure-triplet system founded on the roots of positive unity, simultaneously with his brother Charles Graves, the bishop of Limerick. He afterwards stimulated Hamilton to the study of polyhedra, and was told of the discovery of the icosian calculus. *Wik

1886 Ludwig Georg Elias Moses Bieberbach (4 Dec 1886 in Goddelau, Darmstadt in Hessen, Germany - 1 Sept 1982 in Oberaudorf in Oberbayern, Germany) Born in Goddelau, near Darmstadt, he studied at Heidelberg and under Felix Klein at Göttingen, receiving his doctorate in 1910. His dissertation was titled On the theory of automorphic functions (German: Theorie der automorphen Funktionen). He began working as a Privatdozent at Königsberg in 1910 and as Professor ordinarius at the University of Basel in 1913. He taught at the University of Frankfurt in 1915 and the University of Berlin from 1921–45.
Bieberbach wrote a habilitation thesis in 1911 about groups of Euclidean motions – identifying conditions under which the group must have a translational subgroup whose vectors span the Euclidean space – that helped solve Hilbert's 18th problem. He worked on complex analysis and its applications to other areas in mathematics. He is known for his work on dynamics in several complex variables, where he obtained results similar to Fatou's. In 1916 he formulated the Bieberbach conjecture, stating a necessary condition for a holomorphic function to map the open unit disc injectively into the complex plane in terms of the function's Taylor series. In 1984 Louis de Branges proved the conjecture (for this reason, the Bieberbach conjecture is sometimes called de Branges' theorem). There is also a Bieberbach theorem on space groups.*Wik

1890 Harry Clyde Carver (December 4, 1890 – January 30, 1977) was an American mathematician and academic, primarily associated with the University of Michigan. He was a major influence in the development of mathematical statistics as an academic discipline.
Born in Waterbury, Connecticut, Carver was educated at the University of Michigan, earning his B.S. degree in 1915, and the next year becoming an instructor in mathematics; he taught statistics in actuarial applications. At the time, the University of Michigan was only the second such institution in the United States to offer this type of course, after the pioneering Iowa State University. Carver was appointed assistant professor at Michigan in 1918, then associate professor (1921) and full professor (1936); during this period the University's program in mathematical statistics and probability underwent significant expansion.
In 1930 Carver founded the journal Annals of Mathematical Statistics, which over time became an important periodical in the field. Financial support, however, was lacking in the midst of the Great Depression; in January 1934 Carver undertook financial responsibility for the Annals and maintained the existence of the journal at his own expense. In 1935 he helped to start the Institute of Mathematical Statistics, which in 1938 assumed control over the journal; Samuel S. Wilks succeeded Carver as editor in the same year. The Institute has named its Harry C. Carver Medal after him.
With the coming of World War II, Carver devoted his energies to solving problems in aerial navigation, an interest he maintained for the remainder of his life. *Wik

1924 Frank Press (4 Dec 1924, )American geophysicist known for his investigations of the structure of the Earth's crust and mantle and the mechanics of earthquakes. Press pioneered the use of seismic waves to explore subsurface geological structures and for his pioneering use of waves to explore Earth's deep interior. In 1950, with William Maurice Ewing, a major innovator in modern geology at Columbia University, he invented an improved seismograph,and they published a landmark paper recognized as beginning a new era in structural seismology. While at Caltech (1955-65) and later MIT, Press became knownin public policy circles for his work on seismic detection of underground nuclear tests and for advocacating a national program for earthquake prediction capabilities. *TIS

1938 George Eyre Andrews (December 4, 1938 in Salem, Oregon) is an American mathematician working in analysis and combinatorics. He is currently an Evan Pugh Professor of Mathematics at Pennsylvania State University. He received his PhD in 1964 at University of Pennsylvania where his advisor was Hans Rademacher.
Andrews's contributions include several monographs and over 250 research and popular articles on q-series, special functions, combinatorics and applications. He is considered to be the world's leading expert in the theory of integer partitions.[citation needed] In 1976 he discovered Ramanujan's Lost Notebook. He is highly interested in mathematical pedagogy, and is a vocal critic of the "calculus reform" movement.*Wik


1131 Omar Khayyam (18 May 1048, 4 Dec 1131) Persian poet, mathematician, and astronomer. Khayyam, who was born at Nishapur (now in Iran), produced a work on algebra that was used as a textbook in Persia until this century. In geometry, he studied generalities of Euclid and contributed to the theory of parallel lines. Around 1074, he set up an observatory and led work on compiling astronomical tables, and also contributed to the reform of the Persian calendar. His contributions to other fields of science included developing methods for the accurate determination of specific gravity. He is known to English-speaking readers for his "quatrains" as The Rubáiyát of Omar Khayyám, published in 1859 by Edward Fitzgerald, though it is now regarded as an anthology of which little or nothing may be by Omar. *TIS   A nice blog with more detail about the Persian Polymath is at Galileo's Pendulum .

