## Thursday, 23 November 2017

### On This Day in Math - November 23

Whereas Nature does not admit of more than three dimensions ...
it may justly seem very improper to talk of a solid ...
drawn into a fourth, fifth, sixth, or further dimension.

~John Wallis

The 327th day of the year; 327 is the largest number n so that n, 2n, and 3n together contain every digit from 1-9 exactly once. (Students might search for a smaller number with that quantity) *What's Special About This Number

and from Jim Wilder @wilderlab:
For day 327: 327 is a perfect totient number- φ(327)=216, φ(216)=72, φ(72)=24, φ(24)=8, φ(8)=4, φ(4)=2, φ(2)=1, and 216+72+24+8+4+2+1=327.

The number 327 in base ten is equal to $57_{[64]}$ but also $75_{[46}$

EVENTS

1654 From 10:30 to 12:30 in the evening Pascal experienced a religious ecstasy that called him to give up his intermittent interest in mathematics and to devote his time to religious contemplation. *VFR

1670 James Gregory writes to John Collins, with the first use of what will come to be called the Newton-Gregory interpolation formula. He includes in the letter two enclosures showing how to apply his method to series for sines and logarithms. *Thomas Harriot’s Doctrine of Triangular Numbers, Beery & Stedall, pg 51-52

1706 Jakob Hermann writes to Leibniz about proof that Machin's series converges to pi. *My uncredited notes (sorry)

1821 Thomas Jefferson writes to West Point Instructor Claudius Crozet to thank him for the gift of a copy of his A Treatise on Descriptive Geometry and praised the book, and the author. Jefferson pronounced Crozet, "by far the best mathematician in the United States." *Natl. Archives, Wik (Crozet is sometimes credited with introducing the blackboard into the US, but it seems to have been common at West Point before his arrival there.)

1823 Janos Bolyai wrote to his father “I have made such wonderful discoveries that I am myself lost in astonishment.” This refers to his discovery of Non-Euclidean Geometry that was published in 1833. *Kline, Mathematics. The Loss of Certainty, p. 83 via *VFR

1834 Astronomer Royal Airy Replies to suggestion that he begin a mathematical search for undiscovered planet that would be Neptune by the Reverend T.J. Hussey.
Hussey had mentioned in his letter how he has heard of a possible planet beyond Uranus and looked for it using a reflector telescope, but to no avail. He presented the idea of using mathematics as a tool in the search but admitted to Airy that he would not be of much help in that regard. On Novemeber 23rd Airy writes back to the reverend and admits he too has been preoccupied with a possible planet. He had observed that Uranus' orbit deviated the most in 1750 and 1834, when it would be at the same point. This was strong evidence for an object pulling on the planet, but Airy felt that until more observations were made no mathematical tools would be of help
*from http://theoriginal1701.hubpages.com/hub/The-Drama-of-Neptunes-Discovery

In 1889, the first jukebox was installed when an entrepreneur named Louis Glass and his business associate, William S. Arnold, placed a coin-operated Edison cylinder phonograph in the Palais Royale Saloon in San Francisco. The machine, an Edison Class M Electric Phonograph with oak cabinet, had been fitted locally in San Francisco with a coin mechanism invented and soon patented by Glass and Arnold. This was before the time of vacuum tubes, so there was no amplification. For a nickel a play, a patron could listen using one of four listening tubes. Known as "Nickel-in-the-Slot," the machine was an instant success, earning over $1000 in less than half a year. *TIS 1924 New York Times publishes Hubble's new universe: Between 1922–1923, Hubble's observations had proved conclusively that these nebulae were much too distant to be part of the Milky Way and were, in fact, entire galaxies outside our own. This idea had been opposed by many in the astronomy establishment of the time, in particular by the Harvard University-based Harlow Shapley. (Shapley wrote sarcastically that Hubble's letter informing him of his results was “the most entertaining piece of literature I have seen for a long time.” ) Despite the opposition, Hubble, then a thirty-five year old scientist, had his findings first published in The New York Times on November 23, 1924, and then more formally presented in the form of a paper at the January 1, 1925 meeting of the American Astronomical Society. Hubble's findings fundamentally changed the scientific view of the universe.*Wik 1982 Vatican City issued a set of three stamps commemorating the 400th anniversary of the Gregorian Calendar. The image on the Vatican stamp is from the tomb of Pope Gregory XIII in St. Peter's Basilica. The tomb, the work of Camillo Rusconi, includes a relief showing Clavius kneeling before the Pope, presenting his work as the Pope promulgates the new calendar in 1582. *VFR 1982 Poland issued stamps honoring the mathematicians StanisLlaw Zaremba (1863–1942), WacLlaw Sierpi´nski (1882–1969), Zygmunt Janiszewski (1888–1920), and Stefan Banach (1892-1945). [Scott #2542-5]. *VFR 1992 "Computer industry on the skids" With IBM projected to lose$5 billion in 1992, Business Week describes the computer business as "an industry on the skids." The magazine cited layoffs at most established computer companies, such as IBM, as well as newer firms like Sun Microsystems Inc., as evidence that the industry was saturated. A solution, the article concluded, would be for each business to find its proper niche.*CHM

BIRTHS

1221 Alfonso X of Castile (23 Nov 1221; 4 Apr 1284) Spanish monarch and astronomer who encouraged the preparation of revised planetary tables (1252), published on the day of his accession to the throne as king of Castile and León. These "Alfonsine Tables," a revision and improvement of the Ptolemaic tables, were the best available during the Middle Ages; they were not replaced by better ones for over three centuries. The astronomical data tabulating the positions and movements of the planets was compiled by about 50 astronomers he had assembled for this purpose. He questioned the complexity of the Ptolemaic model centuries before Copernicus. "If the Lord Almighty had consulted me before embarking on the Creation, I would have recommended something simpler." He also wrote a commentary on alchemy. *TIS

