Monday, 18 December 2017

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.


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


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


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 

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

Sunday, 17 December 2017

On This Day in Math - December 17

Davy statue in Penzance

Nothing tends so much to the advancement of knowledge
 as the application of a new instrument.
~Sir Humphry Davy

The 351st day of the year; 351 is a triangular number, and the sum of five consecutive primes. It is also an element in the Padovan sequence, an interesting exploration for students.

351 is the smallest number n so that n, n+1, and n+2 are all the product of four or more primes.

1610 Father Christoph Clavius SJ, the senior mathematician at the Collegio Romano writes to inform Galileo that he and other Jesuits at the college had seen the four moons of Jupiter. Only two months earlier he had said that if Galileo saw "planets" around Jupiter in his glass, then he must have put them there. *David Leverington, Babylon to Voyager and Beyond: A History of Planetary Astronomy

December 17, 1750 - Mr. Theophilus Grew appointed first Master in Mathematics at Academy of Philadelphia (to become the Univ of Pennsylvania). Grew published the first American Trigonometry book while there, “The Description and Use of the Globes..”.  His 1752 Barbados almanack, for the year of our Lord 1752, being bissextile, or leap-year. / By Theophilus Grew, professor of the mathematics was published in 1751 and printed by Ben Franklin. "This is the only recorded sheet almanac extant from the Franklin shop and the only one prepared by Grew which Franklin and Hall are known to have printed."--*C. W. Miller, Franklin (My blog notes about Grew here from U Pa.)

In 1790, Mexico's greatest Aztec relic, an Aztec calendar stone is discovered in Mexico City. The 24-ton "Sun Stone" bears carved astronomical symbols. Based on the movements of the stars, it reflects the Aztecs’ knowledge of astronomy and mathematics. Used to predict the seasons and natural events, it also regulated economic and social activities as well as religious ceremonies. Making it took them 52 years (1427-79), and it is 103 years older than the Gregorian calendar in use in most cultures today. The Spanish buried this colossal monument during the Conquest where the Metropolitan Cathedral stands today in the main plaza of Mexico City. It was lost for 250 years until 1790, when it was accidentally uncovered during repair work on the Cathedral.*TIS

1804 One of the earliest science board games released.
An astronomical board game, folded into cardboard slip case, entitled 'Science in Sport, or the Pleasures of Astronomy; A New & Instructive Pastime. Revised & approved by Mrs. Bryan; Blackheath', 'Published, December 17th 1804, by the Proprietor, John Wallis, No. 16, Ludgate Street, London
The game is based on the traditional Game of the Goose, which was adapted to a wide range of themed boards, many produced by John Wallis, one of the leading publishers of board games in the early 19th century. Margaret Bryan (fl. 1795-1816) ran a girl's school in Blackheath and was author of a number of popular works on science (ZBA4475 is her portrait), and Wallis evidently felt that her association with this game would be a testament to its accuracy, as well as highlighting its suitability for girls' education. The board has 35 numbered 'squares' depicting astronomical objects, instruments and principles as well as astronomers (Ptolemy, Tycho Brahe, Nicholas Copernicus, Isaac Newton) and moral lessons (e.g. a studious and idle boy, the county gaol and an army volunteer). One square shows the man in the moon as an example of ignorance in astronomy. By spinning a 'te-totum', players can travel over the board, the object being to spin numbers up to 35 and reach the final 'square', depicting Flamsteed House: 'Whoever first arrives here is to take the title of Astronomer Royal'. The game involves much rote learning as well as moral lessons en route: within the rules of the game accuracy of knowledge and zeal are rewarded, while ignorance and idleness are punished. The requirements of each square and its consequences were recorded in an accompanying booklet, although this has been lost from this edition. This copy of the game belonged to William Proctor, the father of the astronomer and writer on science, Richard A. Proctor (1837-1888).
*National Maritime Museum, Greenwich, London

1903 The Wright brothers flew their first plane at Kitty Hawk. Following unsuccessful attempt only three days before, the Wright brothers took their newly-built Wright Flyer to Kitty Hawk, North Carolina made "the first sustained and controlled heavier-than-air powered flight". In fact they made four flights that day. Orville made two and Wilber made two. The last of the four flights that day stayed aloft for 59 seconds and traveled 852 feet.
“Wishing to inform their father of the good news and make the press aware of the achievement, Orville sent him the following telegram just hours later.
Note: During the telegram's transmission, '59' seconds mistakenly became '57', and 'Orville' became 'Orevelle'.

176 C KA C8 33 Paid. Via Norfolk Va
Kitty Hawk N C Dec 17
Bishop M Wright
7 Hawthorne St
Success four flights Thursday morning all against twenty one mile wind started from Level with engine power alone average speed through air thirty one miles longest 57 seconds inform Press home Christmas.

Orevelle Wright 525P
*Letters of Note

In 1919, Albert Porta an expert seismographer and meteorologist predicted that a conjunction of six planets on this date would spell the end of the world. The alignment of planets would cause a magnetic current which would pierce the sun and thereby engulf the earth in flames. As the date approached suicides and hysteria were reported throughout the world. *TIS

1969 Egypt issued a stamp to publicize the International Congress for Scientific Accounting which began in Cairo on this date. Pictured are ancient arithmetic and modern computer cards. [Scott #815].


1706 Gabrielle-Émilie Le Tonnelier de Breteuil, Marquise du Châtelet (17 Dec 1706; 10 Sep 1749)  was a French mathematician and physicist who was the mistress of Voltaire. She took to mathematics and the sciences, being exposed to distinguished guests of her aristocratic parents. Emilie was interested in the philosophies of Newton and Leibniz, and dressed as a man to enter the cafes where the scientific discussions of the time were carried on. Châtelet's major work was a translation of Newton's Principia, begun in 1745. Voltaire wrote the preface. The complete work appeared in 1759 and was for many years the only translation of the Principia into French. She died in 1749, a few days after giving birth to her daughter. *TIS

1778 Sir Humphrey Davy Born In his hometown of Penzance, Cornwall, a statue of Davy stands in front of the imposing Market House (now owned by Lloyds TSB) at the top of the town's main street Market Jew Street. The plaque is a nice description of a full life.

