**Biographical history, as taught in our public schools, is still largely a history of boneheads: ridiculous kings and queens, paranoid political leaders, compulsive voyagers, ignorant generals -- the flotsam and jetsam of historical currents. The men who radically altered history, the great scientists and mathematicians, are seldom mentioned, if at all.**

~Martin Gardner

The 294th day of the year; 294 is a practical number because all numbers strictly less than 294 can be formed with sums of distinct divisors of 294.

"The whole case was now passed on the law faculty of the University of Tübingen, Kepler’s Alma Mater, who decided that Katharine should be taken to the hangman and shown the instruments of torture and ordered to confess. On 21st October 1621 this was duly carried out but the stubborn old lady refused to bend she said,"

“Do with me what you want. Even if you were to pull one vein after another out of my body, I would have nothing to admit.” Then she fell to her knees and said a Pater Noster. God would she said, bring the truth to light and after her death disclose that wrong and violence had been done to her. He would not take the Holy Ghost from her and would stand by her.For more about this unusual woman, read Thony Christie's blog at *The Renaissance Mathematicus

**1743**In the United States, on October 21, 1743, Benjamin Franklin tracked a hurricane for the first time. It was the first recorded instance in which the progressive movement of a storm system was recognized.

1796 The date of a still uninterpreted cryptic entry "Vicimus GEGAN"" in Gauss’s scientiﬁc diary. There is a another insertion that also remains uninterpreted. He wrote "REV. GALEN" in the diary on April 8, 1799 *VFR

*Genial Gauss Gottingen |

1803 John Dalton's Atomic Theory was first presented on 21st October 1803 to the Manchester Literary and Philosophical Society of which he was President 1816-1844. *Open Plaques

**1805**British Admiral Nelson defeated the combined French and Spanish ﬂeets in the Battle of Trafalgar by adopting the tactic of breaking the enemy line in two and concentrating his ﬁrepower on a few ships (orthodox tactics had the opponents facing each other in roughly parallel lines—the “line-ahead” formation). For an analysis of why this works see David H. Nash, “Diﬀerential equations and the Battle of Trafalgar”, The College Mathematics Journal, 16(1985), 98–102. *VFR

**1845**After two unsuccessful attempts to present his work in person to the Royal Astronomer Sir George Biddell Airy, John Couch Adams left a copy of his calculation regarding a hypothetical planet at the Royal Observatory. Airy criticized the work and didn’t search for the planet until later. Consequently he didn’t discover Neptune. See 23 September 1846.

1854 Florence Nightingale embarked for the Crimea on 21 October with thirty-eight nurses: ten Roman Catholic Sisters, eight Anglican Sisters of Mercy, six nurses from St. John's Institute, and fourteen from various hospitals. *Victorian Web Org

**1965**Greece issued a postage stamp picturing Hipparchus and an astrolabe to commemorate the opening of the Evghenides Planetarium in Athens. [Scott #835]. *VFR

**In 1976**, the United States made a clean sweep of the Nobel Prizes, winning or sharing awards in chemistry, physics, medicine, economics, and literature. (No peace prize was awarded.)

**1988**Science (pp. 374-375) reported that the 100-digit number 11

^{104}+ 1 was factored by using computers working in parallel using a quadratic sieve method. [Mathematics Magazine 62 (1989), p 70].*VFR

2015 Marty McFly and Doctor Emmet Brown "return" to this date in the future in the 1989 Sci-fi-sequel, Back to the Future II. The "future" included rocket powered skateboards... Do Razors count?

**1687 Nicolaus(I) Bernoulli**(21 Oct 1687 in Basel, Switzerland - 29 Nov 1759 in Basel) Nicolaus Bernoulli was one of the famous Swiss family of mathematicians. He is most important for his correspondence with other mathematicians including Euler and Leibniz. *SAU (Can't tell your Bernoulli's without a scorecard? Check out "A Confusion of Bernoulli's" by the Renaissance Mathematicus.)

