## Tuesday 18 October 2022

### On This Day in Math - October 18

All models are wrong, some models are useful.

~George Box

The 291st day of the year; 291 is the largest number that is not the sum of distinct non-trivial powers.

$\varphi \left(291\right)=192$  The number of integers less than, and relatively prime to 291 is equal to it's reversal, 192.

291 is also equal to the nth prime + n.... but for which n, children?

Because 291 = 6 x 47 + 9, it can be written as the difference of two squares, 291 = 50^2 - 47^2. (An interesting note is that every power of 2^n is either one more or one less than some member of the 6n+9 sequence. The converse is not true, 21 is easy counterexample.

EVENTS
1092 Walcher, the Prior of the monastery in Great Malvern, U.K., carried out the first known Western Experiment to improve astronomical predictions when he pointed an astrolabe toward a lunar eclipse. At this time his astrolabe was one of only a few in Europe. *Jonathan Lyons, The House of Wisdom: How the Arabs Transformed Western Civilization.

1640 Pierre de Fermat (1601–1665) explains his ‘little theorem’ to Bernard Frenicle de Bessey in a follow up to two previous letters. ("On the subject of progressions, I have sent to you in advance the propositions that serve to determine the properties of powers minus one"). The theorem, which states that np−1 ≡ 1 (mod p) if p is prime and relatively prime to n, was proved by Euler in 1736 by induction on n.[Scientiﬁc American, December 1982]
1) When the exponent, n, is composite, 2n-1 is also composite,
2) When the exponent, n, is prime, 2n -2 is divisible by 2*n,
3) When the exponent, n, is prime, the number 2n -1 can not be divided by any number less than 2n+1

*Jacqueline Stedall, Mathematics Emerging

1740  In a letter to Johann Bernoulli, Euler uses imaginary in the exponent. exi + e-xi = 2 cos(x) {note Euler used squareroot of -1 rather than i. Euler would be the first to use i for the imaginary constant, but not until a paper he presents in St. Petersburg in 1777.} Cajori seems to imply, but does not state explicitly, that this is the first time an imaginary has been used as an exponent.

1933 Participants in the first fully international conference on nuclear physics in Rome from October 11–18, 1931, with those mentioned in the text in boldface. Foreground (left to right): Otto Stern (1888–1969), Peter Debye (1884–1966), Owen W. Richardson (1879–1959), Robert A. Millikan (1868–1973), Arthur H. Compton (1892–1962), Marie Curie (1867–1934), Guglielmo Marconi (1874–1937), Niels Bohr (1885–1962), Francis W. Aston (1877–1945), Walther Bothe (1891–1957), Bruno Rossi (1905–1993), and Lise Meitner (1878–1968, obscured). Behind Stern and Debye is Werner Heisenberg (1901–1976, obscured), Lé on Brillouin (1889–1969), Patrick M.S. Blackett (1897–1974, above Brillouin), and John S.E. Townsend (1868–1957). Between Curie and Marconi is Jean Perrin (1870–1942) and behind him is Paul Ehrenfest (1880–1933) and Enrico Fermi (1901–1954). In the row just above Ehrenfest (not the top row) and to his left is (left to right) Emil Rupp (1898-1979), Quirino Majorana (1871–1957), and Antonio Garbasso (1871–1933). Above Marconi is Orso Mario Corbino (1876–1937), above Bohr is Giulio Cesare Trabacchi (1884–1959), and above and to the right of Aston against the wall in profile is Franco Rasetti (1901–2001). Behind and to the left of Meitner is Arnold Sommerfeld (1868–1951). Among those missing from the photograph are Hans Geiger (1882–1945), Wolfgang Pauli (1900–1958), and Lé on Rosenfeld. Source: Reale Accademia d'Italia, Atti dei Convegno (ref. 21), frontispiece.
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1954, Texas Instruments & Industrial Development Engineering Assoc launch the first transistor radio, Regency TR-1,  (Like many other people, I listened to the beep of Sputnick overhead on one of these straining to see it in the sky above me...."beep...beep....")