1616 John Wallis (23 Nov 1616, 28 Oct 1703) British mathematician who introduced the infinity math symbol $\infty$. Wallis was skilled in cryptography and decoded Royalist messages for the Parliamentarians during the Civil War. Subsequently, he was appointed to the Savilian Chair of geometry at Oxford in 1649, a position he held until his death more than 50 years later. Wallis was part of a group interested in natural and experimental science which became the Royal Society, so Wallis is a founder member of the Royal Society and one of its first Fellows. Wallis contributed substantially to the origins of calculus and was the most influential English mathematician before Newton. *TIS

1820 Isaac Todhunter (23 Nov 1820 in Rye, Sussex, England - 1 March 1884 in Cambridge, England) Todhunter is best known for his textbooks and his writing on the history of mathematics. Among his textbooks are Analytic Statics (1853), Plane Coordinate Geometry (1855), Examples of Analytic geometry in Three Dimensions (1858). He also wrote some more elementary texts, for example Algebra (1858), Trigonometry (1859), Theory of Equations (1861), Euclid (1862), Mechanics (1867) and Mensuration (1869).
Among his books on the history of mathematics are A History of the Mathematical Theory of Probability from the Time of Pascal to that of Laplace (1865, reprinted 1965) and History of the Mathematical Theories of Attraction (1873). *SAU

1837 Johannes Diederik van der Waals (23 Nov 1837; 9 Mar 1923) Dutch physicist, winner of the 1910 Nobel Prize for Physics for his research on the gaseous and liquid states of matter. He was largely self-taught in science and he originally worked as a school teacher. His main work was to develop an equation (the van der Waals equation) that - unlike the laws of Boyle and Charles - applied to real gases. Since the molecules do have attractive forces and volume (however small), van der Waals introduced into the theory two further constants to take these properties into account. The weak electrostatic attractive forces between molecules and between atoms are called van der Waals forces in his honour. His valuable results enabled James Dewar and Heike Kamerlingh-Onnes to work out methods of liquefying the permanent gases. *TIS

1853 George Bruce Halsted (23 Nov 1853 in Newark, New Jersey, USA - 16 March 1922 in New York, USA) His main interests were the foundations of geometry and he introduced non-euclidean geometry into the United States, both through his own research and writings as well as by his many important translations. Halsted gave commentaries on the work of Lobachevsky, Bolyai, Saccheri and Poincaré and made translations of their works into English. His work on the foundations of geometry led him to publish Demonstration of Descartes's theorem and Euler's theorem in the Annals of Mathematics in 1885. His other main interest was in mathematical education and, as a mathematics educator, he criticised the careless way that mathematics was presented in the textbooks of the time. He contributed over ninety article to the American Mathematical Monthly and wrote many biographies of mathematicians such as Lambert, Farkas Bolyai, Lobachevsky, De Morgan, Sylvester, Chebyshev, Cayley, Hoüel and Klein. *SAU

1887 Henry Gwyn Jeffreys Moseley (23 Nov 1887; 10 Aug 1915) English physicist who experimentally demonstrated that the major properties of an element are determined by the atomic number, not by the atomic weight, and firmly established the relationship between atomic number and the charge of the atomic nucleus. He began his research under Ernest Rutherford while serving as lecturer at the Univ. of Manchester. Using X-ray photographic techniques, he determined a mathematical relation between the radiation wavelength and the atomic numbers of the emitting elements. Moseley obtained several quantitative relationships from which he predicted the existence of three missing elements (numbers 43, 61, and 75) in the periodic table, all of which were subsequently identified. Moseley was killed in action during WW I.*TIS

1917 Elizabeth Scott (November 23, 1917 – December 20, 1988) was an American mathematician specializing in statistics.
Scott was born in Fort Sill, Oklahoma. Her family moved to Berkeley, California when she was 4 years old. She attended the University of California, Berkeley where she studied mathematics and astronomy. There were few options for further study in astronomy, as the field was largely closed to women at the time, so she completed her graduate studies in mathematics. She received her Ph.D. in 1949, and received a permanent position in the Department of Mathematics at Berkeley in 1951.
She wrote over 30 papers on astronomy and 30 on weather modification research analysis, incorporating and expanding the use of statistical analyses in these fields. She also used statistics to promote equal opportunities and equal pay for female academics.
In 1957 Elizabeth Scott noted a bias in the observation of galaxy clusters. She noticed that for an observer to find a very distant cluster, it must contain brighter than normal galaxies and must also contain a large number of galaxies. She proposed a correction formula to adjust for (what came to be known as) the "Scott effect".
The Committee of Presidents of Statistical Societies awards a prize in her honour to female statisticians.*Wik

