## 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?

EVENTS

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
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1867  Tait began to think about knots and Thomson's second paper on vortex atoms, which appeared in 1869, included diagram of knots and links drawn by Tait. Long before this, however, Maxwell had entered the discussions which went on in letters exchanged by the three Scottish mathematical physicists (  Thomson, Maxwell and Tait.) .
He was interested in knots because of electromagnetic considerations and in a letter to Tait written on the 4 December 1867 he rediscovered an integral formula counting the linking number of two closed curves which Gauss had discovered, but had not published, in 1833. Maxwell also gave equations in three dimensions which represented knotted curves.

 Taits orders of knotedness

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

BIRTHS

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

DEATHS

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