Tuesday 28 November 2023

On This Day in Math November 28


Newton is, of course, the greatest of all Cambridge professors; he also happens to be the greatest disaster that ever befell not merely Cambridge mathematics in particular, but British mathematical science as a whole.
~Leonard Roth
(This quote probably needs a brief explanation for young readers.  The conflict between Newton and Leibniz over the discovery of Calculus isolated England from the more rapidly developing function notations used in Europe. It would not be until the mid 19th century that young  British Intellectuals would press to adopt the continental ideas.)

The 332nd day of the year; 332 is the number of ways to partition 47 into non-zero triangular numbers.  (36 + 10 + 1 would be one such way)

The sum of the first 332 primes is a prime.

As numbers get larger and larger, it would seem that there would be fewer and fewer primes in each century of them, such as from 100 to 199.  But there seem to be a large number of centuries with only six primes.  There are only five year days such that between 100*n and 100*n+99 there are exactly six primes. 332 is one of them.  (there are exactly six primes between 33200 and 33299)


In 2348 BC, a supposed comet under divine guidance passed near Earth, causing the Great Flood, in the opinion of Anglican priest and mathematician, William Whiston. In his time, the water composition of comets was known. He said the forty days of rain resulted from the Earth's travel through the comet's tail. The body's gravity stretched and cracked the earth's brittle crust, and waters arose from the "fountains of the great deep." He explained this in his popular treatise New Theory of the Earth (1696), describing the Book of Genesis in terms of physics based on the Principia written by his mentor, Isaac Newton. Whiston succeeded Newton and became the third Lucasian Professor of Mathematics at Cambridge University (May 1702)*TIS
Whiston was expelled from his chair on 30 October 1710; at the appeal of the heads of colleges. Whiston was removed from his position at Cambridge, and denied membership in the Royal Society for his “heretical” views. He took the “wrong” side in the battle between Arianism and the Trinitarian view, but his brilliance still made the public attend to his proclamations. (V Fred Rickey put it this way, "it is not acceptable to be a unitarian at the College of the Whole and Undivided Trinity".) When he predicted the end of the world by a collision with a comet in October 16th of 1736 the Archbishop of Canterbury had to issue a denial to calm the panic.

1659 The first person to draw a map of Mars that displayed terrain features was the Dutch astronomer Christiaan Huygens. On November 28, 1659 he made an illustration of Mars that showed the distinct dark region now known as Syrtis Major Planum, and possibly one of the polar ice caps. The Italian Jesuit Daniello Bartoli had reported observing two dark patches on Mars in 1651.
Later drawings of Mars By Huygens * @HoooAW

1660 After attending a lecture by Christopher Wren, a group gathered to discuss the founding of “a college for the promoting of physico-mathematical experimental learning.” The result was to become the Royal Society of London. *VFR The Society subsequently petitioned King Charles II to recognise it and to make a royal grant of incorporation. The Royal Charter, which was passed by the Great Seal on 15 Jul 1662, created the Royal Society of London.*TIS
Memorandum November 28 1660: "These persons following according to the usual custom of most of them, met together at Gresham College to hear Mr Wren's lecture, viz. The Lord Brouncker, Mr Boyle, Mr Bruce, Sir Robert Moray, Sir Paule Neile, Dr Wilkins, Dr Goddard, Dr Petty, Mr Ball, Mr Rooke, Mr Wren, Mr Hill. And after the lecture was ended they did according to the usual manner, withdraw for mutual converse."

1679 Newton writes the Royal Society to suggest that if falling objects were studied, they would find a consistent deviation east due to the rotation of the earth.*VFR (Hook will later experiment and observe motion both to the west and the south. (see 6 Jan, 1680))

1772 At the Board meeting of 28 November 1772 Nevil Maskelyne, Astronomer Royal, presented the other astronomer's suggestions 'for improving (Tobias) Mayer's (Lunar) Tables by lessening the Errors in the method of calculation which he had perfected under the encouragement of the Board ; and at the same time reported that he has reduced the Errors of those Tables to about one half'.
Maskelyne is often viewed as an opponent of computing longitude by clock, but as early as 1765 he was quoted as saying, "the calculations would be always somewhat conciser in the method by the watch than in that by the Moon" *Board of Longitude project, Royal Museums Greenwich