Nearby is a house on which a commemorative plaque claims the location as the site of his birth.
Penzance also has a secondary school named Humphry Davy School. Like James Prescott Joule and Isaac Newton, Davy is also remembered in his hometown by a pub – "The Sir Humphry Davy" at 32 Alverton Street, west of the Market House.
The first ever clerihew (a whimsical, four-line biographical poem invented by Edmund Clerihew Bentley) was written about Sir Humphry Davy:

Sir Humphrey [sic] Davy
Abominated gravy.
He lived in the odium
Of having discovered sodium.

Said to have been written as a schoolboy during a chemistry class at St. Paul's School.

1797 Joseph Henry (17 Dec 1797; 13 May 1878) One of the first great American scientists after Benjamin Franklin. Although Henry at an early age appeared to be headed for a career in the theater, a chance encounter with a book of lectures on scientific topics turned his interest to science. He aided Samuel F.B. Morse in the development of the telegraph and discovered several important principles of electricity, including self-induction, a phenomenon of primary importance in electronic circuitry. He was the first Secretary (director) of the Smithsonian Institution (1846-1878), where he established the foundation of a national weather service. For more than thirty years, Henry insisted that basic research was of fundamental importance. *TIS Henry was the first Secretary of the Smithsonian Museum.

1835 Felice Casorati is best remembered for the Casorati-Weierstrass theorem characterizing the behavior of a function near an essential singularity.*SAU

1842 (Marius) Sophus Lie (17 Dec 1842; 18 Feb 1899) was a Norwegian mathematician who made significant contributions to the theories of algebraic invariants, continuous groups of transformations and differential equations. Lie groups and Lie algebras are named after him. Lie was in Paris at the outbreak of the French-German war of 1870. Lie left France, deciding to go to Italy. On the way however he was arrested as a German spy and his mathematics notes were assumed to be coded messages. Only after the intervention of French mathematician, Gaston Darboux, was Lie released and he decided to return to Christiania, Norway, where he had originally studied mathematics to continue his work. *TIS

1861 Arthur Edwin Kennelly (17 Dec 1861; 18 Jun 1939) Irish-American electrical engineer who made innovations in analytic methods in electronics, particularly the definitive application of complex-number theory to alternating-current (ac) circuits. For six years he worked for Thomas Edison at West Orange Laboratory, then branched out as a consultant. Upon his co-discovery (with Oliver Heaviside) of the radio reflecting properties of the ionosphere in the upper atmosphere, the stratum was called the Kennelly- Heaviside layer*TIS

1863 Henri Eugène Padé (December 17, 1863 – July 9, 1953) was a French mathematician, who is now remembered mainly for his development of approximation techniques for functions using rational functions.*Wik He made advances with continued fractions.

1894 Hendrik Anthony Kramers (17 Dec 1894; 24 Apr 1952) Dutch physicist who, with Ralph de Laer Kronig, derived important equations relating the absorption to the dispersion of light. He also predicted (1924) the existence of the Raman effect, an inelastic scattering of light. Kramer's work covers almost the entire field of theoretical physics. He published papers dealing with mathematical formalism of quantum mechanics, and others on paramagnetism, magneto-optical rotation, ferro-magnetism, kinetic theory of gases, relativistic formalisms in particle theory, and on theory of radiation. His work shows outstanding mathematical skill and careful analysis of physical principles. *TIS

1900 Dame Mary Lucy Cartwright (17 Dec 1900 in Aynho, Northamptonshire, England
- 3 April 1998 in Cambridge, England) In 1930 Cartwright was awarded a Yarrow Research Fellowship and she went to Girton College, Cambridge, to continue working on the topic of her doctoral thesis. Attending Littlewood's lectures, she solved one of the open problems which he posed. Her theorem, now known as Cartwright's Theorem, gave an estimate for the maximum modulus of an analytic function which takes the same value no more than p times in the unit disc. To prove the theorem she used a new approach, applying a technique introduced by Ahlfors for conformal mappings.
Cartwright was appointed, on the recommendation of both Hardy and Littlewood, to an assistant lectureship in mathematics in Cambridge in 1934, and she was appointed a part-time lecturer in mathematics the following year. In 1936 she became director of studies in mathematics at Girton College, and in 1938 she began work on a new project which had a major impact on the direction of her research. The Radio Research Board of the Department of Scientific and Industrial Research produced a memorandum regarding certain differential equations which came out of modelling radio and radar work. They asked the London Mathematical Society if they could help find a mathematician who could work on these problems and Cartwright became interested in their memorandum.
The dynamics which lay behind the problems was unfamiliar to Cartwright and so she approached Littlewood for help with this aspect. They began to collaborate studying the equations. Littlewood wrote, "For something to do we went on and on at the thing with no earthly prospect of "results"; suddenly the whole vista of the dramatic fine structure of solutions stared us in the face. "
The fine structure which Littlewood describes here is today seen to be a typical instance of the "butterfly effect". The collaboration led to important results, and these have greatly influenced the direction that the modern theory of dynamical systems has taken. In 1947, largely on the basis of her remarkable contributions in the collaboration with Littlewood, she was elected a Fellow of the Royal Society and, although she was not the first woman to be elected to that Society, she was the first woman mathematician. *SAU

1908 Willard Frank Libby (17 Dec 1908; 8 Sep 1980) American chemist whose technique of carbon-14 (or radiocarbon) dating provided an extremely valuable tool for archaeologists, anthropologists, and earth scientists. For this development he was honoured with the Nobel Prize for Chemistry in 1960. Libby is a specialist in radiochemistry, particularly hot atom chemistry, tracer techniques, and isotope tracer work. He became well-known at Chicago University also for his work with natural tritium, and its use in hydrology and geophysics. On 18 May 1952, he determined that the age of Stonehenge was 1848 BC, based on analysis of radioisotopes in charcoal. *TIS