1955, a new atomic subparticle called a negative proton (antiproton) was discovered at U.C. Berkeley. The hunt for antimatter began in earnest in 1932, with the discovery of the positron, a particle with the mass of an electron and a positive charge. However, creating an antiproton would be far more difficult since it needs nearly 2,000 times the energy. In 1955, the most powerful "atom smasher" in the world, the Bevatron built at Berkeley could provide the required energy. Detection was accomplished with a maze of magnets and electronic counters through which only antiprotons could pass. After several hours of bombarding copper with protons accelerated to 6.2 billion electron volts of energy, the scientists counted a total of 60 antiprotons.*TIS

1962, Dr. James D. Watson of the U.S., Dr. Francis Crick and Dr. Maurice Wilkins of Britain won the Nobel Prize for Medicine and Physiology for their work in determining the double-helix molecular structure of DNA (deoxyribonucleic acid).*TIS

 *Houston Chronicle
1983 physicist Sally Ride (1951-2012) became the first American woman – and 3rd woman of all time – to go into space. She blasted off aboard Challenger, culminating a long journey that started in 1977 when the Ph.D. candidate answered an ad seeking astronauts for NASA missions.

BIRTHS

1863 Alan Archibald Campbell-Swinton, FRS (October 18, 1863, Scotland - February 19, 1930, London) was a Scottish consulting electrical engineer. He was an earlier experimenter in cathode rays and after 1896 he was frequently called upon by the medical profession to take "Roentgen Pictures" of bones.
He described an electronic method of producing television in a June 18,1908 letter to Nature.
He gave a speech in London in 1911 where he described in great detail how distant electric vision could be achieved. This was to be done by using cathode ray tubes (CRTs) at both the transmitting and receiving ends. This was the first iteration of the electronic television which is still in use today. When Swinton gave his speech others had already been experimenting with the use of cathode ray tubes as a receiver, but the use of the technology as a transmitter was unheard of. *Wik

1902 (Ernst) Pascual Jordan (18 October 1902 in Hanover, German Empire; d. 31 July 1980 in Hamburg, Federal Republic of Germany) German physicist who in the late 1920s founded (with Max Born and later Werner Heisenberg) quantum mechanics using matrix methods, showing how light could be interpreted as composed of discrete quanta of energy. Later, (with Wolfgang Pauli and Eugene Wigner), while it was still in its early stages of development, he contributed to the quantum mechanics of electron-photon interactions, now called quantum electrodynamics. He also originated (concurrently with Robert Dicke) a theory of cosmology that proposed to make the universal constants of nature, (such as the universal gravitational constant G), variable over time. *TIS

1919 George Edward Pelham Box (18 October 1919, March 28, 2013, Madison, WI) is a statistician, who has made important contributions in the areas of quality control, time-series analysis, design of experiments, and Bayesian inference.
Box has written research papers and published books. These include Statistics for experimenters (1978), Time series analysis: Forecasting and control (1979, with Gwilym Jenkins) and Bayesian inference in statistical analysis. (1973, with George C. Tiao). Today, his name is associated with important results in statistics such as Box–Jenkins models, Box–Cox transformations, Box–Behnken designs, and others. Box married Joan Fisher, the second of Ronald Fisher's five daughters. In 1978, Joan Fisher Box published a biography of Ronald Fisher, with substantial collaboration of Box. *Wik

In his obituary for Box, Brad Jones of JMP recounted the following, with another fascinating Box quote,
"The last time I saw him was at the JMP Discovery Summit conference in 2009 where I introduced him to give a speech. George got a standing ovation from a crowd of several hundred fans of design of experiments and particularly his work. I will never forget his remarks as the applause died slowly away.

He said, "I feel like the son of the sultan on his 21st birthday when presented with 21 virgins. I know what to do. I just don't know where to start!"

Box died on 28 March 2013. He was 93 years old

1938 Phillip Griffiths (October 18, 1938, Raleigh, North Carolina -  ) is an American mathematician, known for his work in the field of geometry, and in particular for the complex manifold approach to algebraic geometry. He was a major developer in particular of the theory of variation of Hodge structure in Hodge theory and moduli theory.*Wik

