The shortest math joke ever: let
found on Mathematical humor collected by Andrej and Elena Cherkaev
The 325th day of the year; 325 is the smallest number that can be written as the sum of two squares in three different ways. (What is the next such number?)
325 is last year day that is the sum of the first n^2 integers,
On an infinite chessboard, there are 325 different squares that can be reached in 5 knight moves.
EVENTS
1675 Leibniz completes the product rule. In a manuscript only days earlier Leibniz had struggled with the product and quotient rules for differentiation. At first he thought d(uv)= du dv. *F Cajori, History of Mathematics, (pg 208)
1751 “The weather was exceedingly tempestuous, and the sky was overcast with clouds..” so begins An Account of the Eclipse of the Moon, Which Happened Nov. 21, 1751; Observed by Mr. James Short, F. R. S. in Surry-Street *Philosophical Transactions 1751-1752 XLIX
1783 The first manned free balloon flight, often credited to the brothers Montgolfier was actually the work of J. A. C. Charles, for whom Charles Law is named. This was a hydrogen filled balloon, and not the hot air type promoted by the Montgolfiers. It carried chemist Jean Pilatre de Rozier and the Marquis d’Arlandes on a flight that wafted across Paris for 25 minutes, reached a height of 500 feet and traveled five and a half miles. The Montgolfier brothers had unmanned launches on June 5 and September 19, 1783. Among the onlookers was Benjamin Franklin, American emissary to the court of Louis XVI. When asked of what use is ballooning, Franklin replied with emphatic simplicity, “Of what use is a newborn baby?” [Air & Space, vol. 1, p. 72 and Williams, p. 43] Charles and the hydrogen promoters were rivals of the Montgolfiers until Charles' partner, King Louis XVI had offered to send two prisoners on the flight, but Rozier, a professor of physics and chemistry, wanted to deny criminals the glory of being the first men to go into the atmosphere. *TIS Pilatre would become the first aviation casualty the following year when he tried to mix the hot air and hydrogen techniques together to cross the English Channel.
On this day in 1804, Sophie Germain wrote her first letter to Gauss using the pseudonym M. Le Blanc.
Germain obtained lecture notes for many courses from École Polytechnique including Antoine-François Fourcroy's chemistry course and Joseph-Louis Lagrange's analysis course. At the end of Lagrange's lecture course he invited his students to send him their written observations. Using the pseudonym M LeBlanc, Germain submitted a paper whose originality and insight made Lagrange look for its author. We note that the pseudonym "M LeBlanc" was not a made-up name but rather it was the name of the student Antoine-August LeBlanc who had attended the École. He was not very gifted mathematically and had quickly given up his studies at the École Polytechnique.
However, Germain's most famous correspondence was with Gauss. She had developed a thorough understanding of the methods presented in his 1801 Disquisitiones Arithmeticae Ⓣ. Between 1804 and 1809 she wrote a dozen letters to him, initially adopting again the pseudonym "M LeBlanc" because she feared being ignored because she was a woman. After receiving her first letter, Gauss wrote to the astronomer Heinrich Wilhelm Matthias Olbers (1758-1840) (see, for example, :-
I recently had the pleasure of receiving a letter from LeBlanc, a young mathematician in Paris, who made himself enthusiastically familiar with higher mathematics and showed how deeply he penetrated into my 'Disquisitiones Arithmeticae'.
1811 Gauss to Bessel: “One should never forget that the functions, like all mathematical constructions, are only our own constructions.” *VFR
1877 Thomas Edison announced the invention of what he called “The Talking Machine”—the phonograph. *VFR He appears to have envisioned it as a business dictation machine. In Sep 1877, he wrote that its purpose was "to record automatically the speech of a very rapid speaker upon paper; from which he reproduces the same Speech immediately or years afterwards preserving the characteristics of the speakers voice so that persons familiar with it would at once recognize it." The indented tin foil, however, would survive only a few playings. By the first public showing of a phonograph, which took place in New York City in early Feb 1878, its practical applications had not yet been realized.*TIS
1877 Thomas Edison announced the invention of what he called “The Talking Machine”—the phonograph. *VFR He appears to have envisioned it as a business dictation machine. In Sep 1877, he wrote that its purpose was "to record automatically the speech of a very rapid speaker upon paper; from which he reproduces the same Speech immediately or years afterwards preserving the characteristics of the speakers voice so that persons familiar with it would at once recognize it." The indented tin foil, however, would survive only a few playings. By the first public showing of a phonograph, which took place in New York City in early Feb 1878, its practical applications had not yet been realized.*TIS
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Thomas Hill (January 7, 1818 – November 21, 1891) was an American clergyman, mathematician, scientist, philosopher, and educator. He is also the earliest known user of the name tangrams for the Chinese set of seven shapes. He used the term in Geometrical Puzzles for the Young in 1848. The games had been present in the US since 1802, and were a rage in Europe by 1817, Hill graduated from Harvard University in 1845 and became President of Antioch College in 1860. Two years later Antioch was closed because of the U S civil war. He became President of Harvard the same year. He retired from Harvard in 1868.