1920 APL Co-Inventor Kenneth E. Iverson is Born in Camrose, Alberta, Canada. He received a BA in mathematics from Queen’s University in Ontario, a MA and PhD in applied mathematics from Harvard. Iverson taught at Harvard, worked for IBM and I.P. Sharp Research Associates. With Adin D. Falkoff, he developed A Programming Language​ (APL). It was a triumphant start of his career, and for over 35 following years Iverson was able to transform his invention into a successful commercial property. He received the AFIPS Harry Goode Award in 1975, ACM Turing Award in 1979, IEEE Computer Pioneer Award in 1982, and the National Medal of Technology in 1991. *CHM

1941 V. Frederick Rickey born. The math historian who is the first source for this blog.  V. Frederick Rickey, a logician turned historian, earned three degrees from the University of Notre Dame (Ph.D. 1968) and then went to Bowling Green State University where he rose through the professorial ranks to become Distinguished Teaching Professor Emeritus. He has broad interests in the history of mathematics and is especially interested in the development of the calculus.
He has been on leave six times, most recently during the 2007-2008 Academic Year when he was doing research for a book on the history of the Mathematics Department at West Point. His previous leave was spent in Washington D. C. where he was Visiting Mathematician at the MAA Headquarters. While there he was involved in the founding of Math Horizons, a magazine for mathematics undergraduates; became the first editor of electronic services for the MAA and built its first gopher and web pages (both long departed); and wrote a successful NSF proposal for an Institute for the History of Mathematics and Its Use in Teaching.
He loves teaching and enjoys giving lectures to mathematicians about the history of their field. He received the first award from the Ohio Section for Distinguished College or University Teaching of Mathematics, and was in the first group to receive a MAA National Award for teaching. *Biography from Professor Rickey's web page


1851 Olinde Rodrigues was a French mathematician best known for his formula for the Legendre polynomials.*SAU

1857 Sir Francis Beaufort (7 May 1774, 17 Dec 1857) Inventor of the wind force scale. In 1806, British Admiral Sir Francis Beaufort devised a simple scale that coastal observers could use to report the state of the sea to the Admiralty. Originally to describe wind effects on a fully rigged man-of-war sailing vessel, it was later extended to include descriptions of effects on land features as well. Officially adopted in 1838, it uses numbers 0 to 12, to designate calm, light air, light breeze, gentle breeze, moderate breeze, fresh breeze, strong breeze, moderate gale, fresh gale, strong gale, whole gale, storm, and hurricane. Zero (calm) is a wind velocity of less than 1 mph (0.6 kph) and 12 (hurricane) represents a velocity of over 75 mph (120kph). He was Hydrographer of the Navy from 1829-55.*TIS

1907 William Thompson, Lord Kelvin; died of a severe chill on 17 December 1907.
The Royal Society asked the Dean of Westminster if Kelvin could be buried in the Abbey and he agreed. The funeral was on 23 December and he lies to the south of Sir Isaac Newton's grave in the nave. On the previous night the coffin, covered by a purple pall, had rested in St Faith's chapel. The simple stone reads: WILLIAM THOMSON LORD KELVIN 1824-1907.
In 1913 a stained glass window, designed by J.Ninian Comper, was erected near the grave. This contains large figures of King Henry V and Abbot William Colchester and below is an inscription "In memory of Baron Kelvin of Largs. Engineer, Natural Philosopher. B.1824.D.1907". His coat of arms and those of Glasgow University are shown. The window was the gift of engineers from Great Britain and America.

1912 Spiru C. Haret (15 February 1851 – 17 December 1912) was a Romanian mathematician, astronomer and politician. He made a fundamental contribution to the n-body problem in celestial mechanics by proving that using a third degree approximation for the disturbing forces implies instability of the major axes of the orbits, and by introducing the concept of secular perturbations in relation to this.
As a politician, during his three terms as Minister of Education, Haret ran deep reforms, building the modern Romanian education system. He was made a full member of the Romanian Academy in 1892.
He also founded the Astronomical observatory in Bucharest, appointing Nicolae Coculescu as its first director. The crater Haret on the Moon is named after him. *Wik

1940 Alicia Boole Stott (June 8, 1860, Ireland – December 17, 1940, England) was the third daughter of George Boole and Mary Everest Boole, born in Cork, Ireland. Before marrying Walter Stott, an actuary, in 1890, she was known as Alicia Boole. She is best known for coining the term "polytope" to refer to a convex solid in four dimensions, and having an impressive grasp of four-dimensional geometry from a very early age.
She found that there were exactly six regular polytopes in four dimensions and that they are bounded by 5, 16 or 600 tetrahedra, 8 cubes, 24 octahedra or 120 dodecahedra. She then produced three-dimensional central cross-sections of all the six regular polytopes by purely Euclidean constructions and synthetic methods for the simple reason that she had never learned any analytic geometry. She made beautiful cardboard models of all these sections.
After taking up secretarial work near Liverpool in 1889 she met and married Walter Stott in 1890. Stott learned of Pieter Schoute's work on central sections of the regular polytopes in 1895. Schoute came to England and worked with Alicia Stott, persuading her to publish her results which she did in two papers published in Amsterdam in 1900 and 1910.
The University of Groningen honoured her by inviting her to attend the tercentenary celebrations of the university and awarding her an honorary doctorate in 1914.
In 1930 she was introduced to Harold Coxeter and they worked together on various problems. Alicia Boole Stott made two further important discoveries relating to constructions for polyhedra related to the golden section. Coxeter described his time doing joint work with her saying, "The strength and simplicity of her character combined with the diversity of her interests to make her an inspiring friend." *Wik

1964 Victor Francis Hess (24 June 1883, 17 Dec 1964) Austrian-born physicist who was a joint recipient, with Carl D. Anderson of the United States, of the Nobel Prize for Physics in 1936 for his discovery of cosmic rays, high-energy radiation originating in outer space. *TIS

