Pat'sBlog: November 2019

Saturday, 30 November 2019

On This Day in Math - November 30

Gilbert shall live, till Load-stones cease to draw,
Or British Fleets the boundless Ocean awe.

— John Dryden

The 334th day of the year; 334 is an even semi-prime, and together with 335 they form a semi-prime pair. (There will be one more day this year that is part of a semi-prime pair, can you find it?)

D. R. Kaprekar created the name "self number" for numbers that can not be made up as the sum of any number n and the sum of its digits. They are also called Colombian numbers or Devlali numbers. 1, 3, 5, 7, 9, 20, 31, are some of the smaller self-numbers, and of course, 334 is a self number.

334 in base three looks more like a binary number, its 110101. Students might explore other numbers in base three (or four or five) that look binary (ie only made up of zeros and ones).

EVENTS

3340 BC Our ancient Irish ancestors were expert astronomers, who carved images of an eclipse on ancient stone megaliths over 5000 years ago. November 30th 3340 BC: The world's oldest known solar eclipse was recorded in stone.
Substantially older than the recordings made in 2800 BC by the Chinese astronomers, it is situated at Loughcrew in Co Meath. The Irish Neolithic astronomer priests at this site recorded events on 3 stones relating to the eclipse, as seen from that location.
This is the only eclipse that fits these petroglyphs out of 92 solar eclipses tracked by the discoverer, Irish archaeoastronomer Paul Griffin. With none of the technology available to modern mankind, the Neolithic Irish constructed complex structures in stone which not only endured for five millennia, but were built so accurately that they still perform their astronomical functions today. Many historians believe the Celts created a “festival of light” to welcome an eclipse, which they were capable of predicting. *newgrange.com

1536 Lodovico Ferrari arrived at Cardan's house on 30 November, a fourteen year old boy ready to take over his cousin Luke's position and become a servant. Cardan, upon the discovery that the lad could read and write, exempted him from menial tasks and appointed the youngster as his secretary. *SAU (Cardano gives this date as 14 November, and writes that Ludovico ("Luigi") and his brother (Luke?)arrived together. He noted that a magpie chirped in the courtyard so long they knew someone must be arriving. *Tales of Mathematicians and Physicists By Simon Gindikin)

In 1609, the modern face of the moon first emerged when Galileo Galilei in Padua turned his telescope toward the moon, noted the irregularities of the crescent face, and made a drawing to record his discoveries. He made at least five more drawings of the moon over the next eighteen days, prepared careful watercolor sketches from these drawings, and then selected four of these to be engraved for his revolutionary Starry Messenger, which appeared the following March. Galileo's treatise announced to an astonished public that the moon was a cratered chunk of elements - a world - and not some globe of quintessential perfection. It was a new land, to be explored, charted, and named. *TIS

1703 Newton made president of the Royal Society, an office he held until his death.*VFR

1710 John Machin was elected a Fellow of the Royal Society. *SAU

1712 William Jones elected fellow of the Royal Society. In 1706 he introduced the Greek letter π for the ratio of the circumfrence of a circle to a diameter in his book Synopsis palmariarum matheseos (1706). This title is hard to translate. Literally it means a synopsis of the palm leaves of mathematics. Thus it is a compendium of the most praisworthy parts of mathematics. Earlier William Oughtred (1647) and Isaac Barrow (1669) used the same symbol for twice the number. The symbol was not generally used in our sense until Euler, who adopted it in 1737, popularixed π in his Introductio in analysin inﬁnitorum of 1748. See DSB 7, 163, and “The ubiquitous π ” by Dario Castellanos, Mathematics Magazine 61(1988), 67–98, especially p. 91. A nice post by Thony Christie, at The Renaissance Mathematicus discusses Jones part in preserving John Collins Library.

1753 Benjamin Franklin received the Copley Medal, the highest honor of the Royal Society of London, for his “curious experiments and observations on electricity.” He was the ﬁrst American to receive the Copley Medal. Three years later he was elected a member of the Royal Society. *VFR

In 1784, American physician and scientist John Jeffries recorded the first scientific data for free air, to a height of 9,309-ft, during a balloon flight in London, England, including twelve observations of temperature, pressure, and humidity. Jeffries' values agree closely with modern determinations. Jeffries had provided himself with thermometer, barometer, electrometer, hygrometer and timepiece. He also took air samples at different elevations for Cavendish, who subsequently made a chemical analysis of the air. This was the first of two balloon flights Jeffries financed. He flew with Frenchman Jean Pierre Blanchard, who had experience in balloon flight. On 7 Jan 1785, they made the first balloon crossing of the English Channel.*TIS