Jerry Slocum, in his The Tangram Book, credits Hill for inventing the board game Halma, and naming it. Wikipedia credits a Dr Monks from Harvard Medical school
“The improved arithmometer of Thomas Hill from 1857 was the first popular key-driven calculating machine, manufactured in the United States (it seems the key-driven adding machine of his compatriot Parmelee from 1850 remained only on paper). “ *History-computer.com
U.S. Patent 18692, November 24, 1857.
1963 Denmark and Greenland issued almost identical stamps to commemorate the 50th anniversary of the atomic theory of Niels Bohr (1885–1962)*VFR
1969 First ARPANET Link Put Into Service ARPANAT was an early computer network developed by J.C.R. Licklider, Robert Taylor, and other researchers for the U.S. Department of Defense’s Advanced Research Projects Agency (ARPA). It connected a computer at UCLA with a computer at the Stanford Research Institute, Menlo Park, CA. In 1973, the government commissioned Vinton Cerf and Robert E. Kahn to create a national computer network for military, governmental, and institutional use. The network used packet-switching, flow-control, and fault-tolerance techniques developed by ARPANET. Historians consider this worldwide network to be the origin of the Internet. *CHM
1973 Mexico issued a stamp portraying an Aztec calendar stone and another with the mathematician and astronomer Carlos de Siguenza y Gongora (1645–1700). *VFR
1983 A special purpose computer built by Lee Sallows generated the following self-documenting pangram (it contains each letter of the alphabet and what it asserts about itself is true): This pangram contains four a’s, one b, two c’s, one d, thirty e’s, six f’s, five g’s, seven h’s, eleven i’s, one j, one k, two l’s, two m’s, eighteen n’s, fifteen o’s, two p’s, one q, five r’s, twenty-seven s’s, eighteen t’s, two u’s, seven v’s, eight w’s, two x’s, three y’s and one z. See Scientific American, October 1984, p. 26. *VFR
BIRTHS
1694 (François Marie Arouet) Voltaire (21 Nov 1694; 30 May 1778) was a French author who popularized Isaac Newton's work in France by arranging a translation of Principia Mathematica to which he added his own commentary (1737). The work of the translation was done by the marquise de Châtelet who was one of his mistresses, but Voltaire's commentary bridged the gap between non-scientists and Newton's ideas at a time in France when the pre-Newtonian views of Descartes were still prevalent. Although a philosopher, Voltaire advocated rational analysis. He died on the eve of the French Revolution. *TIS
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1718 István Hatvani (21 November 1718, 16 November 1786) a Hungarian mathematician who wrote a pioneering work on probability and statistics. Hatvani was the first Hungarian to present work on statistics. In Introductio ad principia philosophicae solidioris in 1757 he presents tables for the number of births in Debrecen for the years 1750 to 1753 inclusive. He records the number of children who died within a year of being born and, finding a mortality rate of 34.2% which was well above that in other European countries (around 19%), he seeks medical reasons to explain the findings. *SAU
He took a leading role in the development of mathematics at Kharkov University, serving as chairman of the Kharkov Mathematical Society for forty years, from 1906 until his death at the age of 78.*Wik
1926 Albert Nijenhuis (November 21, 1926 – February 13, 2015) was a Dutch-American mathematician who specialized in differential geometry and the theory of deformations in algebra and geometry, and later worked in combinatorics.
His high school studies at the gymnasium in Arnhem were interrupted by the evacuation of Arnhem by the Nazis after the failure of Operation Market Garden by the Allies. He continued his high school mathematical studies by himself on his grandparents’ farm, and then took state exams in 1945.