1973 Charles Greeley Abbot (31 May 1872, 17 Dec 1973)  was an American astrophysicist who is thought to have been the first scientist to suspect that the radiation of the Sun might vary over time. In 1906, Abbot became director of the Smithsonian Astrophysical Observatory and, in 1928, fifth Secretary of the Smithsonian. To study the Sun, SAO established a network of solar radiation observatories around the world-- usually at remote and desolate spots chosen primarily for their high percentage of sunny days. Beginning in May 1905 and continuing over decades, his studies of solar radiation led him to discover, in 1953, a connection between solar variations and weather on Earth, allowing general weather patterns to be predicted up to 50 years ahead.*TIS

1999 Juergen Kurt Moser (July 4, 1928, Königsberg, East Prussia – December 17, 1999, Schwerzenbach, Kanton Zürich, Switzerland) was a German-American mathematician.
He won the first George David Birkhoff Prize in 1968 for contributions to the theory of Hamiltonian dynamical systems, the James Craig Watson Medal in 1969 for his contributions to dynamical astronomy, the L. E. J. Brouwer Medal of the Royal Dutch Mathematical Society in 1984, the Cantor Medal of the Deutsche Mathematiker-Vereinigung in 1992 and the Wolf Prize in 1995 for his work on stability in Hamiltonian systems and on nonlinear differential equations. He was elected to membership of the National Academy of Sciences in 1973 and was corresponding member of numerous foreign academies such as the London Mathematical Society and the Akademie der Wissenschaften und Literatur, Mainz . At three occasions he was an invited speaker at the quadrennial International Congress of Mathematicians, namely in Stockholm (1962) in the section on Applied Mathematics, in Helsinki (1978) in the section on Complex Analysis, and a plenary speaker in Berlin (1998). In 1990 he was awarded an honorary doctorate from the University of Bochum. The Society for Industrial and Applied Mathematics established a lecture prize in his honor in 2000. *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

Saturday, 16 December 2017

On This Day in Math - December 16

The fact that the author thinks slowly is not serious, but the fact that he publishes faster than he thinks is inexcusable.
~Wolfgang Pauli

The 350th day of the year; 350 is S(7,4), a Stirling Number of the second kind.

3502+1 = 122,501 is prime. The last day of the year for which n2 + 1 is prime.

Lucky Sevens, 350 = 73 + 7

Both 350 and 351 are the product of four primes. 350 = 2x5x5x7 and 351 = 3x3x3x13. They are the third, and last pair of consecutive year days that are the product of four primes. (Don't just sit there, find the others!")


1627 Cavalieri announced to Galileo and Cardinal Borromeo that he had completed his Geometria, which contains his method of indivisibles, now known as Cavalieri’s principle. *VFR

1799 Gauss wrote Wolfgang Bolyai that he was sorry they had not discussed the theory of parallels during their student days together at Gottingen (1796–1798). *G. E. Martin, Foundations of Geometry and the Non-Euclidean Plane, p. 306

1861 Weierstrass, who for twelve years had endured painful attacks of vertigo, suffered a complete collapse of his health due to overwork. Henceforth, he always lectured while seated, consigning the blackboard work to an advanced student. Nevertheless, he eventually became a recognized master teacher. *VFR

1897 Marie Curie began her research in an unheated abandoned shed with the piezo-quartz electrometer invented by her husband Pierre and his brother Jacques, a minerology professor.  *Brody & Brody, The Science Class You Wish You Had

1926 In September of this year Samuel Goudsmit and George Eugene Uhlenbeck – both graduate students working under Paul Ehrenfest at the University of Leiden, published a paper on electron spin. The article caught the attention of Warner Heisenberg who wrote a letter to Samuel Goudsmit regarding the concept on December 16. The letter was subsequently misplaced and not found until March of 2017. Esther Goudsmit, daughter of Samuel Goudsmit, sent the letter (in German) and its translation to the Niels Bohr Library & Archives. She had found it in a drawer of miscellany and decided it was important that it be united with the rest of her father’s papers. NBL&A

1941 Pope Pius XII declared Albertus Magnus the patron of all who cultivate the natural sciences. *VFR


1625 Erhard Weigel (December 16, 1625 – March 21, 1699) was a German mathematician, astronomer and philosopher. He earned his Ph.D. from the University of Leipzig. From 1653 until his death he was professor of mathematics at Jena University. He was the teacher of Leibniz in 1663, and other notable students. He also worked to make science more widely accessible to the public, and what would today be considered a populariser of science. Through Leibniz, Weigel is the intellectual forefather of a long tradition of mathematicians that connects a great number of professionals to this day. The Mathematics Genealogy Project lists more than 50,000 "descendants" of Weigel's, including Lagrange, Euler, Poisson and several Fields Medalists. *Wik
A post at the Renaissance Mathematicus about Weigel and some of his lesser known students (most student's would be "lesser known" compared to Leibniz) also pointed out that "Another Weigel innovation in celestial cartography was his eclipse map from 1654. An eclipse map is a map that shows the path on the surface of the earth from which a solar eclipse will be visible. Weigel’s was the first such printed map ever produced. This honour is usually falsely accredited to Edmund Halley for his 1715 eclipse map."
For religious reasons, he wanted to rename all the constellations, and made several globes of the sky with his renamed constellations. The one below is from the Franklin Institute.

1752 Goldbach wrote Euler with a conjecture that every odd number greater than 3 is the sum of an odd number and twice a square (he allowed 02). Euler would reply on Dec 16 that it was true for the first 1000 odd numbers, and then again on April 3, 1753, to confirm it for the first 2500. A hundred years later, German mathematician Moritz Stern found two contradictions, 5777 and 5993. The story appears in Alfred S. Posamentier's Magnificent Mistakes in Mathematics, (but gloriously, has a mistake for the date, using 1852, but such a wonderful book can forgive a print error.)

