Tuesday 7 January 2020

On This Day in Math - January 7

From Galileo's Sidereus Nuncius (p 44)

The purpose of computation is insight, not numbers.
~Richard Hamming

The 7th day of the year; you can double 7! to get the exact number of minutes in a week (7 days).

Mario Livio pointed out that The sum of the squares of the first seven primes was 666, the supposed number of the beast from Revelations. \( 666=2^2+3^2+5^2+7^2+11^2+13^2+17^2 \) . May I add that seems devilishly clever.

Ever wonder if 7 cylinders could be arranged so that each touched the other six? Yep(but eight is up to you)

In the digital expansion of pi, 7 is the last (non-zero) single digit to occur, showing up in the 13th place after the decimal point. (If you randomly drew from nine distinct objects with replacement, How long would it take to get them all,on average?)

And The smallest prime of length 7 containing only the digits 7 and 8 is palindromic: 7778777 *@pickover

Jim Wilder @wilderlab sent this one: 7⁴ = 2401 = (2+4+0+1)⁴

And just for the seventh day of 2016, 2016 is the sum of cubes of seven consecutive integers \(2016 = 3^3 + 4^3 + 5^3 + 6^3 + 7^3 + 8^3 + 9^3 \)


1451 Papal Bull issued by Pope Nicholas V founding University of Glasgow. *@catholiclab

1610 Galileo discovered the first three moons of Jupiter , or the Medicean Stars, as he named them after his patron. *VFR Actually Galileo must have discovered the moons sometime in late December or early January. On January 7, 1610, Galileo wrote a letter containing the first mention of Jupiter’s moons. At the time, he saw only three of them, and he believed them to be fixed stars near Jupiter. He continued to observe these celestial orbs from January 8 to March 2, 1610. In these observations, he discovered a fourth body, and also observed that the four were not fixed stars, but rather were orbiting Jupiter. He discovered the fourth on 13 January. *Wik
and also from the same letter:
In 1610, Galileo dated his first letter describing telescopic observations in which he saw the moon's cratered surface using his twenty-powered spyglass. He wrote, “... it is seen that the Moon is most evidently not at all of an even, smooth, and regular surface, as a great many people believe of it and of the other heavenly bodies, but on the contrary it is rough and unequal. In short it is shown to be such that sane reasoning cannot conclude otherwise than that it is full of prominences and cavities similar, but much larger, to the mountains and valleys spread over the Earth's surface.” Galileo went on to describe the phenomena in considerable detail, rehearsing, as it were, the observations and conclusions he was to publish more elaborately a few months later in Sidereus Nuncius. *TIS

1692 Having died on 31 December from paralysis, Robert Boyle was buried in the churchyard of St Martin-in-the-Fields. His funeral sermon was preached by his friend Bishop Gilbert Burnet with Isaac Newton, Samuel Pepys, John Locke, and John Evelyn in attendance. In his will, Boyle endowed a series of Lectures which came to be known as the Boyle Lectures.

1760 The Great Comet of 1760 (C/1760 A1) was first seen by Abbe Chevalier at Lisbon. Charles Messier also spotted the comet on 8 January. *Wik

In 1785, Frenchman Jean Pierre Blanchard and American physician and scientist John Jeffries made the first air crossing of the English Channel from England to France in a hot-air balloon - the first international flight. This was the second of two balloon flights Jeffries financed. To accompany him, Jeffries chose Blanchard for his prior experience in balloon flight. The voyage across the Channel was successful, though not without difficulty, because to maintain height they were forced to jettison everything in the basket, including rope and most of their clothes. Their previous flight took place on 30 Nov 1784, in London, for the purpose of taking scientific and meteorological measurements.*TIS

1791 Benjaman Bannaker arrived in Washington D.C. to begin laying out the boundaries of the District of Columbia. He did his first observations on Friday the 11th. The first two lines were completed on Saturday. *VFR