DEATHS

1604 Francesco Barozzi (in Latin, Franciscus Barocius) (9 August 1537 – 23 November 1604) was an Italian mathematician, astronomer and humanist. Barozzi helped in the general reappraisal of the geometry of Euclid, and corresponded with numerous mathematicians, including the German Jesuit Christopher Clavius. His original works include Cosmographia in quatuor libros distributa summo ordine, miraque facilitate, ac brevitate ad magnam Ptolemaei mathematicam constructionem, ad universamque
astrologiam institutens (1585), which he dedicated to the Duke of Urbino. This work concerns the cosmography and mathematic systems of Ptolemy. Barozzi also discussed 13 ways of drawing a parallel line in his Admirandum illud geometricum problema tredecim modis demonstratum quod docet duas lineas in eodem plano designare, quae nunquam invicem coincidant, etiam si in infinitum protrahantur: et quanto longius producuntur, tanto sibiinuicem propiores euadant (1586).
In his Opusculum: in quo una Oratio et due Questiones, altera de Certitude et altera de Medietate Mathematicarum continentur, Barozzi stressed that "the certitude of mathematics is contained in the syntactic rigor of demonstrations." Barozzi dedicated this work to Daniele Barbaro.
He also wrote Rythmomachia (1572), which he dedicated to Camille Paleotti, a Senator of Bologna, a work that is based on the mathematical game of the same name, also known as "The Philosophers' Game."
As an antiquarian, he copied many Greek inscriptions on Crete. His collection of inscriptions was later inherited by his nephew Iacopo Barozzi (1562–1617), who edited and expanded it. This collection was later acquired in 1629 by the University of Oxford. They are wide-ranging in date and subject-matter and can still be found in the Bodleian Library.*Wik

1817 James Glenie (Oct 1750 in Leslie, Fife, Scotland - 23 Nov 1817 in Chelsea, London, England ) He was an artillery officer when his regiment was sent out to North America in 1775 at the start of the American War of Independence. During his time in North America with the army Glenie worked on mathematics. In fact, even before being sent to North America, he had discovered what he called the antecedental calculus in 1774. The was an attempt to base Newton's fluxional calculus on the binomial theorem rather than on the concept of motion. He published a number of papers on this and other topics; The division of right lines, surfaces and solids being published in the Philosophical Transactions of the Royal Society in 1776 while The general mathematical laws which regulate and extend proportion universally was published in the same journal in the following year. In 1778 the Royal Society published Glenie's paper on the antecedental calculus. In addition to these papers he had also published a book on gunnery entitled The History of Gunnery with a New Method of Deriving the Theory of Projectiles in 1776. For his achievements in mathematics and its applications he was elected a fellow of the Royal Society on 18 March 1779 while he was still based with the army in Quebec.
He died in poverty. *SAU

1826 Johann Elert Bode (19 Jan 1747, 23 Nov 1826) German astronomer best known for his popularization of Bode's law. In 1766, his compatriot Johann Titius had discovered a curious mathematical relationship in the distances of the planets from the sun. If 4 is added to each number in the series 0, 3, 6, 12, 24,... and the answers divided by 10, the resulting sequence gives the distances of the planets in astronomical units (earth = 1). Also known as the Titius-Bode law, the idea fell into disrepute after the discovery of Neptune, which does not conform with the 'law' - nor does Pluto. Bode was director at the Berlin Observatory, where he published Uranographia (1801), one of the first successful attempts at mapping all stars visible to the naked eye without any artistic interpretation of the stellar constellation figures. *TIS

1844 Thomas Henderson (28 Dec 1798, 23 Nov 1844) Scottish astronomer, the first Scottish Astronomer Royal (1834), who was first to measure the parallax of a star (Alpha Centauri, observed at the Cape of Good Hope) in 1831-33, but delayed publication of his results until Jan 1839. By then, a few months earlier, both Friedrich Bessel and Friedrich Struve had been recognized as first for their measurements of stellar parallaxes. Alpha Centauri can be observed from the Cape, though not from Britain. It is now known to be the nearest star to the Sun, but is still so distant that its light takes 4.5 years to reach us. As Scottish Astronomer Royal in 1834, he worked diligently at the Edinburgh observatory for ten years, making over 60,000 observations of star positions before his death in 1844.*TIS

1864 Friedrich Georg Wilhelm von Struve (15 Apr 1793, 23 Nov 1864) German-Russian astronomer, one of the greatest 19th-century astronomers and the first in a line of four generations of distinguished astronomers. He founded the modern study of binary (double) stars. In 1817, he became director of the Dorpat Observatory, which he equipped with a 9.5-inch (24-cm) refractor that he used in a massive survey of binary stars from the north celestial pole to 15°S. He measured 3112 binaries - discovering well over 2000 - and cataloged his results in Stellarum Duplicium Mensurae Micrometricae (1837). In 1835, Czar Nicholas I persuaded Struve to set up a new observatory at Pulkovo, near St. Petersburg. There in 1840 Struve became, with Friedrich Bessel and Thomas Henderson, one of the first astronomers to detect parallax. *TIS

1910 Octave Chanute(18 Feb 1832, 23 Nov 1910) U.S. aeronaut whose work and interests profoundly influenced Orville and Wilbur Wright and the invention of the airplane. Octave Chanute was a successful engineer who took up the invention of the airplane as a hobby following his early retirement. Knowing how railroad bridges were strengthened, Chanute experimented with box kites using the same basic strengthening metod, which he then incorporated into wing design of gliders. Through thousands of letters, he drew geographically isolated pioneers into an informal international community. He organized sessions of aeronautical papers for the professional engineering societies that he led; attracted fresh talent and new ideas into the field through his lectures; and produced important publications. *TIS The town of Chanute, Kansas is named after him, as well as the former Chanute Air Force Base near Rantoul, Illinois, which was decommissioned in 1993. The former Base, now turned to peacetime endeavors, includes the Octave Chanute Aerospace Museum, detailing the history of aviation and of Chanute Air Force base. He was buried in Springdale Cemetery, Peoria, Illinois. *Wik

1942 Stanisław Saks (December 30, 1897 – November 23, 1942) was a Polish mathematician and university tutor, known primarily for his membership in the Scottish Café circle, an extensive monograph on the Theory of Integrals, his works on measure theory and the Vitali-Hahn-Saks theorem.*Wik