DEATHS

1786 Alexander Wilson FRSE (1714 – 16 October 1786) was a Scottish surgeon, type-founder, astronomer, mathematician and meteorologist. He was the first scientist to record the use of kites in meteorological investigations. Wilson noted that sunspots viewed near the edge of the Sun's visible disk appear depressed below the solar surface, a phenomenon referred to as the Wilson effect. When the Royal Danish Academy of Sciences and Letters announced a prize to be awarded for the best essay on the nature of solar spots, Wilson submitted an entry. On 18 February 1772 the Academy presented Wilson with a gold medal for his work on sunspots.*Wik

1793 John Wilson (6 Aug 1741 in Applethwaite, Westmoreland, England - 18 Oct 1793 in Kendal, Westmoreland, England) In 1764 Wilson was elected a Fellow of Peterhouse and he taught mathematics at Cambridge with great skill, quickly gaining an outstanding reputation for himself. However, he was not to continue in the world of university teaching, for in 1766 he was called to the bar having begun a legal career on 22 January 1763 when he was admitted to the Middle Temple. It was a highly successful career, too.
He is best known among mathematicians for Wilson's theorem which states that
... if p is prime then 1 + (p - 1)! is divisible by p
This result was first published by Waring, without proof, and attributed to Wilson. Leibniz appears to have known the result. It was first proved by Lagrange in 1773 who showed that the converse is true, namely
... if n divides 1 + (n - 1)! then n is prime.
Almost certainly Wilson's theorem was a guess made by him, based on the evidence of a number of special cases, which neither he nor Waring knew how to prove. *SAU

1845 Jean-Dominique Comte de Cassini (30 June 1748 in Paris, France - 18 Oct 1845 in Thury, France)  French mathematician and surveyor who worked on his father's map of France.  He was the son of César-François Cassini de Thury and was born at the Paris Observatory. In 1784 he succeeded his father as director of the observatory; but his plans for its restoration and re-equipment were wrecked in 1793 by the animosity of the National Assembly. His position having become intolerable, he resigned on September 6, and was thrown into prison in 1794, but released after seven months. He then withdrew to Thury, where he died fifty-one years later.
He published in 1770 an account of a voyage to America in 1768, undertaken as the commissary of the French Academy of Sciences with a view to testing Pierre Le Roy’s watches at sea. A memoir in which he described the operations superintended by him in 1787 for connecting the observatories of Paris and Greenwich by longitude-determinations appeared in 1791. He visited England for the purposes of the work, and saw William Herschel at Slough. He completed his father’s map of France, which was published by the Academy of Sciences in 1793. It served as the basis for the Atlas National (1791), showing France in departments.
Cassini’s Mémoires pour servir à l’histoire de l’observatoire de Paris (1810) embodied portions of an extensive work, the prospectus of which he had submitted to the Academy of Sciences in 1774. The volume included his Eloges of several academicians, and the autobiography of his great-grandfather, Giovanni Cassini.*Wik

1871 Charles Babbage,(26 Dec 1792-18 Oct 1871) computer pioneer. His obsession for mechanizing computation made him into an embittered and crotchety old man. He especially hated street musicians, whose activities, he ﬁgured, ruined a quarter of his working potential. *VFR   English mathematician and pioneer of mechanical computation, which he pursued to eliminate inaccuracies in mathematical tables. By 1822, he had a small calculating machine able to compute squares. He produced prototypes of portions of a larger Difference Engine. (Georg and Edvard Schuetz later constructed the first working devices to the same design which were successful in limited applications.) In 1833 he began his programmable Analytical Machine, a forerunner of modern computers. His other inventions include the cowcatcher, dynamometer, standard railroad gauge, uniform postal rates, occulting lights for lighthouses, Greenwich time signals, heliograph opthalmoscope. He also had an interest in cyphers and lock-picking. *TIS

1931 Thomas Alva Edison (11 Feb 1847-18 Oct 1931) Inventor, died in West Orange, NJ. He invented the first phonograph (1877) and the prototype of the practical incandescent electric light bulb (1879). His many inventions led to his being internationally known as "the wizard of Menlo Park", from the name of his first laboratory. By the late 1880s he was contributing to the development of motion pictures. By 1912 he was experimenting with talking pictures. His many inventions include a storage battery, a Dictaphone, and a mimeograph. Meanwhile, he had become interested in the development of a system for widespread distribution of electric power from central generating stations. He held over 1,000 patents.In 1962 his second laboratory and home in West Orange, NJ, would be designated a National Historic Site.*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