His university studies were carried out at the University of Amsterdam, where he received the degree of Candidaat (equivalent to a Bachelor of Science) in 1947, and a Doctorandus (equivalent to a Masters in Science) in 1950, cum laude. He was a Medewerker (associate) at the Mathematisch Centrum (now the Centrum Wiskunde & Informatica) in Amsterdam 1951–1952. He obtained a PhD in mathematics in 1952, cum laude (Theory of the geometric object). His thesis advisor was Jan Arnoldus Schouten.
He came to the United States in 1952 as a Fulbright fellow (1952–1953) at Princeton University. He then studied at the Institute for Advanced Study in Princeton, New Jersey 1953–1955, after which he spent a year as an Instructor in mathematics at the University of Chicago. He then moved to the University of Washington in Seattle, first as an assistant professor and then a professor of mathematics, departing in 1963 for the University of Pennsylvania, where he was a professor of mathematics until his retirement in 1987. He was a Fulbright Professor at the University of Amsterdam in 1963–1964, and a visiting professor at the University of Geneva in 1967–1968, and at Dartmouth College in 1977–1978. Following his retirement, he was a professor emeritus of the University of Pennsylvania and an Affiliate Professor at the University of Washington.
In 1958 he was an invited speaker at the International Mathematical Congress in Edinburgh. He was a J.S. Guggenheim Fellow in 1961–1962, again studying at the Institute for Advanced Study. In 1966 he became a correspondent member of the Royal Netherlands Academy of Arts and Sciences, and in 2012 he became a fellow of the American Mathematical Society.*Wik
At the University of Pennsylvania, his excellent teaching was recognised with the "Good teaching award - Fall 1974" and the "Good teaching award - Spring 1975". His research interest in deformations changed over the years towards combinatorics and, in 1975, he published his most famous work namely the book Combinatorial algorithms written in collaboration with Herbert S Wilf. They wrote in the Preface:-
In the course of our combinatorial work over the past several years, we have been fond of going to the computer from time to time in order to see some examples of the things we were studying. We have built up a fairly extensive library of programs, and we feel that other might be interested in learning about the methods and/or use of the programs. This book is the result.*SAU
1933 Etta Zuber Falconer (November 21, 1933 – September 19, 2002) was an American educator and mathematician the bulk of whose career was spent at Spelman College, where she eventually served as department head and associate provost. She was one of the earlier African-American women to receive a Ph.D. in mathematics.
Falconer began her teaching career in 1954 at Okolona College, where she met and married Dolan Falconer. She remained at Okolona until 1963, when she accepted a position at Howard High School in Chattanooga, Tennessee, where she taught the academic year 1963–64. When her husband was offered a coaching position at Morris Brown College in 1965, the family moved to Atlanta, also the site of Spelman College, an historically black women's college.
Falconer's mother had studied at Spelman, and Falconer approached the head of the mathematics department, telling him that she wanted to teach there She was appointed an instructor in 1965. In 1969 Falconer became the eleventh African American woman to receive a PhD in mathematics. She specialized in Abstract algebra. Falconer advanced to associate professor, leaving Spelman in 1971 to join the mathematics department at Norfolk State University, where she taught for the academic year 1971–1972. Falconer returned to Spelman as professor of mathematics and head of the mathematics department. She held those positions until 1985.
Falconer devoted 37 years of her life to teaching mathematics and improving science education at Spelman College. In 1995, she stated: "My entire career has been devoted to increasing the number of African American women in mathematics and mathematics-related careers." Along with her teaching career, Falconer strived to inspire more African American women to pursue careers in math or science by working with prominent organizations. This included the American Mathematical Society, the Mathematical Association of America, the Associate for Women in Mathematics, and the National Institute of Science.
Falconer was awarded the UNCF Distinguished Faculty Award (1986–1987), the Spelman Presidential Award for Excellence in Teaching (1988), the Spelman Presidential Faculty Award for Distinguished Service (1994).In 1995, Falconer was honored by the Association for Women in Mathematics, who awarded her the Louise Hay Award for outstanding achievements in mathematics education. QEM's Giants in Science Award (1995), and an honorary doctorate of science from the University of Wisconsin-Madison (1996). She was named a Fellow of the American Association for the Advancement of Science in 1999. In 2001, she received the American Association for the Advancement of Science Mentor Award for Lifetime Achievement.