1942 Stanisław Zaremba (October 3, 1863 – November 23, 1942) was a Polish mathematician. His research in differential equations, applied mathematics, classical analysis, particularly on harmonic analysis, was widely recognized. He was a mathematician who contributed to the success of the Polish School of Mathematics through his teaching and organizational skills as well as through his research. Zaremba wrote a number of university textbooks and monographies.*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

## Wednesday, 22 November 2017

### On This Day in Math - November 22

Ulam Spiral
PrimeSpiral_1000.gif
mathworld.wolfram.com

I believe there are
15,747,724,136,275,002,577,605,653,961,181,555,468,044,717,
914,527,116,709,366,231,025,076,185,631,031,296
protons in the universe,
and the same number of electrons.
— Sir Arthur Stanley Eddington

The 326th day of the year; 326 is the maximum number of pieces that may be produced in a pizza with 25 straight cuts. These are sometimes called "lazy caterer numbers" and more generally they are centered polygonal numbers.

326 is also the sum of the first 14 consecutive odd primes: 326 = 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47. *MAA

326 prefixed or followed by any digit still remains composite.  *Derek's Daily Math

EVENTS

1850 J J Sylvester called to the Bar. Rather than practicing law he gave private instruction in mathematics, and counted among his pupils Florence Nightingale. [Osiris, 1(1936), 102] *VFR (This idea of Sylvester tutoring Nightingale, to the best of my knowledge, originates from the Herbert Baker obituary. Karen Hunger Parshall, among others, has questioned the accuracy of this statement.)

1906 An International Radiotelegraphic Convention adopted the S.O.S radio distress signal, ... The Convention met in Berlin in 1906. This body signed an international agreement on November 3, 1906, with an effective date of July 1, 1908. An extensive collection of Service Regulations was included to supplement the Convention, and in particular Article XVI adopted Germany's Notzeichen distress signal as the international standard, stating: "Ships in distress shall use the following signal: · · · — — — · · · repeated at brief intervals".
The first well documented use of the SOS distress call is by the Arapahoe on August 11, 1909, when it suffered a broken shaft in the Atlantic Ocean, near Cape Hatteras, North Carolina. However, an article titled "Notable Achievements of Wireless" in the September, 1910 Modern Electrics suggests that an earlier SOS distress call was transmitted by the Cunard liner Slavonia, on June 10, 1909.
[The wireless operator aboard S.S. Arapahoe, T. D. Haubner, radioed for help. A few months later, Haubner on the S.S. Arapahoe received an SOS from the SS Iroquois, the second use of SOS in America.(*TIS)]
The first radio distress call to be adopted appears to have been "CQD", by the Marconi International Marine Communication Company​, for Marconi-operated shipboard stations. It was announced on January 7, 1904 by the company's "Circular 57" that "...on and after the 1st February, 1904, the call to be given by ships in distress or in any way requiring assistance shall be 'C.Q.D.'." ("CQ" was a general call to all stations; amateur or "ham" radio operators still use it today when soliciting a contact with any station that hears the call.) *Citizens Compendium

BIRTHS

1796 Charles Bonnycastle (22 Nov 1796 - 31 Oct, 1840). The University of Virginia's second Professor of Mathematics, Charles Bonnycastle, was born in Woolwich, England. His father, John, was Professor of Mathematics at the Royal Military Academy there, and so Charles grew up and received his education in an environment that very much influenced his own subsequent career. The contributions that the son made to the thirteenth edition of his father's textbook, Introduction to Algebra (1824), in fact, augmented the credentials he presented to Francis Walker Gilmer, agent for the newly forming University of Virginia.
Bonnycastle actually came to the University at its opening in 1825 as the first professor, not of mathematics, but of natural philosophy (as physics was then called). When Thomas Key, the first Professor of Mathematics, resigned to return to his native England, Bonnycastle shifted over to the mathematical chair and remained in that post until his untimely death on 31 October 1840 at the age of only forty-three. "Old Bonny," as he was fondly called by the students, moved away from what was increasingly becoming the antiquated synthetic approach to mathematical pedagogy that had been so typical of Oxbridge mathematical teaching in the eighteenth and early nineteenth centuries and introduced the more avant-garde analytic approach of late eighteenth-century French authors such as Silvestre Lacroix. In 1834, he published his own textbook, Inductive Geometry, in which he aimed to unite the best of the synthetic and the analytic approaches to geometry for the college- and university-level audience. Bonnycastle also contributed works on mathematical and physical topics to the Transactions of the American Philosophical Society, one of the few venues available in early nineteenth-century America for the publication of original work in the sciences.
Bonnycastle apparently also entrusted a number of mathematical papers to his friend, Princeton physics professor and (after 1846) first Secretary of the Smithsonian Institution, Joseph Henry. Shortly before his death in 1878, Henry deposited these in the library at the University of Virginia. They did not survive the infamous Rotunda fire of 1895. *History of the U V Math Dept. He was buried in University of Virginia Cemetery, Charlottesville, Virginia. His gravestone reads:
Sacred to the memory of
Charles Bonnycastle
late Professor of Mathematics
in the University of Virginia
who was born in London
on the 22nd day of November 1796
was made professor in the University in 1825
and continued in this station until his death
on the 31st of October 1840.
For Michigan residents around Kalamazoo, Charles Bonnycastle's brief stay in the area with his brother Humphrey is still marked by Bonniecastle Lake west of the city.

