## Sunday, 18 December 2022

### On This Day in Math - December 18

First celestial photograph, see 1839 below

Let me tell you how at one time the famous mathematician Euclid became a physician. It was during a vacation, which I spent in Prague as I most always did, when I was attacked by an illness never before experienced, which manifested itself in chilliness and painful weariness of the whole body. In order to ease my condition I took up Euclid's Elements and read for the first time his doctrine of ratio, which I found treated there in a manner entirely new to me. The ingenuity displayed in Euclid's presentation filled me with such vivid pleasure, that forthwith I felt as well as ever.
~Bernhard Bolzano

The 352nd day of the year; there are 352 ways to arrange 9 queens on a 9x9 chessboard so that none are attacking another. (Gauss worked on the generalized queens problem; Students might try to find the number for small n x n boards. A general algorithm is not yet known)

352 has all prime digits, and so does the 352nd prime, 2377.

352 can be written as the sum of  three squares, 8^12 + 12^2 + 12^2; and also as the sum of two consecutive primes, 173 + 179

 *Wik
352 is the last day of the year that appears in the Lazy Caterers Sequence, also called the pancake cutting sequence and the Central Polygonal numbers. The numbers describes the maximum number of pieces that a flat disc (or pancake) could be cut with n straight lines. For 26 straight cuts, that number is 352 pieces. The formula is given by P = $\frac{n^2 + n + 1}{2}$ .

EVENTS

 The Great Comet of 1680 over Rotterdam as painted by Lieve Verschuier *Wik

1680
C/1680 V1, also called the Great Comet of 1680, Kirch's Comet, and Newton's Comet, has the distinction of being the first comet discovered by telescope. Discovered by Gottfried Kirch on 14 November 1680, New Style, it became one of the  brightest comets of the 17th century--reputedly visible even in daytime--and was noted for its spectacularly long tail. Passing only 0.4 AUs from Earth on 30 November, it sped around an incredibly close perihelion of .006 AU (898,000 km) on 18 December 1680, reaching its peak brightness on 29 December as it rushed outward again. It was last observed on 19 March 1681. As of December 2010 the comet was about 252.1 A.U. from the Sun. While the Kirch Comet of 1680-1681 was discovered and subsequently named for Gottfried Kirch , credit must also be given to the Jesuit, Eusebio Kino, who charted the comet’s course. During his delayed departure for Mexico, Kino began his observations of the comet in Cadíz in late 1680. Upon his arrival in Mexico City, he published his Exposisión astronómica de el [sic] cometa (Mexico City, 1681) in which he presented his findings. Kino’s Exposisión astronómica is among one of the earliest scientific treatises published by a European in the New World.  Aside from its brilliance, it is probably most noted for being used by Isaac Newton to test and verify Kepler's laws. *Wik

1703 The astronomer John Flamsteed was not pleased with the choice of successor to Wallis as the Savilian Professor of Geometry, Edmond Halley. In a letter of Flamsteed’s to Sharpe [he] reveals his irritation at the turn of events: Dr. Wallis is dead—Mr. Halley expects his place—who now talks, swears and drinks brandy like a sea-captain” *GERALD L. ALEXANDERSON, MAA Journal Volume 49, Number 3, July 2012,

In 1839, John William Draper took a daguerreotype of the moon, the first celestial photograph made in the U.S. He exposed the plate for 20 minutes using a 5-inch telescope and produced an image one inch in diameter. Draper was a professor of chemistry at New York University, New York City. His research in the effect of light upon chemicals had led him to take up photography. He also made his first satisfactory photographic portrait in 1839. A picture he took (1840) of his sister is the oldest surviving photographic portrait. Draper made important scientific contributions in fields of radiant energy, photochemistry, photography, and electric telegraphy. He also anticipated development of spectrum analysis.*TIS

In 1926, in a letter published in Nature, G.N. Lewis coined the word "photon" when he suggested that it "would seem inappropriate to speak of one of these hypothetical entities as a particle of light, a corpuscle of light, a light quantum, or a light quant, if we are to assume that it spends only a minute fraction of its existence as a carrier of radiant energy, while the rest of the time it remains as an important structural element within the atom. It would also cause confusion to call it merely a quantum, for later it will be necessary to distinguish between the number of these entities present in an atom and the so-called quantum number. I therefore [propose for this] which is not light but plays an essential part in every process of radiation, the name photon.*TIS