DEATHS
1652 Jan Brożek (Ioannes Broscius, Joannes Broscius or Johannes Broscius;) (1 November 1585 – 21 November 1652) was a Polish polymath: a mathematician, astronomer, physician, poet, writer, musician and rector of the Kraków Academy.
Brożek was born in Kurzelów, Sandomierz Province, and lived in Kraków, Staszów, and Międzyrzec Podlaski. He studied at the Kraków Academy (now Jagiellonian University) and at the University of Padua. He served as rector of Jagiellonian University.
He was the most prominent Polish mathematician of the 17th century, working on the theory of numbers (particularly perfect numbers) and geometry. He also studied medicine, theology and geodesy. Among the problems he addressed was why bees create hexagonal honeycombs; he demonstrated that this is the most efficient way of using wax and storing honey.
He contributed to a greater knowledge of Nicolaus Copernicus' theories and was his ardent supporter and early prospective biographer. Around 1612 he visited the chapter at Warmia and with the knowledge of Prince-Bishop Simon Rudnicki took from there a number of letters and documents in order to publish them, which he never did. He contributed to a better version of a short biography of Copernicus by Simon Starowolski. "Following his death, his entire collection was lost"; thus "Copernicus' unpublished work probably suffered the greatest damage at the hands of Johannes Broscius."
Brożek died at Bronowice, now a district of Kraków. One of the Jagiellonian University's buildings, the Collegium Broscianum, is named for him. *Wik
1782 Jacques de Vaucanson (24 Feb 1709, 21 Nov 1782) French inventor of automata - robot devices of later significance for modern industry. In 1737-38, he produced a transverse flute player, a pipe and tabor player, and a mechanical duck, which was especially noteworthy, not only imitating the motions of a live duck, but also the motions of drinking, eating, and "digesting." He made improvements in the mechanization of silk weaving, but his most important invention was ignored for several decades - that of automating the loom by means of perforated cards that guided hooks connected to the warp yarns (later reconstructed and improved by J.-M. Jacquard, it became one of the most important inventions of the Industrial Revolution.) He also invented many machine tools of permanent importance.*TIS
All three of Vaucanson's Automata: the Flute Player, the Digesting Duck, and the Tambourine Player.
1866 Gustav Roch (9 Dec 1839 in Dresden, Germany, 21 Nov 1866 in Venice, Italy) was a German mathematician known for the Riemann-Roch theorem which relates the genus of a topological surface to algebraic properties of the surface. As presented by Roch, the Riemann-Roch theorem related the topological genus of a Riemann surface to purely algebraic properties of the surface. The Riemann-Roch theorem was so named by Max Noether and Alexander von Brill in a paper they jointly wrote 1874 when they refined the information obtained from the theorem. It was extended to algebraic curves in 1929 and then in the 1950s an n-dimensional version, the Hirzebruch-Riemann-Roch theorem, was proved by Hirzebruch and a version for a morphism between two varieties, the Grothendieck-Riemann-Roch theorem, was proved by Grothendieck.
Over the three academic years 1863-64, 1864-65 and 1865-66 Roch gave a number of courses at Halle. These included: Differential and Integral Calculus; Analytic Geometry; and Elliptic and Abelian Functions. Up to this time Roch was still a privatdozent at Halle but in the spring of 1866 the University began to take up referees' reports with a view to appointing him as an extraordinary professor. Heine wrote a strong letter of support and Roch was appointed extraordinary professor at the University of Halle-Wittenberg on 21 August.
However Roch's health was failing and on 13 October he was granted leave for the winter semester of 1866-67 to allow him to regain his health. Roch went to Venice where he hoped the warmer weather would aid his recovery. Sadly, however, it was not to be and he died of consumption in Venice in November at the age of 26 years. Roch's name will live on through the fundamental Riemann-Roch theorem, but it is a tragedy that the young man with so much mathematical promise died when he had only just commenced his career. *SAU
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1970 Sir Chandrasekhara Venkata Raman (7 Nov 1888, 21 Nov 1970)Indian physicist whose work was influential in the growth of science in India. He was the recipient of the 1930 Nobel Prize for Physics for the 1928 discovery now called Raman scattering: a change in frequency observed when light is scattered in a transparent material. When monochromatic or laser light is passed through a transparent gas, liquid, or solid and is observed with the spectroscope, the normal spectral line has associated with it lines of longer and of shorter wavelength, called the Raman spectrum. Such lines, caused by photons losing or gaining energy in elastic collisions with the molecules of the substance, vary with the substance. Thus the Raman effect is applied in spectrographic chemical analysis and in the determination of molecular structure. *TIS
1978 Francesco Giacomo Tricomi studied differential equations which became very important in the theory of supersonic flight. *SAU
