**There are no foolish questions and no man becomes a fool until he has stopped asking questions.**

Charles P Steinmetz

The 299th day of the year. If a cubic cake was cut with 12 straight cuts, it can produce a maximum of 299 pieces.... a good day to "let 'em eat cake."

299= 150^2 - 149^2 = 18^2 - 5^2

There are 299 composite numbers less than 1000 which are products of two primes. (This counts non-distinct semi-primes such as 9=3x3 0r 2 = 5x5},

**EVENTS**

**1639**(OS) Jeremiah Horrocks makes his first written prediction of the 1639 Transit of Venus, in a letter to William Crabtree to alert him – that Venus would pass across the Sun’s disk on 24 November. Although they notified several other acquaintances of the impending event, these two men seem to have been the only recorded astronomers to make measurements of the passage. *Allan Chapman, Jeremiah Horrocks and the transit of Venus of 1639The friends, followers of the new astronomy of Johannes Kepler, were self-taught mathematical astronomers who had worked methodically to correct and improve Kepler's Rudolphine tables by observation and measurement. In 1639, Horrocks was the only astronomer to realise that a transit of Venus was imminent; others became aware of it only after the event when Horrocks's report of it was circulated. Although the friends both died within five years of making their observations, their ground-breaking work was influential in establishing the size of the Solar System; for this and their other achievements Horrocks and Crabtree, along with their correspondent William Gascoigne, are considered to be the founding fathers of British research astronomy.

Horrocks produced several drafts of a Latin treatise Venus in sole visa (Venus seen on the Sun) based on his observations, which he presumably intended to publish, but he died suddenly from unknown causes on 3 January 1641, aged 22.

Memorial to Jeremiah Horrocks in St Michael's Church, Hoole. The Latin is taken from Horrocks's report of the 1639 transit and reads "Ecce gratissimum spectaculum et tot votorum materiem": "oh, most grateful spectacle, the realization of so many ardent desires"

**1675**Leibniz first use of a calculus symbol was in a letter on this date. He wrote that he would use

*w*as the differential of the variable

*y. **Florian Cajori, The History of Notations of the Calculus

The integral symbol was first used by Gottfried Wilhelm Leibniz (1646-1716) on October 29, 1675, in an unpublished manuscript,

*Analyseos tetragonisticae pars secunda*:

Utile erit scribi $\int $ pro omnia, ut $\int $l= omn.l, id est summa ipsoruml.[It will be useful to write $\int $ for omn. so that $\int $l= omn.l, or the sum of all thel's.]

Prior to this he would write "Omnia" or the shortened omn for "everything" or, the sum of all.

*Methodi tangentium inversae exempla,*he first placed

*dx*after the integral symbol, replacing $\frac{\ufffd}{\ufffd}$.

**1676**Newton, through the intermediary of Oldenburg, wrote Leibniz concerning his work on the calculus. An anagram contained the statement of the problem of integrating differential equations. *VFR

The foundations of these operations is evident enough, in fact; but because I cannot proceed with the explanation of it now, I have preferred to conceal it thus: 6accdae13eff7i3l9n4o4qrr4s8t12ux. On this foundation I have also tried to simplify the theories which concern the squaring of curves, and I have arrived at certain general Theorems.

The anagram expresses, in Newton's terminology, the fundamental theorem of the calculus: "Data aequatione quotcunque fluentes quantitates involvente, fluxiones invenire; et vice versa", which means "Given an equation involving any number of fluent quantities to find the fluxions, and vice versa."

**1738**Theophilus Grew, Mathematician advertises his availability for all manner of mathematical instruction in the Philadelphia Gazette.

"Forasmuch as Mathematical Learning is (and has been in all Ages) promoted in most Parts of the World especially in all great Towns, and generally pursued by the Gentry and those of the first Rank, as a necessary Qualification; it is to be hoped that this flourishing City will follow the Example and give it such Encouragement as it justly deserves.Grew would go on to become the first professor of mathematics at the Univ of Pennsylvania when it was founded. *Natl. Archives

In order to which there will be taught this Winter, over against Mr. James Steel’s in Second-Street, Philadelphia; Reading, Writing, Vulgar Arithmetick, Decimal Arithmetick, Accompts, Euclid’s Elements, Practical Geometry, Mensuration, Gauging, Surveying, Algebra, Trigonometry, Geography, Navigation, Astronomy, Dialing, Projection of the Sphere, the Use of Globes, Maps, Quadrants, Scales, sliding Rules, and all other Instruments for the Mathematical Service, by Theophilus Grew, Mathematician."