1810 Gauss wrote his astronomer friend Bessel: “This winter I am teaching two courses for three listeners, of whom one is only modestly prepared, one scarcely modestly prepared, and the third lacks preparation as well as ability. These are the onera of a mathematical professor.”*VFR

1886 Nature Magazine quotes from Sylvester's inaugural address at Oxford related to his meeting with Poincare. "What Briggs said of logarithmes may be said almost in the same words of the subject of this lecture, "This most excellent help to geometry which, being found out, one wonders nobody else fount it out before; when now known, it is so easy." *Nature Vol 33 He also commented on the fact that Poincare lived on Rue Gay-Lussac and wondered, "will our grandchildren live to see..." mathematical street names in London.

1896 Two months after Rontgen discovered X-rays (the x was for unknonwn), Henri Poincare was sent photographs of these X-rays and was so amazed that he passed them on to two doctors and asked if they could duplicate Rontgen's work. On January 23 they would present a paper on their results at the French Academy with Henri Becquerel in the audience. Within months he would discover rays coming from Uranium. *Brody & Brody, The Science Class You Wished You Had

1947 President Henry Wriston of Brown University announced the establishment of a new department: History of Mathematics. It was then, and remains today, the only such department in the U.S. Otto Neugebauer (1899–1990) was named the first head of the department. Today the department is world famous for its work in ancient mathematics and astronomy. *VFR (Is this still the only History of Mathematics Dept in the U.S.?)

1963 Ivan Sutherland introduces the Sketchpad submitting his Ph.D. thesis to MIT. The Sketchpad, one of the earliest programs for the TX-0, allowed direct manipulation of objects on a computer screen. Using the Sketchpad, a user could create and manipulate graphical figures with a light pen. This thesis provided the basis for later graphical user interfaces and is considered one of the seminal papers in computer science. *CHM

1981 Cathleen S. Morawetz, of the Courant Institute, delivered the 54th Gibbs Lecture entitled “The mathematical approach to the sound barrier.” She was the first woman to be invited to give this prestigious address to the AMS. *VFR

2016 2016 The 49th Mersenne prime is discovered. The Great Internet Mersenne Prime Search reported the discovery of the new record largest prime number, 274,207,281 -1. The huge number has 22,338,618 digits. The record prime was found on a computer loaned by Professor Curtiss Cooper at the University of Central Missouri. This is the fourth record GIMPS project prime for Dr. Cooper and his university.
In a strange twist, Dr. Cooper's computer reported the prime in GIMPS on September 17, 2015 but it remained unnoticed until routine maintenance data-mined it on January 7th. The official discovery date is January 7th, the day a human took note of the result. The perfect number associated with this new Mersenne prime is over forty-four million digits long. *GIMPS
I am reminded at moments like this of a comment in Barlow's Number Theory (1811) which list all the then known Mersenne Primes up to M31. This number, "is the greatest that will ever be discovered, for, as they are merely curious without being useful it is not likely any person will attempt to find one beyond it." It is strange that we continue the search. It would be terrible if we did not. (Barlow actually listed the Perfect numbers associated with each Mersenne prime.)


1755 Stephen Groombridge (7 Jan 1755; 30 Mar 1832) English astronomer and merchant, who compiled the Catalogue of Circumpolar Stars (corrected edition published 1838), often known as the Groombridge Catalog. For ten years, from 1806, he made observations using a transit circle, followed by another 10 years adjusting the data to correct for refraction, instrument error and clock error. He retired from the West Indian trade in 1815 to devote full time to the project. He was a founder of the Astronomical Society (1820). His work was continued by others when he was struck (1827) with a "severe attack of paralysis" from which he never fully recovered. The catalog eventually listed 4,243 stars situated within 50° of the North Pole and having apparent magnitudes greater than 9. Editions of the catalog were published posthumously. The 1833 edition was withdrawn due to errors, and corrected in 1838 by A Catalog of Circumpolar Stars, Reduced to January 1, 1810, edited by G. Biddell Airy. *TIS