**1823 Birthdate of Enrico Betti**. In algebra, he penetrated the ideas of Galois by relating them to the work of Ruﬃni and Abel. In analysis, his work on elliptic functions was further developed by Weierstrass. In “Analysis situs”, his research inspired Poincar´e, who coined the term “Betti numbers” to characterize the connectivity of surfaces. *VFR He was the first to give a proof that the Galois group is closed under multiplication. Betti also wrote a pioneering memoir on topology, the study of surfaces and space. Betti did important work in theoretical physics, in particular in potential theory and elasticity.*TIS

**1833 Alfred Bernhard Nobel**(21 Oct 1833; 10 Dec 1896) a Swedish chemist and inventor of dynamite and other, more powerful explosives, was born in Stockholm. An explosives expert like his father, in 1866 he invented a safe and manageable form of nitroglycerin he called dynamite, and later, smokeless gunpowder and (1875) gelignite. He helped to create an industrial empire manufacturing many of his other inventions. Nobel amassed a huge fortune, much of which he left in a fund to endow the annual prizes that bear his name. First awarded in 1901, these prizes were for achievements in the areas of physics, chemistry, physiology or medicine, literature, and peace. The sixth prize, for economics, was instituted in his honour in 1969. *TIS (The well-known anecdote that there is no Nobel prize in mathematics as he thought Mittag-Leﬄer might win it seems to have no basis in fact

**1855 Giovanni Battista Guccia**(21 Oct 1855 in Palermo, Italy - 29 Oct 1914 in Palermo, Italy) Guccia's work was on geometry, in particular Cremona transformations, classification of curves and projective properties of curves. His results published in volume one of the Rendiconti del Circolo Matematico di Palermo were extended by Corrado Segre in 1888 and Castelnuovo in 1897. *SAU

**1882 Harry Schultz Vandiver**(21 Oct 1882 in Philadelphia, Pennsylvania, USA - 9 Jan 1973 in Austin, Texas, USA) Harry developed an antagonism towards public education and left Central High School at an early age to work as a customshouse broker for his father's firm. D H Lehmer writes:

He was self-taught in his youth and must have had little patience with secondary education since he never graduated from high school. This impatience, especially with mathematical education, was to last the rest of his life.When he was eighteen years old he began to solve many of the number theory problems which were posed in the American Mathematical Monthly, regularly submitting solutions. In addition to solving problems, he began to pose problems himself. By 1902 he was contributing papers to the Monthly. For example he published two short papers in 1902 A Problem Connected with Mersenne's Numbers and Applications of a Theorem Regarding Circulants.

In 1904 he collaborated with Birkhoff on a paper on the prime factors of a^n - b^n published in the Annals of Mathematics. In fact the result they proved was not new, although they were not aware of the earlier work which had been published by A S Bang in 1886. Also in the year 1904, Vandiver published On Some Special Arithmetic Congruences in the American Mathematical Monthly and, although still working as an agent for his father's firm, he did attend some graduate lectures at the University of Pennsylvania. He also began reading papers on algebraic number theory and embarked on a study of the work of Kummer, in particular his contributions to solving Fermat's Last Theorem. Over the next few years he published papers such as Theory of finite algebras (1912), Note on Fermat's last theorem (1914), and Symmetric functions formed by systems of elements of a finite algebra and their connection with Fermat's quotient and Bernoulli's numbers (1917).

The outbreak of World War I in 1914 did not directly affect the United States since the Democratic president Woodrow Wilson made a declaration of neutrality. This policy was controversial but popular enough to see him re-elected in 1916. However US shipping was being disrupted (and sunk) by German submarines and, under pressure from Republicans, Wilson declared war on Germany on 6 April 1917. Vandiver joined the United States Naval Reserve and continued to serve until 1919 when the war had ended. After leaving the Naval Reserve, Birkhoff persuaded Vandiver to become a professional mathematician and to accept a post at Cornell University in 1919. Despite having no formal qualifications, his excellent publication record clearly showed his high quality and he was appointed as an instructor. He also worked during the summer with Dickson at Chicago on his classic treatise History of the Theory of Numbers. In 1924 he moved to the University of Texas where he was appointed as an Associate Professor. He spent the rest of his career at the University of Texas, being promoted to full professor in 1925, then named as distinguished professor of applied mathematics and astronomy in 1947. He continued in this role until he retired in 1966 at the age of 84. *SAU

**1893 Bill Ferrar**graduated from Oxford after an undergraduate career interrupted by World War I. He lectured at Bangor and Edinburgh before moving back to Oxford. He worked in college administration and eventually became Principal of Hertford College. He worked on the convergence of series. *SAU

**1914 Martin Gardner**born in Tulsa, Oklahoma. From 1957 to 1980 he wrote the “Mathematical Games” column in Scientiﬁc American. Many of these columns have been collected together into the numerous books that he has written. If you want to know more about the person who has done more to popularize mathematics than any other, see the interview with Gardner in Mathematical People. Proiles and Interviews (1985), edited by Donald J. Albers and G. L. Alexanderson, pp. 94–107. *VFR (My favorite tribute to Martin was this one from Ron Graham, “Martin has turned thousands of children into mathematicians, and thousands of mathematicians into children.”)