**1818**Thomas Jefferson writes Nathaniel Bowditch to offer him the Math Professorship at the newly forming University of Virginia

I have stated that where men of the 1st. order of science in their line can be found in our country, we shall give them a willing preference. we are satisfied that we can get from no country a professor of higher qualifications than yourself for our Mathematical department, and we entertain the hope and with great anxiety that you will accept of it. the house for that Professorship will be ready at midsummer next or soon after, when we should wish that school to be opened. I know the prejudices of every state against the climates of all those South of itself: but i know also that the candid traveller advancing Southwardly, to a certain degree at least, sees that they are more prejudices, and that the real advantages of climate are in the middle & temperate states, and especially when above their tide waters.*Letters of Thomas Jefferson, http://etext.lib.virginia.edu (While little known today, Bowditch was considered on of the first world class mathematicians from the "new world." The figures known as Lissajous figures, are more fittingly often referred to as Bowditch curves.)

**1843**John T Graves replies to Hamilton about the invention of Quaternions,

"There is something in the system which gravels me. I have not yet any clear views as to the extent to which we are at liberty arbitrarily to create imaginaries, and to endow them with supernatural properties.",

"If with your alchemy you can create three pounds of gold, why should you stop there?

Graves is credited by Hamilton with being a critical inspiration in the Quaternions, and would quickly go on to liberty to create imaginaries himself and create the "Octaves", an eight dimensional normed division algebra. Why should you stop there indeed? *Joan Baez Rankin Lecture of September 17, 2008 Glascow

**1847**William Whewell wrote to Aubrey De Vere expressing dismay at the influence of Carlyle's pessimism among his friends and in society. *@GalileosBalls, Twitter

**1893**Williamina Fleming, a "computer" at the Harvard Observatory, examining a photograph taken three months earlier, recognized a dozen prominent hydrogen lines, a spectrum unique to a nova. The first Nova to be detected by spectral photography. Fleming also is recognized for the discovery in 1888 of the Horsehead Nebula.

**1893**Karl Pearson’s ﬁrst statistical publication. *VFR In Pearson' s first published statistical paper of 26 October 1893, he introduced the method of moments as a means of curve fitting asymmetrical distributions. One of his aims in developing the method of moments was to provide a general method for determining the values of the parameters of a frequency distribution. *StatProb web site

**1896**Comptes Rendus publishes, "Extension of the Reimann-Roch Theorem to Algebraic Surfaces. A note by M. M. Noether, presented by M. Hermite *Mathematical Intellignecer vol 8 #4

**1946**A one-page handwritten letter in German from Albert Einstein to Polish American physicist Ludwik Silberstein is dated Oct. 26, 1946. It would not be known of until sometime in 2021 when it was put up for auction by an anonymous collector. The letter, handwritten by Albert Einstein in which he writes out his famous E = mc² equation, sold at auction for more than $1.2 million on 21 May, 2021. There are only three other known examples of Einstein writing the world-changing equation in his own hand. This fourth example is the only one known in a private collection. In 1935 Silberstein claimed that A. Einstein's theory was flawed, in need of a revision. In response, Einstein and Nathan Rosen published a Letter to the Editor in which they pointed out a critical flaw in Silberstein's reasoning. Unconvinced, Silberstein took the debate to the popular press.

**1960**Saga, a silent shoot-em-up Western playlet made on the TX-0 computer, was run on CBS' special for MIT's 100th anniversary. The TX-0 was the first general purpose transistorized computer. The program for Saga comprised 4,096 words of magnetic core storage. The 13,000 lines of code choreographed the movements of each object. A line of direction was written for each action, even if it went wrong. This led to the high point of the show where sheriff put his gun in the holster of the robber resulting in a never ending loop.

Doug Ross explained the rule-based diagram: If the robber drank from alcohol, his judgement would start to decline, but the program would remain logical.*CHM

TX-0 computer circuitry used Philco surface-barrier transistors, which were encapsulated in plug-in vacuum tubes for testing and easy removal.