In 1958, the first American communications satellite was launched. Project SCORE (Signal Communication by Orbiting Relay Equipment) was put into orbit from Cape Canaveral using an Atlas B missile, also the first successful trial of the Atlasas a space launch vehicle. The entire rocket was placed into low orbit with the communications equipment integrated into the fairing pods of the missile. The low orbit limited life expectancy of the satellite to only 2 to 3 weeks, thus limiting opportunities for real­time relay between two ground stations. Therefore, a store­and­forward mode was added by including a tape recorder, which also gave the satellite a worldwide broadcast capability - the world's first satellite to broadcast voice.*TIS

1991 IBM and Siemens AG announce they have developed a prototype 64 megabyte DRAM chip. This development was in line with Moore’s Law which predicts a doubling of the number of transistors etched into silicon every 18 months. *CHM

BIRTHS

1856 Sir J(oseph) J(ohn) Thomson (18 Dec 1856; 30 Aug 1940)  was an English physicist who helped revolutionize the knowledge of atomic structure by his discovery of the electron (1897). He received the Nobel Prize for Physics in 1906 and was knighted in 1908. Thomson experimented with currents of  electricity inside empty glass tubes, investigating a long-standing puzzle known as "cathode rays." His experiments prompted him to make a bold proposal: these mysterious rays are streams of particles much smaller than atoms. He called these particles "corpuscles," and suggested that they might make up all of the matter in atoms. It was startling to imagine a particles inside the atom at a time when most people thought that the atom was indivisible, the most fundamental unit of matter.*TIS

1917 Roger Conant Lyndon (18 Dec 1917 in Calais, Maine, USA - 8 June 1988 in Ann Arbor, Michigan) was an American mathematician, for many years a professor at the University of Michigan. He is known for Lyndon-words (a type of combinatorial string topic), the Curtis–Hedlund–Lyndon theorem, Craig–Lyndon interpolation and the Lyndon–Hochschild–Serre spectral sequence. *Wik

1942 Lenore Blum​ (December 18, 1942, New York) is a distinguished professor of Computer Science at Carnegie Mellon. She received her Ph.D. in mathematics from the Massachusetts Institute of Technology in 1968. Her dissertation was on Generalized Algebraic Structures and her advisor was Gerald Sacks. She then went to the University of California at Berkeley as a Postdoctoral Fellow and Lecturer in Mathematics. In 1973 she joined the faculty of Mills College where in 1974 she founded the Mathematics and Computer Science Department (serving as its Head or co-Head for 13 years). In 1979 she was awarded the first Letts-Villard Chair at Mills.
In 1983 Blum won an NSF CAREER award to work with Michael Shub for two years at the CUNY Graduate Center. They worked on secure random number generators and evaluating rational functions, see Blum Blum Shub. In 1987 she spent a year at IBM. In 1989 she published an important paper with Michael Shub and Stephen Smale on NP completeness, recursive functions and universal Turing machines, see Blum–Shub–Smale machine. In 1990 she gave an address at the International Congress of Mathematicians on computational complexity theory and real computation. In 1992 Blum became the deputy director of the Mathematical Sciences Research Institute, otherwise known as MSRI. After visiting the City University of Hong Kong for a year, she moved to her current position at Carnegie Mellon in 1999. [1] In 2002 she was selected to be a Noether Lecturer.
Lenore Blum is married to Manuel Blum and mother of Avrim Blum. All three are MIT alumni and professors of Computer Science at Carnegie Mellon.*Wik

DEATHS

1559  Cuthbert Tunstall (1474 in Hackforth, Yorkshire, England - 18 Dec 1559 in Lambeth, London, England) wrote the first printed work published in England devoted exclusively to mathematics. It was an arithmetic book De arte supputandi libri quattuor (1522) based on Pacioli's Suma. It makes no claim to originality. *SAU   His life was primarily as a diplomat and bishop and shows no evidence of exceptional mathematical ability in what I have found, yet Grynaeus dedicated the first printed Greek edition of Euclid to him: "....since he has explained the calculating of numbers so clearly.   One of his biographers wrote of him, "A gentle man given to collecting coins and gardening, he was probably the most respected bishop and scholar in sixteenth century England."