1980 László Rédei (Rákoskeresztúr, 15 November, 1900—Budapest, 21 November, 1980) was a Hungarian mathematician.
His mathematical work was in algebraic number theory and abstract algebra, especially group theory. He proved that every finite tournament contains an odd number of Hamiltonian paths. He gave several proofs of the theorem on quadratic reciprocity. He proved important results concerning the invariants of the class groups of quadratic number fields. In several cases, he determined if the ring of integers of the real quadratic field Q(√d) is Euclidean or not. He successfully generalized Hajós's theorem. This led him to the investigations of lacunary polynomials over finite fields, which he eventually published in a book. He introduced a very general notion of skew product of groups, both the Schreier-extension and the Zappa-Szép product are special case of. He explicitly determined those finite noncommutative groups whose all proper subgroups were commutative (1947). This is one of the very early results which eventually led to the classification of all finite simple groups.*Wik
1991 Hans Zassenhaus (28 May 1912 in Koblenz-Moselweiss, Germany - 21 Nov 1991 in Columbus, Ohio, USA) did important work on Group Theory and Lie algebras. His work on computational algebraic number theory seems to have started when he visited Caltec in 1959 and collaborated with Taussky-Todd. He put forward a program to develop methods for computational number theory which, given an algebraic number field, involved calculating its Galois group, an integral basis, the unit group and the class group. He contributed himself in a major way to all four of these tasks.
Zassenhaus worked on a broad range of topics and, in addition to those mentioned above, he worked on nearfields, the theory of orders, representation theory, the geometry of numbers and the history of mathematics. He loved teaching and wrote several articles on the topic such as On the teaching of algebra at the pre-college level. *SAU
1993 Bruno Rossi (13 Apr 1905, 21 Nov 1993)Italian pioneer in the study of cosmic radiation. In the 1930s, his experimental investigations of cosmic rays and their interactions with matter laid the foundation for high energy particle physics. Cosmic rays are atomic particles that enter earth's atmosphere from outer space at speeds approaching that of light, bombarding atmospheric atoms to produce mesons as well as secondary particles possessing some of the original energy. He was one of the first to use rockets to study cosmic rays above the Earth's atmosphere. Finding X-rays from space he became the grandfather of high energy astrophysics, being largely responsible for starting X-ray astronomy, as well as the study of interplanetary plasma. *TIS
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| Rossi's Cosmic ray telescope*Wik |
1996 Abdus Salam (29 Jan 1926, 21 Nov 1996) Pakistani nuclear physicist who shared the 1979 Nobel Prize for Physics with Steven Weinberg and Sheldon Lee Glashow. Each had independently formulated a theory explaining the underlying unity of the weak nuclear force and the electromagnetic force. His hypothetical equations, which demonstrated an underlying relationship between the electromagnetic force and the weak nuclear force, postulated that the weak force must be transmitted by hitherto-undiscovered particles known as weak vector bosons, or W and Z bosons. Weinberg and Glashow reached a similar conclusion using a different line of reasoning. The existence of the W and Z bosons was eventually verified in 1983 by researchers using particle accelerators at CERN. *TIS
2022 Oleksandr Mykolayovych Sharkovsky[a] (Ukrainian: Олекса́ндр Миколайович Шарко́вський; 7 December 1936 – 21 November 2022) was a Soviet and Ukrainian mathematician most famous for developing Sharkovsky's theorem on the periods of discrete dynamical systems in 1964. Sharkovsky created the foundations of the topological theory of one-dimensional dynamic systems, a theory that today is one of the tools for researching evolutionary problems of the most diverse nature.
He was a corresponding member of the Academy of Sciences of the Ukrainian SSR (1978), and academician of the National Academy of Sciences of Ukraine (2006). Prize laureate of the National Academy of Sciences of Ukraine named after M. M. Bogolyubov and M. O. Lavretiev.
Credits
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell
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