1877 Luigi Bianchi received his degree in mathematics. His work on metric diﬀerential geometry found application in Einstein’s studies on relativity.*VFR

In 1904, the first electron tube, a diode thermionic valve, was invented by John Ambrose Fleming. The valve consists of a carbon or tungsten filament lamp, to which is added a metal plate (insulated from the filament), and a connecting wire brought through the glass wall of the bulb to a third terminal outside. When battery current is applied to the filament making it incandescent, the space between the filament and the insulated plate will be found to conduct elecrons in only one direction. That means if the valve is connected in a circuit in with an oscillating current, its one-way conductivity will convert the oscillating current into a unidirectional current capable of actuating a telephone receiver. He notified Marconi in a 30 Nov 1904 letter.*TIS

1917 Bose Institute founded. Bose Institute is a research institute in the fields of Physics, Chemistry, Plant biology, Microbiology, Biochemistry, Biophysics, Animal physiology, Immunotechnology and Environmental science. The institute was established in 1917 by Acharya Jagdish Chandra Bose, who was the founder of modern scientific research in India. Bose Institute pioneered the concept of inter-disciplinary research in India in synch with global trends. Its alumni have achieved renown in India and the world.
Acharya Jagadish Chandra Bose founded the Institute on 30'th November 1917 with the following opening speech:

“I dedicate today this Institute as not merely a laboratory but a temple .... In the pursuit of my investigations I was unconsciously led into the border region of physics and physiology. To my amazement, I found boundary lines vanishing, and points of contact emerging, between the realms of the living and the non-living .... The lectures given here will not be mere repetitions of second-hand knowledge. They will announce new discoveries, demonstrated for the first time in these halls. Through regular publication of the work of the Institute, these Indian contributions will reach the whole world. They will become public property. No patents will ever be taken. The spirit of our national culture demands that we should forever be free from the desecration of utilizing knowledge only for personal gain."

*Wik

In 1954, in Sylacauga, Alabama, USA, Ann Hodges, 32, was bruised on the arm and hip by a meteorite that fell through the roof of her house into her living room. It smashed the case of her wooden radio and struck her as she lay resting on her sofa. The 9-lb (4-kg), 6 in (15 cm) diameter fragment came from a larger, likely more than 150-lb, chondrite meteorite that exploded over central Alabama about 2 pm, according to reports from people in several states that saw a bright flash across the sky. This remains (2006) the only recorded instance of a person being hit by a meteorite. She donated it in 1956 to the Alabama Museum of Natural History, and it is known by her name as the Hodges Meteorite.*TIS
I imagine Ms Hodges never heard "Stars Fell on Alabama" in quite the same way again.

1959 The first two IBM 7090 computers are delivered. Along with the faster version, which IBM released three years later, the series was a popular family of transistorized mainframes. Designed for scientific research and large-scale technological application, the computers were used in such projects as the Mercury and Gemini space flights and the Ballistic Missile Early Warning System. *CHM

1967 Ireland issued two stamps to commemorate the tercentenary of the birth of Jonathan Swift, author of Gulliver’s Travels. If you have read this book, then you know why this entry is included here; if you haven’t, then you should, and then you would. [Scott #240-241]. *VFR (For one example, see Bob M's comment below, Thanks Bob)

BIRTHS
1549 Sir Henry Savile (30 Nov 1549 in Bradley (near Halifax), Yorkshire, England - 19 Feb 1622 in Eton, Berkshire, England) Savile was an English mathematician who founded professorships of geometry and astronomy at Oxford. It is interesting to read Savile's comments in these lectures on why he felt that mathematics at that time was not flourishing. Students did not understand the importance of the subject, Savile wrote, there were no teachers to explain the difficult points, the texts written by the leading mathematicians of the day were not studied, and no overall approach to the teaching of mathematics had been formulated. Of course, as we shall see below, fifty years later Savile tried to rectify these shortcomings by setting up two chairs at the University of Oxford. *SAU

1602 Otto von Guericke (originally spelled Gericke) (November 20, 1602 – May 11, 1686 (Julian calendar); November 30, 1602 – May 21, 1686 (Gregorian calendar)) was a German scientist, inventor, and politician. He is best remembered for his invention of the Magdeburg hemispheres, popularized in the writings of Caspar Schott. His major scientific achievements were the establishment of the physics of vacuums, the discovery of an experimental method for clearly demonstrating electrostatic repulsion, and his advocacy of the reality of "action at a distance" and of "absolute space". *Wik