1799 Étienne Montucla (5 September 1725 – 18 December 1799) was a French historian of mathematics who wrote in 1754 a history of the problem of squaring the circle. He also wrote the first truly comprehensive classical history of mathematics,Histoire des mathématiques. Late in his life, Montucla's friends persuaded him to work on a new edition of his famous Histoire des mathématiques. In August 1799 Montucla published new editions through Agasse in Paris of the two volumes originally published in 1758. Montucla extensively revised and enlarged the two volumes. He had intended to extend his cover of history to the end of the 18th century and part of the third volume on this topic was printed by the time he died, four months after the publication of the new editions of 1799. Lalande, with the help of some other scientists, completed volumes three and four to give the coverage that Montucla had intended. Volume three covered 18th century pure mathematics, optics and mechanics in 832 pages, while the fourth volume covered 18th century astronomy, mathematical geography and navigation in 688 pages.*SAU In 1778 he re-edited Jacques Ozanam's Recreations mathématiques, afterwards published in English by Charles Hutton (4 vols, London, 1803).*Wik Huttons translation is free on Google Books

1848 Bernhard Bolzano (5 Oct 1781, 18 Dec 1848) Bohemian mathematician and theologian who made significant contributions to both mathematics and the theory of knowledge. He provided a more detailed proof for the binomial theorem in 1816 and suggested the means of distinguishing between finite and infinite classes. Bolzano helped to establish the foundations of analysis (for example, the Bolzano-Weierstrass theorem), attempted to elaborate mathematical method, and anticipated some basic ideas of Cantor's set theory. His major work, Wissenschaftslehre (1837), contains various contributions to logic and semantics concerning the relations of compatibility, derivability, and consequence, the deduction theorem, and the logic of classes, entailment, and probability.*TIS

1855 Jacques Charles-François Sturm (29 Sep 1803, 18 Dec 1855) French mathematician whose work resulted in Sturm's theorem, an important contribution to the theory of equations. As tutor of the de Broglie family in Paris (1823-24), Sturm met many of the leading French scientists and mathematicians. In 1826, with the Swiss engineer Daniel Colladon, he made the first accurate determination of the velocity of sound in water and a year later wrote a prizewinning essay on compressible fluids. In 1829, he found the number of real roots of a given polynomial in a given interval. *TIS

1880 Michel Chasles (15 Nov 1793, 18 Dec 1880) French mathematician who, independently of the Swiss-German mathematician Jakob Steiner, elaborated the theory of modern projective geometry, the study of the properties of a geometric line or plane figure that remain unchanged when the figure is projected onto a plane from a point not on either the plane or the figure. In his text Traité de géométrie in 1852 Chasles discusses cross ratio, pencils and involutions, all notions which he introduced. Chasles was the victim of a celebrated fraud paying the equivalent of 20,000 pounds for various letters from famous men of science and others which turned out to be forged. *TIS

1970 Pao-Lu Hsu (1 Sept 1910 in Beijing, China - 18 Dec 1970 in Beijing, China) Hsu passed examinations in 1936 at Peking University and obtained a scholarship to enable him to continue his graduate studies in Britain. He spent four years in Britain mainly at University College, London but he also spent some time studying at Cambridge. Certainly University College, London was an excellent place for Hsu to study as his mathematical interests were in probability and statistics. Egon Pearson, following the retirment of his father Karl Pearson as Galton Professor of Statistics, had been made Reader and became Head of the Department of Applied Statistics three years before Hsu arrived there. Jerzy Neyman had been appointed in 1934 while R A Fisher held Karl Pearson's Galton Chair of Statistics and was Head of the Department of Eugenics at University College. Lehmann writes, "During this period Hsu wrote a remarkable series of papers on statistical inference which show the strong influence of the Neyman-Pearson point of view."
Hsu's first two papers were published in the Statistical Research Memoirs which were edited by Jerzy Neyman and Egon Pearson. One concerned what is now known as the Behrens-Fisher problem, while the second Hsu examined the problem of optimal estimators of the variance in the Gauss-Markov model.
In 1938 Hsu, while still undertaking research for his doctorate, too up a position as lecturer in Egon Pearson's Department. He was awarded the degree of Ph.D. and then that of D.Sc. from University College, London, in 1938 and 1940, respectively. Anderson, Chung and Lehmann write, "[Hsu's] British education formed his taste in mathematics; he preferred the hard and concrete to the general and abstract. "
By 1940 China was engaged in World War II fighting against the Japanese invasion and Britain was involved in the war against Germany. Hsu chose to leave Britain to return to his homeland of China where he was appointed as Professor at Peking University. It was a period of great difficulty and hardship for Hsu. He corresponded with Neyman during the years 1943-44, who by this time was at Berkeley in the United States, about statistical matters but he mentions in these letters the great hardship he was suffering, particularly suffering starvation.
It is a great tribute to Hsu's determination to devote himself to statistics that he managed to continue his research during these difficult war years. Many of his publications on multivariate analysis from this period show that he had been strongly influenced by R A Fisher while at University College. His role in promoting the use of matrix theory in statistics should also be emphasized. These papers brought him to, "... the forefront of the development of the mathematical theory of multivariate analysis. "
Attempts were made to get Hsu to the United States. In 1945 he arrived in the USA just in time for the First Berkeley Symposium on Probability and Statistics. During the next two years he taught at the University of California, Columbia University, and the University of North Carolina where he was offered an associate professorship.
After spending 1946-47 at the University of North Carolina at Chapel Hill, in 1947 Hsu returned to his professorship at Peking University. *SAU