**BIRTHS**

**1796 James Curley**(Irish: Séamus MacThoirealaigh (26 October 1796 – 24 July 1889) was an Irish-American astronomer. He was born at Athleague, County Roscommon, Ireland. His early education was limited, though his talent for mathematics was discovered, and to some extent developed, by a teacher in his native town. He left Ireland in his youth, arriving in Philadelphia on 10 October 1817. Here he worked for two years as a bookkeeper and then taught mathematics at Frederick, Maryland. In 1826 he became a student at the old seminary in Washington, DC, intending to prepare himself for the Catholic priesthood, and at the same time taught one of its classes. The seminary, however, which had been established in 1820, was closed in the following year and he joined the Society of Jesus on 29 September 1827. After completing his novitiate he again taught in Frederick and was sent in 1831 to teach natural philosophy at Georgetown University. He also studied theology and was ordained priest on 1 June 1833. His first Mass was said at the Visitation Convent, Georgetown, where he afterwards acted as chaplain for fifty years.He spent the remainder of his life at Georgetown, where he taught natural philosophy and mathematics for forty-eight years. He planned and superintended the building of the Georgetown Observatory in 1844 and was its first director, filling this position for many years. One of his earliest achievements was the determination of the latitude and longitude of Washington, D.C. in 1846. His results did not agree with those obtained at the Naval Observatory, and it was not until after the laying of the first transatlantic cable in 1858 that his determination was found to be nearer the truth. *Wik

**1846 Lewis Boss**(26 Oct 1846; 12 Oct 1912) American astronomer best known for his compilation of two catalogs of stars (1910, 1937). In 1882 he led an expedition to Chile to observe a transit of Venus. About 1895 Boss began to plan a general catalog of stars, giving their positions and motions. After 1906, the project had support from the Carnegie Institution, Washington, D.C. With an enlarged staff he observed the northern stars from Albany and the southern stars from Argentina. With the new data, he corrected catalogs that had been compiled in the past, and in 1910 he published the Preliminary General Catalogue of 6,188 Stars for the Epoch 1900. The work unfinished upon his death was completed by his son Benjamin in 1937 (General Catalogue of 33,342 Stars for the Epoch 1950, 5 vol.)*TIS

**1849 Georg Frobenius**(26 Oct 1849; 3 Aug 1917) German mathematician who made major contributions to group theory, especially the concept of abstract groups (with Ludwig Stickleberger) and the theory of finite groups of linear substitutions (with Issai Schur), that later found important uses in the theory of finite groups as it applies to quantum mechanics. He also contributed to means of solving linear homogenous differential equations. The fact so many of Frobenius's papers read like present day text-books on the topics which he studied is a clear indication of the importance that his work, in many different areas, has had in shaping the mathematics which is studied today.*TIS

**1877 Max Mason**(26 Oct 1877; 23 Mar 1961) American mathematical physicist, educator, and science administrator. During World War I he invented several devices for submarine detection - several generations of the Navy's "M," or multiple-tube, passive submarine sensors. This apparatus focused sound to ascertain its source. To determine the direction from which the sound came, the operator needed only to seek the maximum output on his earphones by turning a dial. The final device had a range of 3 miles. Mason's special interest and contributions lay in mathematics (differential equations, calculus of variations), physics (electromagnetic theory), invention (acoustical compensators, submarine-detection devices), and the administration of universities and foundations. *TIS

**1885 Niels Erik Norlund**(26 Oct 1885 in Slagelse, near Soro, Sjaelland, Denmark - 4 July 1981 in Copenhagen, Denmark) In 1907 he was awarded a gold medal for an essay on continued fractions and his resulting two publications were in 1908: Sur les différences réciproques; and Sur la convergence des fractions continues both published in Comptes Rendus de l'Academie des Sciences. These publications in the most prestigious French journal earned Norlund an international reputation despite still being an undergraduate. In the summer of 1910 he earned a Master's degree in astronomy and in October of that year he successfully defended his doctoral thesis in mathematics Bidrag til de lineaere differentialligningers Theori. In the same year he published the 100-page paper Fractions continues et différences réciproques as well as Sur les fractions continues d'interpolation, a paper on Halley's comet, and an obituary of his teacher Thorvald Thiele. Norlund's sister Margrethe married Niels Bohr whose brother, Harald, was also an outstanding mathematician. In 1955 Norland reached retirement age. That mathematics was his first love now became clear, for once he gave up the responsibilities of the Geodesic Institute he returned to mathematics research. He published Hypergeometric functions in 1955 which was reviewed by Arthur Erdélyi, "This is one of those rare papers in which sound mathematics goes hand in hand with excellent exposition and style; and the reader is both instructed and delighted. It is likely to become the standard memoir on the generalized hypergeometric series ... " The paper Sur les fonctions hypergéométriques d'ordre supérieur (1956) gives a very full, rigorous and classical treatment of some integrals from generalized hypergeometric function theory.*SAU