1711 Ebenezer Kinnersley (30 Nov 1711; 4 Jul 1778) English-born American experimenter and inventor who investigated electricity. In 1748 Kinnersley demonstrated that the electric fluid actually passed through water, using a 10-ft long trough of water. In 1751, as one of the earliest popularizers of science, he began delivering lectures on "The Newly Discovered Electrical Fire." His experiments discovered the difference between the electricity that was produced by the glass and sulphur globes, which he communicated to Benjamin Franklin at Philadelphia, since they showed beyond a doubt that the positive and negative theory was correct. He also sought ways to protect buildings from lightning, invented an electric thermometer (c. 1755), and demonstrated that electricity can produce heat.*TIS

1756 Ernst Florens Friedrich Chladni (30 Nov 1756; 3 Apr 1827) German physicist, known as the "father of acoustics" for his mathematical investigations of sound waves. Chladni figures, seen when thin plates covered in sand at set in vibration, are complex patterns of vibration with nodal lines that remain stationary and retain sand. He demonstrated these to an audience of scientists in 1809. He measured the speed of sound in various gases by determining the pitch of the note of an organ pipe filled with different gases. To determine the speed of sound in solids, Chladni, used analysis of the nodal pattern in standing-wave vibrations in long rods. He performed on the euphonium, an instrument he invented, made of glass and steel bars vibrated by rubbing with a moistened finger. He also investigated meteorites.*TIS

1869 Nils Dalén (30 Nov 1869; 9 Dec 1837)Swedish engineer who won the Nobel Prize for Physics in 1912 for his invention of the automatic sun valve, or Solventil, which regulates a gaslight source by the action of sunlight, turning it off at dawn and on at dusk or at other periods of darkness. It rapidly came into worldwide use for buoys and unmanned lighthouses. While recovering from an accident, convalescing at home, he noticed how much time his wife spent caring for their wood-burning stove. He decided to invent a more efficient and cost-effective stove. In 1922, Dalen's Amalgamated Gas Accumulator Co. patented his design and put the first AGA stoves into production. These stoves produced a radiant heat that kept the kitchen warm. The AGA remains popular today.*TIS (My wife's favorite entry. Her first experience with an AGA was to turn materials for a pie into pure carbonized dust.)

1891 Edward Lindsay Ince (30 Nov 1891 in Amblecote, Staffordshire, England
- 16 March 1941 in Edinburgh, Scotland) Ince graduated from Edinburgh and researched at Edinburgh and Cambridge. He worked at universities in Leeds, Liverpool, Cairo, Edinburgh and Imperial College London before moving back to Edinburgh as Head of Technical Mathematics. He worked on Special Functions. *SAU

1910 Franz Leopold Alt (November 30, 1910 – July 21, 2011) was an Austrian-born American mathematician who made major contributions to computer science in its early days. He was best known as one of the founders of the Association for Computing Machinery, and served as its president from 1950 to 1952. *Wik

1936 Dmitri Victorovich Anosov (November 30, 1936 in Moscow, ) is a Soviet and Russian mathematician, known for his contributions to dynamical systems theory.
He is a full member of the Russian Academy of Sciences and a laureate of the USSR State Prize (1976). He was a student of Lev Pontryagin.*Wik

DEATHS
1603 William Gilbert (24 May 1544, 30 Nov 1603) English scientist, the "father of electrical studies" and a pioneer researcher into magnetism, who spent years investigating magnetic and electrical attractions. Gilbert coined the names of electric attraction, electric force, and magnetic pole. He became the most distinguished man of science in England during the reign of Queen Elizabeth I. Noting that a compass needle not only points north and south, but also dips downward, he thought the Earth acts like a bar magnet. Like Copernicus, he believed the Earth rotates on its axis, and that the fixed stars were not all at the same distance from the earth. Gilbert thought it was a form of magnetism that held planets in their orbits. *TIS