1827 Sir Sandford Fleming (7 Jan 1827; 22 Jul 1915) Scottish surveyor and leading railway engineer who divided the world into time zones. He emigrated at age 17 years to Quebec, Canada, on 24 Apr 1845, as a surveyor. Later he became one of the foremost railway engineers of his time. While in charge of the initial survey for the Canadian Pacific Railway, the first Canadian railway to span the continent, he realized the problems of coordinating such a long railway. This lead him to the idea of time zones, which contribution to the adoption of the present system of time zones earned him the title of "Father of Standard Time." Fleming also designed the first Canadian postage stamp. Issued in 1851, it cost three pennies and depicted the beaver, now the national animal of Canada.*TIS

1834 Johann Philipp Reis (7 Jan 1834; 14 Jan 1874) German physicist whose invention of an early telephone preceded Bell's work. After years of experimentation, by the age of 27, he constructed a rudimentary transmitter by placing an animal ear membrane in front of an electrical contact. A galvanic inductor oscillated in the receiver in the same manner as the transmitted signal. Reis's instrument conveyed certain sounds, poorly, but no more than that; intelligible speech could not be reproduced. Reis was ready to present his device to Frankfurt's Physics Association (Der Physikalische Verein) on 26 Oct 1861. He gave a lecture titled "Telephony Using Galvanic Current" ("Das Telefonieren durch galvanischen Strom"). During this, the first public demonstration of the successful conversion of electrical into auditory waves, verses of a song were transmitted from the lecture room to a hospital room over a 300-ft away. Reis coined the word "telephone" for his device. The professors to whom this invention was presented were not very impressed and this version of the "telephone" never received any financial support and no patent ensued. Reis' devices were fragile and clumsy laboratory models, never put to public use.*TIS

1859 Marie Georges Humbert (7 Jan 1859 in Paris, France - 22 Jan 1921 in Paris, France) His doctorate extended Clebsch's work on curves. He then studied Abel's work which he developed and put into a geometric setting. It was as a direct consequence of his work on using abelian functions in geometry which won for him the 1892 Académie des Sciences prize for work on Kummer surfaces. As Costabel writes, "He thus enriched analysis and gave the complete solution of the two great questions of the transformation of hyperelliptic functions and of their complex multiplication. "
He also extended work of Hermite considering applications to number theory throughout his life.
Humbert would be better known today if the area of mathematics in which he worked had remained in favor. Since it has now become merely something of an historical curiosity rather than mainstream mathematics, his contribution is less well known. It does, however, indicate the quality of his mathematics that, despite this, his name and results are known today. To some extent this is a consequence of the fact that although he worked in a specialized area he had a remarkably broad knowledge of mathematics and his results form links between areas. *SAU

1871 Birthdate of (Félix-Édouard-Justin-) Émile Borel. “In Paris as a scholarship student preparing for the university, he entered the family circle of G. Darboux through friendship with his son, saw the “good life” of a leading mathematician, and set his heart on it.” *VFR (7 Jan 1871; 3 Feb 1956) was a French mathematician who (with René Baire and Henri Lebesgue), was among the pioneers of measure theory and its application to probability theory. In one of his books on probability, he proposed the thought experiment that a monkey hitting keys at random on a typewriter keyboard will - with absolute certainty - eventually type every book in France's Bibliothèque nationale de France (National Library). This is now popularly known as the infinite monkey theorem. He was first to develop (1899) a systematic theory for a divergent series. He also published (1921-27) a number of research papers on game theory and became the first to define games of strategy. *TIS

1904 Gordon Thomas Whyburn (January 7 1904 , September 8 1969) American mathematician who worked on the topology of point sets. *Wik