1803 Giusto Bellavitis (22 Nov 1803 in Bassano, Vicenza, Italy - 6 Nov 1880 in Tezze (near Bassano) Italy ) Bellavitis solved various mechanical problems by original methods, among them Hamilton's quaternions. He developed very personal critical observations about the calculus of probabilities and the theory of errors. He also explored physics, especially optics and electrology, and chemistry. As a young man, Bellavitis weighted the problem of a universal scientific language and published a paper on this subject in 1863. He also devoted time to the history of mathematics and, among other things, he vindicated Cataldi by attributing the invention of continued fractions to him. *SAU

1840 Émile Michel Hyacinthe Lemoine (22 Nov 1840 in Quimper, France - 21 Feb 1912 in Paris, France) Lemoine work in mathematics was mainly on geometry. He founded a
new study of properties of a triangle in a paper of 1873 where he studied the point of intersection of the symmedians of a triangle. He had been a founder member of the Association Française pour l'Avancement des Sciences and it was at a meeting of the Association in 1873 in Lyon that he presented his work on the symmedians.
A symmedian of a triangle from vertex A is obtained by reflecting the median from A in the bisector of the angle A. He proved that the symmedians are concurrent, the point where they meet now being called the Lemoine point. Among other results on symmedians in Lemoine's 1873 paper is the result that the symmedian from the vertex A cuts the side BC of the triangle in the ratio of the squares of the sides AC and AB. He also proved that if parallels are drawn through the Lemoine point parallel to the three sides of the triangle then the six points lie on a circle, now called the Lemoine circle. Its centre is at the mid-point of the line joining the Lemoine point to the circumcentre of the triangle. Lemoine gave up active mathematical research in 1895 but continued to support the subject. He had helped to found a mathematical journal, L'intermédiaire des mathématiciens., in 1894 and he became its first editor, a role he held for many years. *sau

1904 Louis-Eugène-Félix Néel (22 Nov 1904; 17 Nov 2000) French physicist, corecipient (with the Swedish astrophysicist Hannes Alfvén) of the Nobel Prize for Physics in 1970 for his pioneering studies of the magnetic properties of solids. His contributions to solid-state physics have found numerous useful applications, particularly in the development of improved computer memory units. About 1930 he suggested that a new form of magnetic behavior might exist - called antiferromagnetism. Above a certain temperature (the Néel temperature) this behaviour stops. Néel pointed out (1947) that materials could also exist showing ferrimagnetism. Néel has also given an explanation of the weak magnetism of certain rocks, making possible the study of the past history of the Earth's magnetic field.*TIS

DEATHS

1784 Paolo Frisi (13 Apr 1728, 22 Nov 1784) Italian mathematician, astronomer, and physicist who is best known for his work in hydraulics (he designed a canal between Milan and Pavia). He was, however, the first to introduce the lightning conductor into Italy. His most significant contributions to science, however, were in the compilation, interpretation, and dissemination of the work of other scientists, such as Galileo Galilei and Sir Isaac Newton. His work on astronomy was based on Newton's theory of gravitation, studying the motion of the earth (De moto diurno terrae). He also studied the physical causes for the shape and the size of the earth using the theory of gravity (Disquisitio mathematica, 1751) and tackled the difficult problem of the motion of the moon. *TIS

1880 James Craig Watson (January 28, 1838 – November 22, 1880) was a Canadian-American astronomer born in the village of Fingal, Ontario Canada. His family relocated to Ann Arbor, Michigan in 1850.
At age 15 he was matriculated at the University of Michigan, where he studied the classical languages. He later was lectured in astronomy by professor Franz Brünnow.
He was the second director of Detroit Observatory (from 1863 to 1879), succeeding Brünnow. He wrote the textbook Theoretical Astronomy in 1868.
He discovered 22 asteroids, beginning with 79 Eurynome in 1863. One of his asteroid discoveries, 139 Juewa was made in Beijing when Watson was there to observe the 1874 transit of Venus. The name Juewa was chosen by Chinese officials (瑞華, or in modern pinyin, ruìhuá). Another was 121 Hermione in 1872, from Ann Arbor, Michigan, and this asteroid was found to have a small asteroid moon in 2002.
He was a strong believer in the existence of the planet Vulcan, a hypothetical planet closer to the Sun than Mercury, which is now known not to exist (however the existence of small Vulcanoid planetoids remains a possibility). He believed he had seen such two such planets during a July 1878 solar eclipse in Wyoming.
He died of peritonitis at the age of only 42. He had amassed a considerable amount of money through non-astronomical business activities. By bequest he established the James Craig Watson Medal, awarded every three years by the National Academy of Sciences for contributions to astronomy.
The asteroid 729 Watsonia is named in his honour, as is the lunar crater Watson. *Wik

1907 Asaph Hall (15 Oct 1829; 22 Nov 1907) American astronomer, discovered and named the two moons of Mars, Phobos and Deimos, and calculated their orbits.Born in Goshen, Conn. and apprenticed as a carpenter at age 16, he had a passion for geometry and algebra. Hall obtained a position at the Harvard Observatory in Cambridge, Mass. in 1857 and became an expert computer of orbits. In August 1862, he joined the staff of the Naval Observatory in Washington, D.C. where he made his discoveries, in mid- Aug 1877, using the Observatory's 26-inch "Great Equatorial" refracting telescope, then the largest of its kind in the world. He stayed there 30 years until 1891. His son, Asaph Hall, Jr., followed him and worked at the Observatory at various times between 1882-1929.*TIS