1776 Johann Wilhelm Ritter (16 Dec 1776; 23 Jan 1810) German physicist who discovered the ultraviolet region of the spectrum (1801) and thus helped broaden man's view beyond the narrow region of visible light to encompass the entire electromagnetic spectrum from the shortest gamma rays to the longest radio waves. After studying Herschel's discovery of infrared radiation, he observed the effects of solar radiation on silver salts and deduced the existence of radiation outside the visible spectrum. He also made contributions to spectroscopy and the study of electricity. *TIS

1804 Viktor Bunyakovsky (16 Dec 1804 in Bar, Podolskaya gubernia (now Vinnitsa oblast), Ukraine - 12 Dec 1889 in St Petersburg, Russia) worked on Number Theory as well as geometry, mechanics and hydrostatics. He discovered the Cauchy-Schwarz inequality 25 years before Cauchy or Schwarz.*SAU

1826 Giovanni Battista Donati (16 Dec 1826; 20 Sep 1873) Italian astronomer who, on 5 Aug 1864, was first to observe the spectrum of a comet (Tempel 1864 II), showing not merely reflected sunlight but also spectral lines from luminous gas forming the comet tail when near the Sun. Earlier, he discovered the comet known as Donati's Comet at Florence, on 2 Jun 1858. When the comet was nearest the earth, its triple tail had an apparent length of 50°, more than half the distance from the horizon to the zenith and corresponding to the enormous linear figure of more than 72 million km (about 45 million mi). With an orbital period estimated at more than 2000 years, it will not return until about the year 4000.*TIS

1828 Alexander Ross Clarke (16 Dec 1828; 11 Feb 1914) English geodesist with the Army Ordnance Survey who made calculations of the size and shape of the Earth (the Clarke ellipsoid) were the first to approximate accepted modern values with respect to both polar flattening and equatorial radius. The figures from his second determination (1866) became a standard reference for U.S. geodesy for most of the twentieth century until satellites could improve accuracy. In 1880, Clarke coined the term "Geodesy" when he published his famous book by that title. He wrote articles on mathematical geography and geodesy and also contributed "The Figure of the Earth" in the Encyclopedia Britannica. His military service with the Ordnance Survey lasted 27 years.*TIS

1849 Gyula Kőnig (16 December 1849 – 8 April 1913) was a Hungarian mathematician. He was born in Győr, Hungary and died in Budapest. His mathematical publications in foreign languages appeared under the name Julius König. His son Denes Konig is the famous graph theorist.Kőnig worked in many mathematical fields. His work on polynomial ideals, discriminants and elimination theory can be considered as a link between Leopold Kronecker and David Hilbert as well as Emmy Noether. Later on his ideas were simplified considerably, to the extent that today they are only of historical interest.
Kőnig already considered material influences on scientific thinking and the mechanisms which stand behind thinking.
“ The foundations of set theory are a formalization and legalization of facts which are taken from the internal view of our consciousness, such that our 'scientific thinking' itself is an object of scientific thinking."
But mainly he is remembered for his contributions to and his opposition against set theory.*Wik

1857 Edward Emerson Barnard (16 Dec 1857; 6 Feb 1923)
astronomer who pioneered in celestial photography, specializing in wide-field photography. From the time he began observing in 1881, his skill and keen eyesight combined to make him one of the greatest observers. Barnard came to prominence as an astronomer through the discovery of numerous comets. In the 1880s, a patron of astronomy in Rochester, N.Y. awarded $200 per new comet was found. Barnard discovered eight - enough to build a "comet house" for his bride. At Lick Observatory (1888-95) he made the first photographic discovery of a comet; photographed the Milky Way; and discovered the fifth moon of Jupiter. Then he joined Yerkes Observatory, making his Photographic Atlas of Selected Regions of the Milky Way.*TIS

1887 Johann Radon (16 Dec 1887 in Tetschen, Bohemia (now Decin, Czech Republic)
- 25 May 1956 in Vienna, Austria) Radon applied the calculus of variations to differential geometry which led to applications in number theory. It was while he was studying applications of the calculus of variations to differential geometry that he discovered curves which are now named Radon curves. His best known results involve combining the integration theories of Lebesgue and Stieltjes which first appeared in his habilitation dissertation and then in a second important work Über lineare Funktionaltransformationen und Funktionalgleichungen (1919).
During 1918-19 he worked on affine differential geometry, then in 1926 he considered conformal differential geometry. His wide interests led him to study Riemannian geometry and geometrical problems which arose in the study of relativity. *SAU

1905 Piet Hein (December 16, 1905–April 17, 1996) was a Danish scientist, mathematician, inventor, designer, author, and poet, often writing under the Old Norse pseudonym "Kumbel" meaning "tombstone". His short poems, known as gruks or grooks (Danish: Gruk), first started to appear in the daily newspaper "Politiken" shortly after the Nazi occupation in April 1940 under the pseudonym "Kumbel Kumbell"
The Soma cube is a solid dissection puzzle invented by Piet Hein in 1933 during a lecture on quantum mechanics conducted by Werner Heisenberg. Seven pieces made out of unit cubes must be assembled into a 3x3x3 cube. The pieces can also be used to make a variety of other 3D shapes. Piet Hein created the superellipse which became the hallmark of modern Scandinavian architecture.
In addition to the thousands of grooks he wrote, Piet Hein devised the games of Hex, Tangloids, Morra, Tower, Polytaire, TacTix, Nimbi, Qrazy Qube, Pyramystery, and the Soma cube. He advocated the use of the superellipse curve in city planning, furniture making and other realms. He also invented a perpetual calendar called the Astro Calendar and marketed housewares based on the superellipse and Superegg. *Wik
My Favorite of his grooks is this one:
Problems worthy
of attack
prove their worth
by hitting back.