1907 Raymond Edward Alan Christopher Paley (7 January 1907 – 7 April 1933) was an English mathematician. Paley was born in Bournemouth, England. He was educated at Eton. From there he entered Trinity College, Cambridge where he showed himself the most brilliant student among a remarkable collection of fellow undergraduates. He won a Smith's Prize in 1930 and was elected a fellow of Trinity College.
His contributions include the Paley construction for Hadamard matrices (closely related to the Paley graphs in graph theory) and his collaboration with Norbert Wiener in the Paley–Wiener theorem (harmonic analysis). He collaborated with A. Zygmund on Fourier series (see also Paley–Zygmund inequality) and worked with J. E. Littlewood on what became known as Littlewood–Paley theory, an application of real-variable techniques in complex analysis.
On 7 April 1933, Paley died in a skiing accident when skiing alone at an altitude of 9,600 ft in Banff, Alberta. He was killed by an avalanche at Deception Pass, Fossil Mountain, in the Canadian Rockies. His death was witnessed by companions lower down the mountainside. Park wardens and a member of the Royal Canadian Mounted Police recovered the body. He is buried in the Banff town cemetery.*Wik


1893 Josef Stefan (24 Mar 1835, 7 Jan 1893) Austrian physicist who proposed a law of radiation (1879) stating that the amount of energy radiated per second from a black body is proportional to the fourth power of its absolute temperature. (A black body is a theoretical object that absorbs all radiation that falls on it.) This law is known as Stefan's law or the Stefan-Bolzmann law. He also studied electricity, the kinetic theory of gases and hydrodynamics.*TIS

1935 Ivan Vsevolodovich Meshchersky (10 Aug 1859 in Arkhangelsk, Russia - 7 Jan 1935 in Leningrad, USSR (now St Petersburg, Russia)) mathematician who gained fame for his work on mechanics, notably the motion of bodies of variable mass. *Wik

1935 Sir Alfred Ewing (27 Mar 1855, 7 Jan 1935) was a Scottish physicist who discovered and named hysteresis (1881), the resistance of magnetic materials to change in magnetic force. Ewing was born and educated in Dundee and studied engineering on a scholarship at Edinburgh University. He helped Sir William Thomson, later Lord Kelvin in a cable laying project. In 1878 he became professor of Mechanical Engineering and Physics at Tokyo University, where he devised instruments for measuring earthquakes. In 1903 he moved to the Admiralty as head of education and training, where during WW I, he and his staff took on the task of deciphering coded messages. *TIS

1943 Nikola Tesla (10 Jul 1856, 7 Jan 1943)Serbian-American inventor and researcher who designed and built the first alternating current induction motor in 1883. He emigrated to the United States in 1884. Having discovered the benefits of a rotating magnetic field, the basis of most alternating-current machinery, he expanded its use in dynamos, transformers, and motors. Because alternating current could be transmitted over much greater distances than direct current, George Westinghouse bought patents from Tesla the system when he built the power station at Niagara Falls to provide electricity power the city of Buffalo, NY.*TIS

1974 Charles Alfred Coulson FRS (13 December 1910, Dudley, England – 7 January 1974, Oxford, England) was a British applied mathematician, theoretical chemist and religious author.
His major scientific work was as a pioneer of the application of the quantum theory of valency to problems of molecular structure, dynamics and reactivity. He shared his deep religious belief, as a Methodist lay preacher, with the general public in radio broadcasts, served on the World Council of Churches from 1962 to 1968 and was Chairman of Oxfam from 1965 to 1971.
Coulson was a Senior Lecturer in the Mathematics Department of University College, Dundee, which was administratively part of the University of St. Andrews from 1938 to 1945. He held a Fellowship at the University of Oxford from 1945 to 1947, when he took up the newly appointed Chair of Theoretical Physics at King's College London. He returned to Oxford in 1952 as Rouse Ball Professor of Mathematics and Fellow of Wadham College. He set up and directed the Mathematical Institute. In 1972 he was appointed to the newly created Chair of Theoretical Chemistry, which has since been named for him.
He was elected a Fellow of the Royal Society of Edinburgh in 1941 and a Fellow of the Royal Society of London in 1950. He was awarded the Davy Medal of the Royal Society in 1970, the Faraday and Tilden Medals of the Chemical Society in 1968 and 1969 respectively, and received a dozen honorary degrees from English and other universities. He was a member of the International Academy of Quantum Molecular Science.
In each of his successive appointments, Coulson attracted an active and enthusiastic group of graduate students, short and long term visitors, many of whom held senior university and industrial positions in England and other countries. Many of his students went on to make major contributions in several fields of endeavour.
Coulson was an excellent cricketer and chess player, a warm family man and had a strong sense of humour. He and Eileen were gracious hosts to his students and his associates. The conference in his honour at Brasenose College in 1967 had an impressive international attendance, despite the difficulty of organizing it during a postal strike. *Wik