**1902 Henrietta Hill Swope**(26 October 1902; Saint Louis, Missouri - 24 November 1980; Pasadena, California)was an American astronomer. She was the eldest child of Gerard and Mary Dayton (Hill) Swope; her mother was the daughter of Thomas Hill, president of Harvard University, 1862-1868. She received her A.B. from Barnard College in 1926 and her A.M. from Radcliffe College in 1928. In 1936, while assistant at the Harvard Observatory (1928-1942), she was a member of the expedition sent jointly by the Harvard Observatory and the Massachusetts Institute of Technology to study the solar eclipse in Soviet Central Asia. During World War II she was staff member of the M.I.T. Radiation Laboratory and then served as a mathematician in the Hydrographic Office of the U.S. Department of the Navy. From 1947 to 1952 she taught astronomy at Barnard College and in 1952 was appointed assistant, later research fellow, at the Mt. Wilson and Palomar Observatories in California. After her retirement in 1968, she continued to work at the Observatories.

HHS was a member of the American Astronomical Society; she received the AAS Annie Jump Cannon Prize in 1968 for her research on photometry and variable stars. She was responsible for developing a new yardstick for measuring the universe: calibrating distance by determining the brightness of stars. She received the Distinguished Alumna Award of Barnard College in 1975 and the Barnard Medal of Distinction in 1980.

The Swope Telescope at the Las Campanas Observatory in Chile is named in her honor, as is asteroid 2168 Swope.

**1911 Shiing-shen Chern**(26 Oct 1911; 3 Dec 2004) Chinese-American mathematician and educator whose researches in differential geometry include the development of the Chern characteristic classes in fibre spaces, which play a major role in mathematics and in mathematical physics. "When Chern was working on differential geometry in the 1940s, this area of mathematics was at a low point. Global differential geometry was only beginning, even Morse theory was understood and used by a very small number of people. Today, differential geometry is a major subject in mathematics and a large share of the credit for this transformation goes to Professor Chern." *TIS

**1930 Walter Feit**(26 Oct 1930 in Vienna, Austria - 29 July 2004 in Branford, Connecticut, USA) was an Austrian mathematician who (with John Thompson) proved one of the most important theorems about finite simple groups. In 1990 his 60th birthday was celebrated with an 'International Symposium on the Inverse Galois Problem' held in Oxford. His retirement from Yale in October 2003 was marked with the holding of a 'Conference on Groups, Representations and Galois Theory' in his honour. Feit died after a long illness at the Connecticut Hospice in Branford, Connecticut, USA. A memorial service was held on Sunday 10 October 2004 at the New Haven Lawn Club, New Haven, Connecticut. *SAU

**DEATHS**

**1817 Aida Yasuaki**Aida Yasuaki (会田 安明, February 10, 1747 – October 26, 1817) a Japanese mathematician who published about 2000 works. Aida compiled Sampo tensi shinan which appeared in 1788. It is a book of geometry problems, developing formulae for ellipses, spheres, circles etc. Aida explained the use of algebraic expressions and the construction of equations. He also worked on number theory and simplified continued fraction methods due to Seki. *SAU

He made significant contributions to the fields of number theory and geometry, and furthered methods for simplifying continued fractions.

Aida created an original symbol for "equal". This was the first appearance of the notation for equal in East Asia.

**1923 Charles Proteus Steinmetz**(9 Apr 1865- 26 Oct 1923) German-born American inventor and electrical engineer whose theories and mathematical analysis of alternating current systems helped establish them as the preferred form of electrical energy in the United States, and throughout the world. In 1893, Steinmetz joined the newly organized General Electric Company where he was an engineer then consultant until his death. His early research on hysteresis (loss of power due to magnetic resistance) led him to study alternating current, which could eliminate hysteresis loss in motors. He did extensive new work on the theory of a.c. for electrical engineers to use. His last research was on lightning, and its threat to the new AC power lines. He was responsible for the expansion of the electric power industry in the U.S. *TIS

**1933 Albert Wangerin**(November 18, 1844 – October 25, 1933) worked on potential theory, spherical functions and differential geometry.*SAU He wrote an important two volume treatise on potential theory and spherical functions. Theorie des Potentials und der Kugelfunktionen I was published in 1909 and Theorie des Potentials und der Kugelfunktionen II was published in 1921. Wangerin functions are named for him.