1995 Konrad Zuse (22 Jun 1910, 18 Dec 1995) German engineer who in 1941 constructed the first fully operational program-controlled electromechanical binary calculating machine, or digital computer, called the Z3. Earlier, Zuse developed and built the Z1 the first binary digital computer in the world (1936-8) and two more machines before the end of WW II, but he was unable to convince the Nazi government to support his work. He created a basic programming system known as Plankalkül with which he designed a chess playing program.The Z3 was destroyed in 1944 during the war. Next came the more sophisticated Z4, which was the only Zuse Z-machine to survive the war, by several moves to new locations away from air raids. During the last days of war it was hidden. In 1950, he took it to Zurich. *TIS In an interesting coincidence, the first paper of Roger Lyndon, who was born on this date) was on the Zuse computer . In the paper he described the Z4, Zuse's relay-type digital computer which was discovered by advancing British and American troops. The nearly completed computer had been hidden by Zuse in the cellar of a house in the small village of Hinterstein in Bavaria. *SAU

1995 Nathan Rosen (22 Mar 1909, 18 Dec 1995) U.S.-born Israeli theoretical physicist who in 1935 collaborated with Albert Einstein and Boris Podolsky on a much-debated refutation of the theory of quantum mechanics; he later came to accept the theory. The famous Einstein-Podolsky-Rosen critique of quantum mechanics was published in the 1935 Physical Review. (A New York Times obituary described The Physical Review as "one of the most impenetrable periodicals in the English language.") Rosen founded the Institute of Physics at Technion in Haifa.*TIS

2007 Samuel Karlin (June 8, 1924 - December 18, 2007) was an American mathematician at Stanford University in the late 20th century.
Karlin earned his undergraduate degree from Illinois Institute of Technology; and then his doctorate in mathematics from Princeton University in 1947 (at the age of 22) under the supervision of Salomon Bochner. He was on the faculty of Caltech from 1948–56, before becoming a professor of mathematics and statistics at Stanford.
Throughout his career, Karlin made fundamental contributions to the fields of mathematical economics, bioinformatics, game theory, evolutionary theory, biomolecular sequence analysis, and total positivity. He did extensive work in mathematical population genetics. In the early 1990s, Karlin and Stephen Altschul developed the Karlin-Altschul statistics, a basis for the highly used sequence similarity software program BLAST.
Karlin authored ten books and more than 450 articles. Karlin was a member of both the American Academy of Arts and Sciences and the National Academy of Sciences. In 1989, President George H. W. Bush bestowed Karlin the National Medal of Science "for his broad and remarkable researches in mathematical analysis, probability theory and mathematical statistics, and in the application of these ideas to mathematical economics, mechanics, and population genetics."
Karlin's three children all became scientists. One of his sons, Kenneth D. Karlin, is a professor of chemistry at Johns Hopkins University and the 2009 winner of the American Chemical Society's F. Albert Cotton Award for Synthetic Chemistry.  His other son, Manuel, is a physician in Portland, Oregon. His daughter, Anna R. Karlin, is a theoretical computer scientist, the Microsoft Professor of Computer Science & Engineering at the University of Washington. *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