1944 Sir Arthur Stanley Eddington (28 Dec 1882, 22 Nov 1944) English astrophysicist, and mathematician known for his work on the motion, distribution, evolution and structure of stars. He also interpreted Einstein's general theory of relativity. He was one of the first to suggest (1917) conversion of matter into radiation powered the stars. In 1919, he led a solar eclipse expedition which confirmed the predicted bending of starlight by gravity. He developed an equation for radiation pressure. In 1924, he derived an important mass-luminosity relation. He also studied pulsations in Cepheid variables, and the very high densities of white dwarfs. He sought fundamental relationships between the prinicipal physical constants. Eddington wrote many books for the general reader, including Stars And Atoms  . *TIS  One of my favorite stories about Eddington is this one: Ludwick Silberstein approached Eddington and told him that people believed he was one of only three people in the world who understood general relativity, and that included Einstein. When Eddington didn't respond for a moment he prodded, come on, don't be modest, and Eddington replied, "Oh, no.  It's not that.  I was just trying to figure out who the third was?"  *Mario Livio, Brilliant Blunders

1986 Nikolai Grigor'evich Chudakov (14 Dec 1904 in Lysovsk, Novo-Burassk, Saratov, Russia - 22 Nov 1986 in Saratov, Russia) Chudakov established a number of important results in number theory. He gave an estimate for the bounds of the zeta-function in the critical strip using techniques which had been introduced a few years earlier by Vinogradov. As a consequence of this work he was able to give a substantially improved remainder term in the asymptotic formula for the number of primes less than a fixed number N. Also, by these method, he improved the estimate for the difference between two consecutive primes. In his later work he extended these results to apply to arbitrary arithmetic progressions. In 1947 Chudakov published On Goldbach-Vinogradov's theorem in the Annals of Mathematics. In this paper he proves Vinogradov's theorem that every large odd integer is representable as a sum of three odd primes. *SAU

1996 Garrett Birkhoff (January 19, 1911, Princeton, New Jersey, USA – November 22, 1996, Water Mill, New York, USA) was an American mathematician. He is best known for his work in lattice theory.During the 1930s, Birkhoff, along with his Harvard colleagues Marshall Stone and Saunders Mac Lane, substantially advanced American teaching and research in abstract algebra. During and after World War II, Birkhoff's interests gravitated towards what he called "engineering" mathematics. Birkhoff's research and consulting work (notably for General Motors) developed computational methods besides numerical linear algebra, notably the representation of smooth curves via cubic splines.
The mathematician George Birkhoff (1884–1944) was his father.*Wik

2007 Andrew Ronald Mitchell (22 June 1921 – 22 November 2007), popularly known as Ron Mitchell, was a British applied mathematician and numerical analyst. He was a professor of mathematics at the University of St Andrews, Dundee, Scotland. He was known for his contribution to the field of numerical analysis of partial differential equations in general and finite difference method and finite element method in particular. Mitchell has authored several influential books on numerical solution of partial differential equations, including "The Finite Element Analysis in Partial Differential Equations" with Richard Wait and "The Finite Difference Method in Partial Differential Equations" with David F. Griffiths.*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

## Tuesday, 21 November 2017

### On This Day in Math - November 21

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

## Monday, 20 November 2017

### On This Day in Math - November 20

The history of astronomy is a history of receding horizons.

— Edwin Powell Hubble

The 324th day of the year; 324 is the largest possible product of positive integers with a sum of 16. (Students, Can you find the integers. Try to find the similar maximum product with a sum of 17)).
324 is also the sum of four consecutive primes, 324 = 73 + 79 + 83 + 89

If you have a square array of 324 dots (that's 18x18) you can carefully paint them each in one of four colors so that no four corners of a rectangle (with sides horizontal and vertical) are the same color. you can also do that for any smaller square, but not for any larger. Here is a 17x17 to ponder

EVENTS

1629 In a letter to Marin Mersenne, Descartes … went on to postulate another kind of language in which ideas would be represented so clearly that errors of judgment would be 'almost impossible'. To realize such a language, all of our thoughts would first have to be given a proper order 'like the natural order of the numbers'; and this presupposes the 'true philosophy', by which the analysis and ordering of thoughts would be carried out. Although Descartes pursues the plan no further, he is optimistic that 'such a language is possible and that the knowledge on which it depends can be discovered'. *Donald Rutherford,

1711 Robert Simson submitted to a simple test of his mathematical knowledge and was duly admitted as professor of mathematics at the University of Glasgow. His most inﬂuential work was a definitive edition of Euclid’s Elements in 1749. *VFR  The pedal line of a triangle is sometimes called the "Simson line" after him, although it does not actually appear in any work of Simson.

1843 Sylvester departs US for England and describes his life as "Pretty much a blank." After resigning from Un of Va. after only four months, J. J. Sylvester lived with a brother in New York City while trying to find work in the US. Finally giving up, her returned to England with no job or prospects for one. *James Joseph Sylvester: Life and Work in Letters
edited by Karen Hunger Parshall

1980, Steve Ptacek in Solar Challenger piloted its first solar-powered flight. The aircraft was designed and built by AeroVironment, Inc. (founded in 1971 by ultra-light airplane innovator, Dr. Paul MacCready). An earlier, 71-ft wingspan, solar-powered design, the Gossamer Penguin, after test flights, flew about 1.95 miles at a public demonstration on 7 Aug 1980. Solar Challenger built upon this experience to be a piloted, solar-powered aircraft strong enough to handle both long and high flights when encountering normal turbulence. With only a 46.5-ft wingspan, it had a huge horizontal stabilizer and had enough wing area for 16,128 solar cells. After design modifications, Ptacek flew across the English Channel flight on 7 July 1981.*VFR