1574 Georg Joachim Rheticus (16 Feb 1514, 4 Dec 1574) Austrian-born astronomer and mathematician who was among the first to adopt and spread the heliocentric theory of Nicolaus Copernicus. He was first taught by his father, a physician, who was beheaded for sorcery in 1528, while Rheticus was still a teenager. He is best known as the first disciple of Copernicus. In 1540, Rheticus published the first account of the heliocentric hypothesis which had been elaborated by Copernicus, entitled Narratio prima, which was explicitly authorised by Copernicus, who also asked for his friend's aid in editing the edition of his De revolutionibus orbium coelestium ("On the revolutions of the heavenly spheres"). Rheticus was the first mathematician to regard the trigonometric functions in terms of angles rather than arcs of a circle.*TIS
The First Copernican: Georg Joachim Rheticus and the Rise of the Copernican Revolution

(I have seen his date of death also listed as the Dec 5th)

1798 Luigi Galvani (9 Sep 1737, 4 Dec 1798) Italian physician and physicist studied the structure of organs and the physiology of tissues who is best known for his investigation of the nature and effects of what he conceived to be electricity in animal tissue. He observed how frog muscles twitched when they were touched by metal contacts but he wrongly attributed this to innate "animal electricity" (the current was actually produced by the metal contacts). This was disputed by Alessandro Volta who, in the course of this argument, invented his electrochemical cell. The current produced by this device was for many years called galvanic electricity. The galvanometer was named after him.*TIS

1850 William Sturgeon (22 May 1783, 4 Dec 1850) English electrical engineer who devised the first electromagnet capable of supporting more than its own weight (1825). The 7-oz (200-g) magnet supported 9-lb (4-kg) of iron with a single cell's current. He built an electric motor (1832) and invented the commutator, now part of most modern electric motors. In 1836, he invented the first suspended coil galvanometer, a device for measuring current. Sturgeon also worked on improving the voltaic battery, developing a theory of thermoelectricity, and even atmospheric charge conditions. From 500 kite flights made in calm weather, he found the atmosphere is consistently charged positively with respect to the Earth, and increasingly so at increased height.*TIS

1893 John Tyndall (2 Aug 1820, 4 Dec 1893)British physicist who demonstrated why the sky is blue. His initial scientific reputation was based on a study of diamagnetism. He carried out research on radiant heat, studied spontaneous generation and the germ theory of disease, glacier motion, sound, the diffusion of light in the atmosphere and a host of related topics. He showed that ozone was an oxygen cluster rather than a hydrogen compound, and invented the firemans respirator and made other less well-known inventions including better fog-horns. One of his most important inventions, the light pipe, has led to the development of fibre optics. The modern light instrument is known as the gastroscope, which enables internal observations of a patient's stomach without surgery. Tyndall was a very popular lecturer. *TIS

1934 Sir Horace Lamb (27 Nov 1849, 4 Dec 1934) English mathematician who contributed to the field of mathematical physics. Topics he worked on include wave propagation, electrical induction, earthquakes, and the theory of tides. He wrote important papers on the oscillations of a viscous spheroid, the vibrations of elastic spheres, waves in elastic solids, electric waves and the absorption of light. In a famous paper in the Proceedings of the London Mathematical Society he showed how Rayleigh's results on the vibrations of thin plates fitted with the general equations of the theory. Another paper reported on his study of the propagation of waves on the surface of an elastic solid where he tried to understand the way that earthquake tremors are transmitted around the surface of the Earth.*TIS

1948 Frank Albert Benford, Jr., (1883 Johnstown, Pennsylvania – December 4, 1948) was an American electrical engineer and physicist best known for rediscovering and generalizing Benford's Law, a statistical statement about the occurrence of digits in lists of data.
Benford is also known for having devised, in 1937, an instrument for measuring the refractive index of glass. An expert in optical measurements, he published 109 papers in the fields of optics and mathematics and was granted 20 patents on optical devices.
His date of birth is given variously as May 29 or July 10, 1883. After graduating from the University of Michigan in 1910, Benford worked for General Electric, first in the Illuminating Engineering Laboratory for 18 years, then the Research Laboratory for 20 years until retiring in July 1948. He died suddenly at his home on December 4, 1948. *Wik

1978 Samuel Abraham Goudsmit (11 Jul 1902, 4 Dec 1978) Dutch-born U.S. physicist who, with George E. Uhlenbeck, a fellow graduate student at the University of Leiden, Neth., formulated (1925) the concept of electron spin. It led to recognition that spin was a property of protons, neutrons, and most elementary particles and to a fundamental change in the mathematical structure of quantum mechanics. Goudsmit also made the first measurement of nuclear spin and its Zeeman effect with Ernst Back (1926-27), developed a theory of hyperfine structure of spectral lines, made the first spectroscopic determination of nuclear magnetic moments (1931-33), contributed to the theory of complex atoms and the theory of multiple scattering of electrons, and invented the magnetic time-of-flight mass spectrometer (1948).*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