He was also known for writing of textbooks, encyclopaedias and his historical writings.*Wik

**1968 Sergei Natanovich Bernstein**(March 5, 1880 – October 26, 1968) was a Russian and Soviet mathematician. His doctoral dissertation, submitted in 1904 to the Sorbonne, solved Hilbert's nineteenth problem on the analytic solution of elliptic differential equations. Later, he published numerous works on Probability theory, Constructive function theory, and mathematical foundations of genetics. From 1906 until 1933, Bernstein was a member of the Kharkov Mathematical Society. *Wik

**1970 Marcel Gilles Jozef Minnaert**(12 Feb 1893; 26 Oct 1970 at age 77)

Flemish astronomer and solar physicist who was one of the pioneering solar researchers during the first half of the 20th century. Applying solar spectrophotometry, he was one of the first to make quantitative measurements of the intensity distribution inside Fraunhofer lines, and interpret from them information about the outer solar layers. His range of study also included comets, nebulae and lunar photometry. During the time he was director of the observatory at the University of Utrecht, (1937-1963) he created a modern astronomical institute to study solar and stellar spectra with resources including a solar telescope, spectrograph, photometer, and mechanical workshop. Minnaert also maintained a strong interest in the education of physics teachers, and as a university professor gave clear, enthusiastic and well-prepared lectures. *TIS

**1983 Alfred Tarski**(14 Jan 1902, 26 Oct 1983) Polish-born American mathematician and logician who made important studies of general algebra, measure theory, mathematical logic, set theory, and metamathematics. Formal scientific languages can be subjected to more thorough study by the semantic method that he developed. He worked on model theory, mathematical decision problems and with universal algebra. He produced axioms for "logical consequence", worked on deductive systems, the algebra of logic and the theory of definability. Group theorists study 'Tarski monsters', infinite groups whose existence seems intuitively impossible. *TIS

**1984 Mark Kac**(3 Aug 1914 in Krzemieniec, Poland, Russian Empire - 26 Oct 1984 in California, USA) pioneered the modern development of mathematical probability, in particular its applications to statistical physics. The method of quantization now in use involves the Feynman-Kac path integral, named after Richard Feynman and Mark Kac. He published a classic text Statistical Independence in Probability, Analysis and Number Theory in 1959. To many Kac will be remembered best for a paper he wrote for the American Mathematical Monthly in 1966. This is the famous paper Can One Hear the Shape of a Drum? and Kac received the Chauvenet Prize from the Mathematical Association of America in 1968 for the, "most outstanding expository article on a mathematical topic by a member of the Association." *SAU

**1998 Kenkichi Iwasawa**(11 Sept 1917 in Shinshuku-mura (near Kiryu), Gumma Prefecture, Japan - 26 Oct 1998 in Tokyo, Japan ) In the late 1960s Iwasawa made a conjecture for algebraic number fields which, in some sense, was the analogue of the relationship which Weil had found between the zeta function and the divisor class group of an algebraic function field. This conjecture became known as "the main conjecture on cyclotomic fields" and it remained one of the most outstanding conjectures in algebraic number theory until it was solved by Mazur and Wiles in 1984 using modular curves. "it is no exaggeration to say that Iwasawa's ideas have played a pivotal role in many of the finest achievements of modern arithmetical algebraic geometry on such questions as the conjecture of B Birch and H Swinnerton-Dyer on elliptic curve; the conjecture of B Birch, J Tate, and S Lichtenbaum on the orders of the K-groups of the rings of integers of number fields; and the work of A Wiles on the modularity of elliptic curves and Fermat's Last Theorem." *SAU

2013

2013

**Elza Furtado Gomide**(August 20, 1925 – October 26, 2013) was a Brazilian mathematician and the first woman to receive a doctorate in mathematics from the University of São Paulo, in 1950, and the second in Brazil. Gomide was involved in the creation of the Society of Mathematics of São Paulo and was elected head of the department of mathematics of the University of São Paulo in 1968. (The first Brazilian woman to receive a doctorate in mathematics and the first Brazilian woman to join the Brazilian Academy of Sciences was *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

## No comments:

Post a Comment