2008 Conficker, also known as Downup, Downadup and Kido, is a computer worm targeting the Microsoft Windows operating system that was first detected on this day in November 2008. It uses flaws in Windows software and dictionary attacks on administrator passwords to propagate while forming a botnet, and has been unusually difficult to counter because of its combined use of many advanced malware techniques. The Conficker infected millions of computers including government, business and home computers in over 200 countries, making it the largest known computer worm infection since the 2003 Welchia. *Wik

BIRTHS

1602 Otto von Guericke (20 Nov 1602; 11 May 1686) German physicist who investigated the properties of a vacuum invented (1654) the first piston air pump to produce a vacuum. While mayor of Madgeburg, in 1663, he demonstrated that two 51 cm diameter copper hemispheres with air pumped out of their interior would be so strongly held together by the force of air pressure that teams of horses harnessed to each hemisphere were not able to pull the hemispheres apart. He studied the role of air in combustion and respiration. With his invention of the first electrostatic machine - a rotating ball of sulphur electrified by friction against his hand - he produced sizeable sparks and showed that like charges repel each other.*TIS

1792 Nikolai Ivanovich Lobachevsky born. (November 20, 1792 – February 12, 1856 (O.S.)) was a Russian mathematician and geometer, renowned primarily for his pioneering works on hyperbolic geometry, otherwise known as Lobachevskian geometry. William Kingdon Clifford called Lobachevsky the "Copernicus of Geometry" due to the revolutionary character of his work. Russia did not convert to the Gregorian Calendar until after the communist revolution in 1918. The new style dates were (December 1, 1792 – February 24, 1856 *Wik
And if you've never heard Tom Lehrer's fantastic musical creation about Lobachevsky. He admits the topic has no relation to the man, but the name just fit so well.

1873 William W(eber) Coblentz (20 Nov 1873; 15 Sep 1962) an American physicist and astronomer whose work lay primarily in infrared spectroscopy. In 1905 he founded the radiometry section of the National Bureau of Standards, which he headed for 40 years. Coblentz measured the infrared radiation from stars, planets, and nebulae and was the first to determine accurately the constants of blackbody radiation, thus confirming Planck's law. *TIS

1889 Edwin Powell Hubble (20 Nov 1889; 28 Sep 1953) American astronomer, born in Marshfield, Mo., who is considered the founder of extragalactic astronomy and who provided the first evidence of the expansion of the universe. In 1923-5 he identified Cepheid variables in "spiral nebulae" M31 and M33 and proved conclusively that they are outside the Galaxy. His investigation of these objects, which he called extragalactic nebulae and which astronomers today call galaxies, led to his now-standard classification system of elliptical, spiral, and irregular galaxies, and to proof that they are distributed uniformly out to great distances. Hubble measured distances to galaxies and their redshifts, and in 1929 he published the velocity-distance relation which is the basis of modern cosmology. *TIS
The late Bill Buegsen was a resident who was proud of the achievements of Marshfield's native son, so he designed a one-fourth replica of the original Hubble Space Telescope. The Hubble Telescope replica was dedicated on July 4, 1994 and is located on Clay Street, on the west side of the Webster County Courthouse in Marshfield, Mo. It took approximately three months to build, is approximately twelve feet long, ten feet wide and weighs twelve hundred pounds. There is also an Elementary school named for Hubble. The city is on the famous Route 66 just 30 minutes east of Springfield, Mo. *Marshfield Tourist Office web site

1893 André Bloch (20 Nov 1893 in Besançon, France - 11 Oct 1948 in Paris, France) attended the École Polytechnique in 1913 then was drafted in 1914. An accident at the front made him unfit for military service. On 17 Nov 1917, at a family meal, he murdered one of his brothers, his uncle and his aunt. He was confined to a psychiatric hospital (Saint-Maurice Hospital) where he worked on a large range of topics, function theory, geometry, number theory, algebraic equations and kinematics.
Bloch wrote many important papers, corresponding with Hadamard, Mittag-Leffler, Pólya and Henri Cartan (Élie Cartan's son). He was a model patient who refused to go out saying Mathematics is enough for me. Bloch explained the murders to his doctor saying It's a matter of mathematical logic. There had been mental illness in my family. He saw it as his eugenic duty! The Académie awarded him the Becquerel Prize just before his death. *SAU

1917 Leonard Jimmie Savage (20 November 1917 – 1 November 1971) was an American mathematician and statistician. Nobel Prize-winning economist Milton Friedman said Savage was "one of the few people I have met whom I would unhesitatingly call a genius." His most noted work was the 1954 book Foundations of Statistics, in which he put forward a theory of subjective and personal probability and statistics which forms one of the strands underlying Bayesian statistics and has applications to game theory.
During World War II, Savage served as chief "statistical" assistant to John von Neumann, the mathematician credited with building the first electronic computer.
One of Savage's indirect contributions was his discovery of the work of Louis Bachelier on stochastic models for asset prices and the mathematical theory of option pricing. Savage brought the work of Bachelier to the attention of Paul Samuelson. It was from Samuelson's subsequent writing that "random walk" (and subsequently Brownian motion) became fundamental to mathematical finance.
In 1951 he introduced the minimax regret criterion used in decision theory.
The Hewitt–Savag *Wik

1924 Benoit Mandelbrot (20 Nov 1924 in Warsaw, Poland - 14 Oct 2010 in Cambridge, Massachusetts, USA) was largely responsible for the present interest in Fractal Geometry. He showed how Fractals can occur in many different places in both Mathematics and elsewhere in Nature.*SAU