Among Babinet's accomplishments are the 1827 standardization of the Ångström unit for measuring light using the red Cadmium line's wavelength, and the principle (Babinet's principle) that similar diffraction patterns are produced by two complementary screens. He was the first to suggest using wavelengths of light to standardize measurements. His idea was first used between 1960 and 1983, when a meter was defined as a wavelength of light from krypton gas.

In addition to his brilliant lectures on meteorology and optics research, Babinet was also a great promoter of science, an amusing and clever lecturer, and a brilliant, entertaining and prolific author of popular scientific articles. Unlike the majority of his contemporaries, Babinet was beloved by many for his kindly and charitable nature. He is known for the invention of polariscope and an optical goniometer. *Wik

**1881 Heinrich Eduard Heine**(16 March 1821 in Berlin, Germany - 21 Oct 1881 in Halle, Germany) Heine is best remembered for the Heine-Borel theorem. He was responsible for the introduction of the idea of uniform continuity.*SAU

**1967 Ejnar Hertzsprung**(8 Oct 1873, 21 Oct 1967) Danish astronomer who classified types of stars by relating their surface temperature (or colour) to their absolute brightness. A few years later Russell illustrated this relationship graphically in what is now known as the Hertzsprung-Russell diagram, which has become fundamental to the study of stellar evolution. In 1913 he established the luminosity scale of Cepheid variable stars.*TIS

**1969 WacLlaw Sierpinski**(14 March 1882 in Warsaw, - 21 Oct 1969 in Warsaw) His grave carries—according to his wish—the inscription: Investigator of inﬁnity. [Kuratowski, A Half Century of Polish Mathematics, p. 173; Works, p. 14] *VFR Sierpinski's most important work is in the area of set theory, point set topology and number theory. In set theory he made important contributions to the axiom of choice and to the continuum hypothesis. *SAU

**2000 Dirk Jan Struik**(30 Sept 1894 , 21 Oct 2000) Dirk Jan Struik (September 30, 1894 – October 21, 2000) was a Dutch mathematician and Marxian theoretician who spent most of his life in the United States.

In 1924, funded by a Rockefeller fellowship, Struik traveled to Rome to collaborate with the Italian mathematician Tullio Levi-Civita. It was in Rome that Struik first developed a keen interest in the history of mathematics. In 1925, thanks to an extension of his fellowship, Struik went to Göttingen to work with Richard Courant compiling Felix Klein's lectures on the history of 19th-century mathematics. He also started researching Renaissance mathematics at this time.

Struik was a steadfast Marxist. Having joined the Communist Party of the Netherlands in 1919, he remained a Party member his entire life. When asked, upon the occasion of his 100th birthday, how he managed to pen peer-reviewed journal articles at such an advanced age, Struik replied blithely that he had the "3Ms" a man needs to sustain himself: Marriage (his wife, Saly Ruth Ramler, was not alive when he turned one hundred in 1994), Mathematics, and Marxism.

It is therefore not surprising that Dirk suffered persecution during the McCarthyite era. He was accused of being a Soviet spy, a charge he vehemently denied. Invoking the First and Fifth Amendments of the U.S. Constitution, he refused to answer any of the 200 questions put forward to him during the HUAC hearing. He was suspended from teaching for five years (with full salary) by MIT in the 1950s. Struik was re-instated in 1956. He retired from MIT in 1960 as Professor Emeritus of Mathematics.

Aside from purely academic work, Struik also helped found the Journal of Science and Society, a Marxian journal on the history, sociology and development of science.

In 1950 Stuik published his Lectures on Classical Differential Geometry.

Struik's other major works include such classics as A Concise History of Mathematics, Yankee Science in the Making, The Birth of the Communist Manifesto, and A Source Book in Mathematics, 1200-1800, all of which are considered standard textbooks or references.

Struik died October 21, 2000, 21 days after celebrating his 106th birthday. *Wik

**2002 Bernhard Hermann Neumann**(15 Oct 1909 in Berlin, Germany - 21 Oct 2002 in Canberra, Australia) Neumann is one of the leading figures in group theory who has influenced the direction of the subject in many different ways. While still in Berlin he published his first group theory paper on the automorphism group of a free group. However his doctoral thesis at Cambridge introduced a new major area into group theory research. In his thesis he initiated the study of varieties of groups, that is classes of groups defined which are by a collection of laws which must hold when any group elements are substituted into them. *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

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