1925 IBM-701 Team Member William F. McClelland is born in Bronxville, N.Y. He received a BS from MIT in 1947 and immediately joined IBM Watson Laboratory. At IBM he programmed the SSEC (Selective Sequence Electronic Calculator) for John von Neumann and was chairman of the Mathematics Planning Group in 1951-1953. This group developed computer specifications to solve complex mathematical problems, performed basic research in the use of a stored-binary calculator, and wrote and tested programs that were supplied to the customers of the 701.
McClelland had held various management and marketing position at IBM until his retirement in 1982. *CHM

1687 Sir William Petty FRS (26 May 1623 – 16 December 1687) was an English economist, scientist and philosopher. He first became prominent serving Oliver Cromwell and Commonwealth in Ireland. He developed efficient methods to survey the land that was to be confiscated and given to Cromwell's soldiers. He also managed to remain prominent under King Charles II and King James II, as did many others who had served Cromwell.
He was Member of the Parliament of England briefly and was also a scientist, inventor, and entrepreneur, and was a charter member of the Royal Society. It is for his theories on economics and his methods of political arithmetic that he is best remembered, however, and to him is attributed the philosophy of 'laissez-faire' in relation to government activity. He was knighted in 1661. He was the great-grandfather of Prime Minister William Petty Fitzmaurice, 2nd Earl of Shelburne and 1st Marquess of Lansdowne.
Petty was a founder member of The Royal Society. He was born and buried in Romsey, and was a friend of Samuel Pepys.
He is best known for economic history and statistic writings, pre-Adam Smith. Of particular interest were Petty's forays into statistical analysis. Petty's work in political arithmetic, along with the work of John Graunt, laid the foundation for modern census techniques. Moreover, this work in statistical analysis, when further expanded by writers like Josiah Child documented some of the first expositions of modern insurance. Vernon Louis Parrington notes him as an early expositor of the labour theory of value as discussed in Treatise of Taxes in 1692.
Petty was knighted in 1661 by Charles II and returned to Ireland in 1666, where he remained for most of the next twenty years. *Wik

1933 Ludwig Schlesinger (1 Nov 1864 in Nagyszombat, Hungary (now Trnava, Tyrnau, Slovakia)- 16 Dec 1933 in Giessen, Germany was a mathematician, born in what is now Slovakia, who worked on differential equations. *SAU

1934 Gustav de Vries (22 Jan 1866 in Amsterdam, The Netherlands
- 16 Dec 1934 in Haarlem, The Netherlands) was a Dutch mathematician who introduced the famous Korteweg-de Vries equation which characterizes traveling waves. *SAU

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

Friday, 15 December 2017

On This Day in Math - December 15

The reason why new concepts in any branch of science are hard to grasp is always the same; contemporary scientists try to picture the new concept in terms of ideas which existed before.
~Freeman Dyson

The 349th day of the year; 349 is a prime, and the sum of three consecutive primes.

349 is the last day-number of the year that will be a member of a twin prime.

349 is also the largest day-number that is a prime such that p- product of its digits and p+product of its digits are both also prime; for 349, 349 + 3*4*9 = 457 and 349 - 3*4*9 = 241.. and 349, 457 and 241 are all prime. *Ben Vitale


1610 Father Christoph Clavius SJ writes Galileo to ask about why his large aperture was partly covered; Galileo would answer on the 30th that he did this for two reasons:
The first is to make it possible to work it more accurately because a large surface is
more easily kept in the proper shape than a smaller one. The other reason is that if
one wants to see a larger space in one glance, the glass can be uncovered, but it is then
necessary to put a less acute glass near the eye and shorten the tube, otherwise the
objects will appear very fuzzy. *Aalbert Vvan Helden, Galileo and the Telescope; Origins of the Telescope - Royal Netherlands Academy of Arts and Sciences, 2010

In 1612, Simon Marius, namer of Jupiter's 4 inner satellites, is first to observe Andromeda galaxy through a telescope. He described it in the preface to his Mundus Jovialis as, 'like the flame of a candle seen through horn'. Marius vrs Galileo is well covered in this blog at the Renaissance Mathematicus  .

1693 The House of Commons established the British National Debt by issuing one-million GBP of annuities. *Against the Gods: The Remarkable Story of Risk By Peter L. Bernstein

1742 Euler gave the first clear statement of the fundamental theorem of algebra: every algebraic equation of degree n has exactly n complex roots. Imprecise statements of the result were given earlier by Peter Rothe (1608) and Albert Girard (1629). Incorrect proofs were given by d’Alembert (1746), Euler (1749), Foncenex (1759), Lagrange (1772) and Laplace (1795), but a correct proof (and the name) had to await Gauss’s doctoral dissertation of 1799, who discovered it in the fall of 1797 when he was 20. * E. Smith, Source Book, p. 292

1859 Gustav R. Kirchhoff distillated from the sun spectra which elements are present in the sun. *SOLAR ECLIPSE NEWSLETTER

1887 Nature quotes J. J. Sylvester: “Perhaps I may, without immodesty, lay claim to the appellation of the mathematical Adam, as I believe that I have given more names (passed into general circulation) to the creatures of the mathematical reason than all the other mathematicians of the age combined.” [p. 162] *VFR (Among the many terms he created were matrix, discriminant, invariant, totient, and Jacobian)

1890 Karl Pearson is appointed Gresham Professor of Geometry. The first whose name is commonly known since Robert Hooke died in 1703. The terms “standard deviation” and “histogram” were first used in his lectures at Gresham College. *Gresham Geometry lecture by Robin Wilson, 2008

1896 Hollerith Agrees to Supply Machines for Russian Census:
Hollerith’s Census Machine was first employed by the U.S. Census Bureau in 1890 as the result of a crisis in counting a rapidly-increasing U.S. population. Methods based on Hollerith's machine served for almost 60 years until the Bureau adopted electron.*CHM (Image at Top, from

1928 To commemorate the International Congress of Medicine at Cairo, Egypt issued a postage stamp picturing Imhotep (c. 3000 BC). [Scott #153] *VFR

1965 Richard Feynman, having just won the Nobel Prize, makes a bet with CERN Director Viktor Weisskop that he will not hold a "responsible" position within the next ten years. A wager he will win. *Brain Pickings

1983 Grace Hopper was presented with the star to signify her promotion to Commodore (later Rear Admiral) by President Ronald Regan in a special White house ceremony. *WM

In 2001, the Leaning Tower of Pisa, Italy, was reopened to the public after a $27 million realignment that took over a decade. *TIS (sotto voce "But still, it leans!")