1955 Ray Ozzie, who designed the Lotus Notes office management software for Lotus Development Corporation, is born in Chicago, IL. Ozzie graduated from the University of Illinois at Urbana-Champaign (UIUC) in 1979. During this time Ray worked at the Computer-based Education Research Lab (CERL) on the PLATO operating system. He was impressed with PLATO’s real-time communications and has often publicly credited his CERL experience as the inspiration for Lotus Notes. In 1984 Mitch Kapor, founder of Lotus Development Corporation, supported the idea to develop a PLATO-like product for PC by funding Iris Associates, Inc. In August 1986 Lotus Notes was complete becoming the first example of groupware and a commercial success. In 1997 Ozzie left Iris Associates to start a new venture, Rythmix Corp.*CHM

1963 Sir William Timothy Gowers, FRS (20 November 1963, ) is a British mathematician. He is a Royal Society Research Professor at the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge, where he also holds the Rouse Ball chair, and is a Fellow of Trinity College, Cambridge. In 1998 he received the Fields Medal for research connecting the fields of functional analysis and combinatorics.*Wik

DEATHS

1713 Thomas Tompion (baptised 25 Jul 1639, 20 Nov 1713) Most famous English clockmaker of his time, especially known for watchmaking improvements. He worked closely with experimental physicist Robert Hooke, and in 1675, following Hooke's design, Tompion made one of the first English watches regulated by a balance spring. In 1695, with Edward Barlow and William Houghton, he patented the cylinder escapement (a controlling device) that allowed use of a horizontal wheel, enabling Tompion to make the first of the flat and more compact watches.*TIS

1764 Christian Goldbach (18 Mar 1690, 20 Nov 1764)Russian mathematician whose contributions to number theory include Goldbach's conjecture, formulated in a letter to Leonhard Euler dated 7 Jul 1742. Stated in modern terms it proposes that: "Every even natural number greater than 2 is equal to the sum of two prime numbers." It has been checked by computer for vast numbers - up to at least 4 x 1014 - but still remains unproved. Goldbach made another conjecture that every odd number is the sum of three primes, on which Vinogradov made progress in 1937. (It has been checked by computer for vast numbers, but remains unproved.) Goldbach also studied infinite sums, the theory of curves and the theory of equations. *TIS

1856 Farkas Bolyai (9 Feb 1775, 20 Nov 1856) Hungarian mathematician, poet, and dramatist who spent a lifetime trying to prove Euclid's (fifth) postulate that parallel lines do not meet. While studying at the University of Göttingen, he met as a fellow student, the noted German mathematician Carl F. Gauss, with whom he corresponded as a life-long friend. Bolyai taught mathematics, physics and chemistry at Marosvásárhely all his life. He discouraged his son, János Bolyai, from studying the parallel axiom as he had, writing in a letter to him: "For God's sake, please give it up. Fear it no less than the sensual passion, because it, too, may take up all your time and deprive you of your health, peace of mind and happiness in life." *TIS

1882 Henry Draper (7 Mar 1837, 20 Nov 1882) American physician and amateur astronomer who made the first photograph of the spectrum of a star (Vega), in 1872. He was also the first to photograph a nebula, the Orion Nebula, in 1880. For his photography of the transit of Venus in 1874, Congress ordered a gold medal struck in his honour. His father, John William Draper, in 1840 had made the first photograph of the Moon.*TIS

1934 Willem de Sitter (6 May 1872, 20 Nov 1934) Dutch mathematician, astronomer, and cosmologist who developed theoretical models of the universe based on Albert Einstein's general theory of relativity. He worked extensively on the motions of the satellites of Jupiter, determining their masses and orbits from decades of observations. He redetermined the fundamental constants of astronomy and determined the variation of the rotation of the earth. He also performed statistical studies of the distribution and motions of stars, but today he is best known for his contributions to cosmology. His 1917 solution to Albert Einstein's field equations showed that a near-empty universe would expand. Later, he and Einstein found an expanding universe solution without space curvature.*TIS

1960 Hidehiko Yamabe (山辺 英彦 Yamabe Hidehiko?, August 22, 1923 in Ashiya, Hyōgo, Japan – November 20, 1960 in Evanston, Illinois) was a Japanese mathematician. His most notable work includes the final solution of Hilbert's fifth problem.
After graduating from the University of Tokyo in 1947, Yamabe became an assistant at Osaka University. From 1952 until 1954 he was an assistant at Princeton University, receiving his Ph.D. from Osaka University while at Princeton. He left Princeton in 1954 to become assistant professor at the University of Minnesota. Except for one year as a professor at Osaka University, he stayed in Minnesota until 1960. Yamabe died suddenly of a stroke in November 1960, just months after accepting a full professorship at Northwestern University. *Wik

1986 Arne Carl-August Beurling (February 3, 1905 – November 20, 1986) was a Swedish mathematician and professor of mathematics at Uppsala University (1937–1954) and later at the Institute for Advanced Study in Princeton, New Jersey.
Beurling worked extensively in harmonic analysis, complex analysis and potential theory. The "Beurling factorization" helped mathematical scientists to understand the Wold decomposition, and inspired further work on the invariant subspaces of linear operators and operator algebras.
In the summer of 1940 he single-handedly deciphered and reverse-engineered an early version of the Siemens and Halske T52 also known as the Geheimfernschreiber (secret teletypewriter) used by Nazi Germany in World War II for sending ciphered messages.[1] The T52 was one of the so-called "Fish cyphers", that using, transposition, created nearly one quintillion (893 622 318 929 520 960) different variations. It took Beurling two weeks to solve the problem using pen and paper. Using Beurling's work, a device was created that enabled Sweden to decipher German teleprinter traffic passing through Sweden from Norway on a cable. In this way, Swedish authorities knew about Operation Barbarossa before it occurred. Not wanting to reveal how this knowledge was attained the Swedish warning was not treated as credible by Soviets. *Wik

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