1889 The Gilbert Club was officially formed on 28 November 1889. Advertised by a specially printed circular sent to select scientists, engineers, and other enthusiasts, the proposed association was also mentioned in the Times and in the leading British and American scientific weeklies, Nature and Science. By the time of the inaugural meeting, eighty-seven members had already signed up, many of whom were gathered in the chambers of the Society of Arts that afternoon to hear Silvanus Phillips Thompson describe the eminence and importance of William Gilbert of Colchester (1544-1603), the doctor whose early experimental investigations "constituted the absolute starting-point of the science of electricity."
The Gilbert Club counted among its first members numerous Fellows of the Royal Society and other prominent scientists in all fields, including Lord Rayleigh, John Tyndall, John Lubbock, Oliver Lodge, and the Presidents of the Physical Society and the Royal College of Surgeons. Leading these luminaries at the inaugural meeting was the most famous living British physicist and current President of the Institution of Electrical Engineers, Sir William Thomson (later Lord Kelvin). *Canadian Journal of History, 2003

William Gilbert M.D. demonstrating his experiments before Queen Elizabeth I (painting by A. Auckland Hunt)


1895 The day (I suspect) that the term "Octonions" was introduced into mathematical vocabulary. On this day a paper from Alex McAuley of the Univ of Tasmania was read to the Royal Society of London by Rev N. M. Ferrers with the title Octonions. The first sentence says, "Octonions is a name adapted for various reasons in place of Clifford's Bi-quaternions." Hamilton had already used the latter term in an altogether different sense. *Proceedings of the Royal Society of London, Volume 59

1936 This is the earliest exact date I can find where L. R. Ford presented information about his ideas on Ford Circles. He presented his idea at a meeting of the American Mathematical Society at Lawrence Kansas. (If someone knows dates of presentations at Rice, Univ of Texas, etc I would love to have those dates and any information on which parts were presented). *Am Mathematical Monthly, 1938.

In 1967, the first pulsating radio source (pulsar) was detected by an alert graduate student, Jocelyn Bell (see 15 July, 1943), then working under the direction of Prof. A. Hewish at the Mullard Radio Astronomy Observatory, Cambridge, England. They were using a special radio telescope, a large array of 2,048 aerials covering an area of 4.4 acres. The discovery of these fascinating objects opened new horizons in studies as diverse as quantum-degenerate fluids, relativistic gravity and interstellar magnetic fields. Under extraordinary physical conditions, radiation is generated and appears pulsed with a clock-like precision synchronously with the pulsar rotational period. These periods range from 1.57 milliseconds to 5.1 sec. *TIS

Jocelyn Bell, June 1967

2023  For the first time ever, a commercial plane flew across the Atlantic Ocean without using fossil fuels.
Virgin Atlantic said the test flight Tuesday from London to New York was powered only by sustainable aviation fuel, or SAF, a broad category of jet fuel that creates fewer carbon emissions than standard kerosene blends. The fuel on this flight was made from waste fats and plant sugars and emits 70% less carbon than petroleum-based jet fuel, according to a press release. It landed at John F. Kennedy International Airport on Tuesday afternoon.


1700 Nathaniel Bliss (28 Nov 1700; 2 Sep 1764) Britain's fourth Astronomer Royal, though only for the two years before his death. In 1736, Bliss became rector of St Ebbe's Oxford, and in 1742, he followed Halley as Savilian Professor of Geometry. Bliss occasionally assisted James Bradley, third A.R. In 1761, he made observations of the transit of Venus when Bradley was unable to do so due to poor health. Bliss succeeded Bradley in 1762. On 1 Apr 1764 Bliss published his observations of the annular eclipse visible from Greenwich. Besides his Observatory work, Bliss also worked for and with the Earl of Macclesfield, on astronomical problems. This work included making meridian observations of a comet approaching the Sun around 1744 at Shirburn Castle and at Greenwich.*TIS

1772 Luke Howard, FRS (28 November 1772 – 21 March 1864) was a British manufacturing chemist and an amateur meteorologist with broad interests in science. His lasting contribution to science is a nomenclature system for clouds, which he proposed in an 1802 presentation to the Askesian Society.
He has been called "the father of meteorology" because of his comprehensive recordings of weather in the London area from 1801 to 1841 and his writings, which transformed the science of meteorology. *Wik

A depiction of a cumulostratus cloud, included in Howard's 'On the modification of clouds'

1898 John Wishart FRSE (28 November 1898 – 14 July 1956) was a Scottish mathematician and agricultural statistician.
He worked successively at University College London with Karl Pearson, at Rothamsted Experimental Station with Ronald Fisher, and then as a reader in statistics in the University of Cambridge where he became the first Director of the Statistical Laboratory in 1953. He was elected a Fellow of the Royal Society of Edinburgh in 1931, and edited Biometrika from 1937. The Wishart distribution is named after him.
Wishart died at age 57 in a bathing accident in Acapulco while representing the Food and Agriculture Organization on a mission to set up a research centre.*Wik
In statistics, the Wishart distribution is a generalization to multiple dimensions of the gamma distribution. 