1732 Wenceslaus Johann Gustav Karsten (15 Dec 1732 in Neubrandenburg, Mecklenburg-Strelitz, Germany - 17 April 1787 in Halle, Germany) He wrote an important article in 1768 Von den Logarithmen vermeinter Grössen in which he discussed logarithms of negative and imaginary numbers, giving a geometric interpretation of logarithms of complex numbers as hyperbolic sectors, based on the similarity of the equations of the circle and of the equilateral hyperbola. *SAU

1802 János Bolyai (15 Dec 1802; 27 Jan 1860) Hungarian mathematician and one of the founders of non-Euclidean geometry - geometry that does not include Euclid's axiom that only one line can be drawn parallel to a given line through a point not on the given line. His father, Farkas Bolyai, had devoted his life to trying to prove Euclid's famous parallel postulate. Despite his father's warnings that it would ruin his health and peace of mind, János followed in working on this axiom until, in about 1820, he came to the conclusion that it could not be proved. He went on to develop a consistent geometry (published 1882) in which the parallel postulate is not used, thus establishing the independence of this axiom from the others. He also did valuable work in the theory of complex numbers. *TIS

1823 Mikhail Vasilyevich Ostrogradsky , (September 24, 1801 – January 1, 1862) was an Russian / Ukrainian mathematician, mechanician and physicist. Ostrogradsky is considered to be a disciple of Leonhard Euler and one of the leading mathematicians of Imperial Russia.
Ostrogradsky was born in Pashennaya, Poltava Governorate, Russian Empire (today Ukraine). From 1816 to 1820 he studied under Timofei Fedorovich Osipovsky (1765–1832) and graduated from the University of Kharkiv. When 1820 Osipovsky was suspended on religious grounds, Ostrogradsky refused to be examined and he never received his Doctor's degree. From 1822 to 1826 he studied at the Sorbonne and at the Collège de France in Paris, France. In 1828 he returned to the Russian Empire and settled in Saint Petersburg, where he was elected a member of the Academy of Sciences, Also he becomes the professor of the Main military engineering School of the Russian empire.
He worked mainly in the mathematical fields of calculus of variations, integration of algebraic functions, number theory, algebra, geometry, probability theory and in the fields of mathematical physics and classical mechanics. In the latter his most important work includes researches of the motion of an elastic body and the development of methods for integration of the equations of dynamics. Here he continued works of Euler, Joseph Louis Lagrange, Siméon-Denis Poisson and Augustin Louis Cauchy. His work in these fields was in Russia continued by Nikolay Dmitrievich Brashman (1796–1866), August Yulevich Davidov (1823–1885) and specially by the brilliant work of Nikolai Yegorovich Zhukovsky (1847–1921).
Ostrogradsky did not appreciate the work on non-Euclidean geometry of Nikolay Ivanovich Lobachevsky from 1823 and he rejected it, when it was submitted for publication in the Saint Petersburg Academy of Sciences.*Wik

1827 Samuel Roberts FRS (15 December 1827, Horncastle, Lincolnshire – 18 September 1913, London) was a British mathematician.
Roberts studied at Queen Elizabeth's Grammar School, Horncastle. He matriculated in 1845 at the University of London, where he earned in 1847 his bachelor's degree in mathematics and in 1849 his master's degree in mathematics and physics, as first in his class. Next he studied law and became a solicitor in 1853. After a few years of law practice he abandoned his law career and returned to mathematics, although he never had an academic position. He had his first mathematical paper published in 1848. In 1865 he was an important participant in the founding of the London Mathematical Society (LMS). From 1866 to 1892 he acted as legal counsel for LMS, from 1872 to 1880 he was the organization's treasurer, and from 1880 to 1882 its president. In 1896 he received the De Morgan Medal of the LMS. In 1878 he was elected FRS.
Roberts published papers in several fields of mathematics, including geometry, interpolation theory, and Diophantine equations.
Roberts and Pafnuty Chebyschev are jointly credited with the Roberts-Chebyshev theorem related to four-bar linkages *Wik

1834 Charles Augustus Young (15 Dec 1834; 3 Jan 1908) American astronomer who made the first observations of the flash spectrum of the Sun, proved the gaseous nature of the sun's corona and discovered the reversing layer of the solar atmosphere. He was a pioneer in the study of the spectrum of the sun and experimented in photographing solar prominences in full sunlight. On 22 Dec 1870, at the eclipse in Spain, he saw the lines of the solar spectrum all become bright for perhaps a second and a half (the "flash spectrum") and announced the "reversing layer." By exploring from the high altitude of Sherman, Wy. (1872), he more than doubled the number of bright lines he had observed in the chromosphere, By a comparison of observations, he concluded that magnetic conditions on the earth respond to solar disturbances. *TIS

1847 Achille Marie Gaston Floquet (December 15, 1847, Épinal–October 7, 1920, Nancy) was a French mathematician, best known for his work in mathematical analysis, especially in theory of differential equations.*Wik

1852 Antoine-Henri Becquerel (15 Dec 1852; 25 Aug 1908) was a French physicist who discovered radioactivity. In 1903 he shared the Nobel Prize for Physics with Pierre and Marie Curie. His early researches were in optics, then in 1896 he accidentally discovered radioactivity in fluorescent salts of uranium. He left some uranium mineral crystals in a drawer on a plate in black paper. Later, he developed the plate and found it was fogged, even though the crystals without ultraviolet radiation from sunlight were not fluorescing. Thus the salt was a source of a penetrating radiation. Three years afterwards he showed that it consists of charged particles that are deflected by a magnetic field. Initially, the rays emitted by radioactive substances were named after him. *TIS

1912 Reuben Louis Goodstein (15 December 1912 in London – 8 March 1985 in Leicester) was an English mathematician with a strong interest in the philosophy and teaching of mathematics. He earned his PhD from the University of London in 1946 while still working in Reading. Goodstein also studied under Wittgenstein and John Littlewood.
He published many works on finitism and the reconstruction of analysis from a finitistic viewpoint, for example "Constructive Formalism. Essays on the foundations of mathematics." Goodstein's theorem was among the earliest examples of theorems found to be unprovable in Peano arithmetic but provable in stronger logical systems (such as second order arithmetic). He also introduced a variant of the Ackermann function that is now known as the hyperoperation sequence, together with the naming convention now used for these operations (tetration, pentation, etc.).*Wik