1984 Alfred Kastler (3 May 1902, 7 Jan 1984) French physicist who won the Nobel Prize for Physics in 1966 for his discovery and development of methods for observing Hertzian resonances within atoms. This research facilitated the greater understanding of the structure of the atom by studying the radiations that atoms emit when excited by light and radio waves. He developed a method called "optical pumping" which caused atoms in a sample substance to enter higher energy states. This idea was an important predecessor to the development of masers and the lasers which utilized the light energy that was re-emitted when excited atoms released the extra energy obtained from optical pumping.*TIS

1989 John Frank Adams (5 Nov 1930 in Woolwich, London, England -7 Jan 1989 Near Brampton, Huntingdonshire, England) was an English algebraic topologist who pioneered methods for calculating the homotopy of spheres. *Wik

1998 Richard Wesley Hamming (11 Feb 1915, 7 Jan 1998)  was an American mathematician who devised computer Hamming codes - error-detecting and correcting codes (1947). These add one or more bits to the transmission of blocks of data, used for a parity check, so that errors can be corrected automatically. By making a resend of bad data unnecessary, efficiency improved for modems, compact disks and satellite communications. He also worked on programming languages, numerical analysis and the Hamming spectral window (used to smooth data before Fourier analysis is carried out). He taught at University of Louisville, then during WW II worked (1945) on computers with the Manhattan Project creating the atomic bomb. From 1946, he spent 30 years with Bell Telephone Labs, eventually becoming head of computing science research.*TIS

2004 Oswald Garrison Villard (17 Sep 1916, 7 Jan 2004) American electronics engineer who developed over-the-horizon radar (a way to detect objects out of direct sight by bouncing radar off the ionosphere, an electrically charged layer in the upper atmosphere) so radar could peer around the Earth's curvature to detect aircraft and missiles thousands of miles away. His interest in electricity began with a copy of Harper's Electricity Book for Boys. At age 12, he put together a radio from a kit. During WW II, he researched countermeasures to protect Allied forces against enemy radio and radar devices. He made pioneering studies of radar jamming. In 1947, he designed a simplified voice transmitter permitting two-way communication on a single radio channel, such as a telephone conversation.*TIS

2012 Herbert Saul Wilf (1931-2012) was a mathematician, specializing in combinatorics and graph theory. He was the Thomas A. Scott Professor of Mathematics in Combinatorial Analysis and Computing at the University of Pennsylvania. He wrote numerous books and research papers. Together with Neil Calkin he founded The Electronic Journal of Combinatorics in 1994 and was its editor-in-chief until 2001.
In number theory, the Calkin–Wilf tree is a tree in which the vertices correspond 1-for-1 to the positive rational numbers. The tree is rooted at the number 1, and any rational number expressed in simplest terms as the fraction a/b has as its two children the numbers a/(a + b) and (a + b)/b. Every positive rational number appears exactly once in the tree.
The sequence of rational numbers in a breadth-first traversal of the Calkin–Wilf tree is known as the Calkin–Wilf sequence.*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

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