1905 Albert William Tucker (28 November 1905 – 25 January 1995) was a Canadian-born American mathematician who made important contributions in topology, game theory, and non-linear programming.In the 1960s, he was heavily involved in mathematics education, as chair of the AP Calculus committee for the College Board (1960–1963), through work with the Committee on the Undergraduate Program in Mathematics (CUPM) of the MAA (he was president of the MAA in 1961–1962), and through many NSF summer workshops for high school and college teachers.
In the early 1980s, Tucker recruited Princeton history professor Charles Gillispie to help him set up an oral history project to preserve stories about the Princeton mathematical community in the 1930s. With funding from the Sloan Foundation, this project later expanded its scope. Among those who shared their memories of such figures as Einstein, von Neumann, and Gödel were computer pioneer Herman Goldstine and Nobel laureates John Bardeen and Eugene Wigner.
Albert Tucker noticed the leadership ability and talent of a young mathematics graduate student named John G. Kemeny, whose hiring Tucker suggested to Dartmouth College. Following Tucker's advice, Dartmouth recruited Kemeny, who became Chair of the Mathematics Department and later College President. Years later, Darthmouth College recognized Albert Tucker with an honorary degree. Tucker died in Highstown, N.J. in 1995 at age 89. *Wik

1950 Russell Alan Hulse (28 Nov 1950, )American physicist who in 1993 shared the Nobel Prize for Physics with his former teacher, the astrophysicist Joseph H. Taylor, Jr., for their joint discovery of the first binary pulsar (1974). This is an astronomical system of two celestial bodies so close they are separated by only several times the distance between the moon and the earth. Their findings, first reported in 1978, constitute the first indirect proof of the existence of the gravitational waves predicted by Albert Einstein in his theory of relativity. *TIS

1821 Samuel Vince (6 April 1749; Fressingfield – 28 November, 1821; Ramsgate) was an English clergyman, mathematician and astronomer at the University of Cambridge.
The son of a plasterer, Vince was admitted as a sizar to Caius College, Cambridge in 1771. In 1775 he was Senior Wrangler, and Winner of the Smith Prize at Cambridge. Migrating to Sidney Sussex College in 1777, he gained his M.A. in 1778 and was ordained a clergyman in 1779.
He was awarded the Copley Medal in 1780 and was Plumian Professor of Astronomy and Experimental Philosophy at Cambridge from 1796 until his death.
As a mathematician, Vince wrote on many aspects of his expertise, including logarithms and imaginary numbers. His Observations on the Theory of the Motion and Resistance of Fluids and Experiments upon the Resistance of Bodies Moving in Fluids had later importance to aviation history. He was also author of the influential A Complete System of Astronomy (3 vols. 1797-1808).
Vince also published the pamphlet The Credibility of Christianity Vindicated, In Answer to Mr. Hume's Objections; In Two Discourses Preached Before the University of Cambridge by the Rev. S. Vince. In this work, Vince made an apology of the Christian religion and, like Charles Babbage, sought to present rational arguments in favor of the belief in miracles, against David Hume's criticism. *Wik

1872  Mary Somerville, a Scottish mathematician and science writer, died Nov. 28, 1872, at the venerable age of 91. Somerville was one of the most highly praised female scientific writers of the 19th century. Between 1798 and 1825, the French mathematician Pierre Simon de Laplace published his Traité de mécanique céleste, a comprehensive 5-volume updating of Isaac Newton's celestial physics. Somerville read and digested the entire work, and in 1831, she published Mechanism of the Heavens, a rather free translation of Laplace's work and considerably easier to understand than the original. Laplace said to her, before he died in 1827, that there had been only three women who understood his work: Mary Somerville, Caroline Herschel, and a Mary Grieg whom he had never met. Little did Laplace know that Mary Somerville had been Mary Grieg before her first husband died, so she actually occupied 2/3 of Laplace's list.