1912 Emil Grosswald (December 15, 1912 – April 11, 1989) was a Romanian-American mathematician who worked primarily in number theory. His career is closely associated with that of his teacher, Hans Rademacher. *Wik

1916 Maurice Hugh Frederick Wilkins (15 Dec 1916; 5 Oct 2004) was a New Zealand-born British biophysicist, whose X-ray diffraction studies of deoxyribonucleic acid (DNA) were significant in the determination of the molecular structure of DNA accomplished by James Watson and Sir Francis Crick. For this work the three scientists shared the 1962 Nobel Prize for Physiology or Medicine. *TIS

1923 Freeman (John) Dyson (15 Dec 1923, ) is an English-born American physicist and educator best known for his speculative work on extraterrestrial civilizations. As an imaginative scientist he proposed that a highly advanced technological civilization would ultimately completely surround its host star with a huge shell to capture 100% of the useful radiant energy. This "Dyson shell", would have a gigantic cluster of artificial planetoids ("Dyson cloud") with billions of billions of inhabitants who would make use of the energy captured by the Dyson shell. He also made the intriguing speculation that a Dyson shell viewed from other galaxies would have a highly distinctive, unnatural light. He suggests astronomers search for such tell-tale colored stars, which should signify advanced, intelligent life. *TIS (One of Dyson's earliest memories of his calculating power was at a time when he was still being put down for naps. He set about summing the fractions 1+1/2 + 1/4 ... and realized that they added up to two. At a time when most of us were still trying to figure out what fractions were, Dyson summed an infinite converging sequence.)
I came across another beautiful anecdote about Dyson's incredible mental computational ability on the Math Frolic blog Posted by "Shecky Riemann":
Freeman Dyson sitting around a table with a bunch of scientists where the question arises, is there an integer such that by moving the last digit to the front (say 1234 to 4123) you can arrive at a result such that the new integer is exactly double the value of the original integer? In a matter of seconds, Dyson essentially responds (to a stunned group), “Oh, that’s not difficult, but of course the smallest such number is 18 digits long.” AND, he was right!


1921 Leo Königsberger (15 October 1837 – 15 December 1921) was a German mathematician, and historian of science. He is best known for his three-volume biography of Hermann von Helmholtz, which remains the standard reference on the subject.
The biography of Helmholtz was published in 1902 and 1903. He also wrote a biography of C. G. J. Jacobi.
Königsberger's own research was primarily on elliptic functions and differential equations. He worked closely with Lazarus Fuchs, a childhood friend. *Wik

1958 Wolfgang Pauli (25 Apr 1900, 15 Dec 1958) Austrian-born American winner of the Nobel Prize for Physics in 1945 for his discovery in 1925 of the Pauli exclusion principle, which states that in an atom no two electrons can occupy the same quantum state simultaneously. This principle clearly relates the quantum theory to the observed properties of atoms. *TIS

1970 Sir Ernest Marsden (19 Feb 1889, 15 Dec 1970) British-born New Zealand nuclear physicist who worked under Ernest Rutherford investigating atomic structure with Hans Geiger. Marsden visually counted scintillations from alpha particles after passing through gold foil and striking a phosphorescent screen. That some of these were observed scattered at surprisingly large angles led to Rutherford's theory of the nucleus as the massive, tiny centre of the atom. Later, Marsden's own experiments, working in New Zealand, hinted suggested transmutation of elements was possible when alpha particles bombarding nitrogen nuclei produced scattered particles of greater speed than the original radiation. *TIS

1970 Theodore Samuel Motzkin (26 March 1908–15 December 1970) was an Israeli-American mathematician. Motzkin received his Ph.D. in 1934 from the University of Basel under the supervision of Alexander Ostrowski.
He was appointed at UCLA in 1950 and worked there until retirement.
The Motzkin transposition theorem, Motzkin numbers and the Fourier–Motzkin elimination are named after him. Motzkin first developed the "double description" algorithm of polyhedral combinatorics and computational geometry.[3] He was the first to prove the existence of principal ideal domains that are not Euclidean domains.
The quote "complete disorder is impossible," describing Ramsey theory is attributed to him. *Wik

1971 Paul Pierre Lévy (15 Sep 1886, 15 Dec 1971) was a French mining engineer and mathematician. He contributed to probability, functional analysis, partial differential equations and series. He also studied geometry. In 1926 he extended Laplace transforms to broader function classes. He undertook a large-scale work on generalized differential equations in functional derivatives. *TIS

2000 George Eric Deacon Alcock (August 28, 1912 – December 15, 2000)
George Alcock was an English astronomer. He was one of the most successful visual discoverers of novae and comets. He was also a very good (probably under-respected) teacher of the 4th year at Southfields Junior School in Stanground, Peterborough. In 1953 he decided to start searching for comets and in 1955 began searching for novae. His technique was to memorize the patterns of thousands of stars, so that he would visually recognize any intruder.
In 1959 he discovered comet C/1959 Q1 (Alcock), the first comet discovered in Britain since 1894, and only five days later discovered another, C/1959 Q2 (Alcock). He discovered two more comets in 1963 and 1965. He later discovered his first nova, Nova Delphini 1967 (HR Delphini), which turned out to have an unusual light curve. He discovered two more novas, LV Vul (in 1968) and V368 Sct (in 1970). He found his fifth and final comet in 1983: C/1983 H1 (IRAS-Araki-Alcock). In 1991 he found the nova V838 Her.
Alcock won the Jackson-Gwilt Medal of the Royal Astronomical Society in 1963 and Amateur Achievement Award of the Astronomical Society of the Pacific in 1981. After his death, a plaque was placed in Peterborough Cathedral in his memory. *TIA

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