The shortest math joke ever: let $\epsilon < 0 $

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, \( 325 = \sum\limits_{i=1}^{5^2} i \)

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.

**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

**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

**1867 Dmitrii Matveevich Sintsov**(21 November 1867 – 28 January 1946) was a Russian mathematician known for his work in the theory of conic sections and non-holonomic geometry.

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

**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

**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

**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 programme 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. *SA

**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

**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

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