In 1834, Somerville published the first of a number of popular scientific books, On the Connexion of the Physical Sciences.  Interestingly, the philosopher William Whewell wrote a review of On the Connexion of the Sciences in 1834, and in the review he coined the word "scientist" as an appropriate name for a person who dabbles in experimental natural philosophy. *Linda Hall Org
In 1835 she and Caroline Herschel were elected as the first female Honorary Members of the Royal Astronomical Society.
When John Stuart Mill organized a massive petition to Parliament to give women the right to vote, he made sure that the first signature on the petition would be Somerville's. *Wik

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

1943 Eduard Helly (1 June 1884 in Vienna, Austria - 28 Nov 1943 in Chicago, Illinois, USA) Helly worked on functional analysis and proved the Hahn-Banach theorem in 1912 fifteen years before Hahn published essentially the same proof and 20 years before Banach gave his new setting. *SAU
Helly worked as a tutor, Gymnasium teacher, and textbook editor until World War I, when he enlisted in the Austrian army. He was shot in 1915, and spent the rest of the war as a prisoner of the Russians. In one prison camp in Berezovka, Siberia, he organized a mathematical seminar in which Tibor Radó, then an engineer, began his interest in pure mathematics.
In the same 1912 paper in which he introduced Helly's selection theorem concerning the convergence of sequences of functions, Helly published a proof of a special case of the Hahn–Banach theorem, 15 years before Hans Hahn and Stefan Banach discovered it independently.

1952 Fritz Carlson (23 July 1888 in Vimmerby, Sweden - 28 Nov 1952 in Stockholm, Sweden) His main work focused on the theory of analytic functions. Some of his most well-known contributions are a theorem connected to the Phragmén-Lindelöf principle, a theorem about the zeros of the V-function and several theorems about power series with integer coefficients. Such names as Carlson inequality, Carlson - Levin constants, Carlson theorem in complex analysis, Pólya - Carlson theorem on rational functions and Carlson theorem on Dirichlet series are well-known in mathematics. *SAU

1954 Enrico Fermi (29 Sep 1901, 28 Nov 1954) Italian-born American physicist who was awarded the Nobel Prize for physics in 1938 as one of the chief architects of the nuclear age. He was the last of the double-threat physicists: a genius at creating both esoteric theories and elegant experiments. In 1933, he developed the theory of beta decay, postulating that the newly-discovered neutron decaying to a proton emits an electron and a particle he called a neutrino. Developing theory to explain this decay later resulted in finding the weak interaction force. He developed the mathematical statistics required to clarify a large class of subatomic phenomena, discovered neutron-induced radioactivity, and directed the first controlled chain reaction involving nuclear fission. *TIS Emilio Segre tells this story in his biography of Fermi: "Fermi told me that one of his great intellectual efforts was his attempt to understand - at the age of ten- what was meant by the statement that the equation x2 + y2 = z2 represents a circle.  Someone must have stated the fact to him, but he had to discover the meaning by himself."
Fermi, while working in Los Alamos once calculated very high odds that the Earth should have been visited by aliens repeatedly over history. He sometimes would call out, "Where are they?"
Once, it was said, Fermi uttered his famous question in the presence of Lio Szilard, who responded, "They are among us, but they call themselves Hungarians." *P Ballew "Where are They?".... We are here!
Enrico Fermi between Franco Rasetti (left) and Emilio Segrè in academic dress

1954 Herbert Bright, developer of one of the first FORTRAN user programs (and consequently, the first error message), dies at 67. Bright had been a promoter of security through data encryption, as well as a research engineer at AT&T Laboratories. He also held various executive offices in the Association for Computing Machinery (ACM).*CHM

1968 Jean Frédéric Auguste Delsarte (October 19, 1903, Fourmies – November 28, 1968, Nancy) was a French mathematician known for his work in mathematical analysis, in particular, for introducing mean-periodic functions and generalized shift operators. He was one of the founders of the Bourbaki group.*Wik

1968 Leonard Roth (29 August 1904 Edmonton, London, England – 28 November 1968 Pittsburgh, Pennsylvania) was a mathematician working in the Italian school of algebraic geometry. He introduced an example of a unirational variety that was not rational (though his proof that it was not rational was incomplete).*Wik

1969 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(Cornell Univ., 1925). 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.
Cox studied at Indiana University Bloomington. Besides mathematics, Cox also took courses in German, English, Latin, history, hygiene, chemistry, education, philosophy and physics. There were three other Black students in his class. He received his bachelor's degree in 1917, at a time when the transcript of every Black student had the word "Colored" printed across it. He received A's on all his exams while at Indiana

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

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