1647 (Francesco) Bonaventura Cavalieri (1598, 30 Nov 1647) Italian mathematician who made developments in geometry that were precursors to integral calculus. Cavalieri's theory of indivisibles, presented in his Geometria indivisibilis continuorum nova (1635) was a development of Archimedes' method of exhaustion incorporating Kepler's theory of infinitesimally small geometric quantities. The area and volume of various geometric figures can easily be found with this method. He was largely responsible for introducing logarithms as a computational tool in Italy through his book Directorium Generale Uranometricum, including logarithms of trigonometric functions for astronomers. He also wrote on optics and astronomy. Galileo thought highly of his writing, and corresponded with him. *TIS

1720 Pierre Jartoux (c1670; Embrun, France.- 30 Nov, 1720, Manchuria) known in China as Du Demei, Jartoux was a Jesuit Priest who went to live and work in China. His knowledge came to the attention of the Emperor and he was called to Peking (Beijing) to work in the calendar bureau. The emperor took notice of his skills in theoretical mathematics as well as with clocks and other mechanical devices. When not occupied at court, Jartoux ministered to Christians in the capital. In 1708 he assisted two Jesuit confreres, Joachim Bouvet and Jean-Baptiste Regis, in the first stages of making a map of the Chinese empire. His travels took him to the Great Wall north of the capital and throughout Manchuria, where he also ministered to the Christians. Illness forced him to return to Peking, where he began to collate the maps of the provinces in preparation for a general atlas. The final version was presented to the emperor one year after Jartoux died in Manchuria.
He is remembered here for his influence on the introduction of some Western mathematical ideas into the mathematical culture of China and Japan. In China his influence on shows in the 1759 work of Mei Juecheng, the Chishui yizhen (Pearls recovered from the Red River). This contained the infinite series expansion for sin(x) which was discovered by James Gregory and Isaac Newton. In fact it was Jartoux who introduced the infinite series for the sine into China in 1701 and it was known there by the name 'formula of Master Du'. In fact Pearls recovered from the Red River was one of two chapters that Mei Juecheng appended to the works of Mei Wending that he was editing and republishing. Mei Juecheng's study of the motion of the moon to provide improved predictions of eclipses of the moon used the best of European and Chinese astronomical data, and surpassed both cultures work.
In Japan, he was probably the source of the critical equation in the "yenri" (Circle Principle) presented by Takebe. His use of a "Wallis-like" infinite series was accompanied by a very unsatisfactory explanation of his development of the series. D. E. Smith and Mikami believe that he acquired the formula from Jartoux, who had passed on the same series (along with five others) to Mei Juecheng who added three to it in the above mentioned Chinese work. * SAU, Smith/Mikami "A History of Japanese Mathematics"

1761 John Dollond (10 Jun 1706, 30 Nov 1761) British maker of optical and astronomical instruments who developed (1758) and patented an achromatic (non- colour- distorting) refracting telescope and a practical heliometer, a telescope used to measure the Sun's diameter and the angles between celestial bodies. In the 1730's, Chester More Hall, an attorney with an interest in telescopes, first discovered that flint glass appeared to have a greater color dispersion than crown glass did at the same magnifications. Hall reasoned that if he cemented the concave face of a flint glass lens to the convex face of a crown glass lens, he could remove the dispersion properties (and thus, chromatic aberration) from both lenses simultaneously. Dollond learned of the technique in the 1750's and developed it.*TIS

1836 Pierre-Simon Girard (Caen, 4 November 1765 – Paris, 30 November 1836) was a French mathematician and engineer, who worked on fluids.
A prodigy who invented a water turbine at age 10, Girard worked as an engineer at the École Nationale des Ponts et Chaussées. He was in charge of planning and construction of the Amiens canal and the Ourcq canal. He collaborated with Gaspard de Prony on the Dictionnaire des Ponts et Chaussées (Dictionary of Bridges and Highways). He wrote works on fluids and on the strength of materials.*Wik

1850 Germain Henri Hess (7 Aug 1802, 30 Nov 1850) Swiss-born Russian chemist whose studies of heat in chemical reactions formed the foundation of thermochemistry. He formulated an empirical law, Hess's law of constant heat summation (1840), which states that the heat evolved or absorbed in a chemical process is the same whether the process takes place in one or in several steps. It is explained by thermodynamic theory, which holds that enthalpy is a state function. Chemists have made great use of the law of Hess in establishing the heats of formation of compounds which are not easily formed from their constituent elements. His early investigations concerned minerals and the natural gas found near Baku, and he also discovered the oxidation of sugars to yield saccharic acid.*TIS

1921 Hermann Amandus Schwarz (25 Jan 1843 in Hermsdorf, Silesia (now Poland)
- 30 Nov 1921 in Berlin, Germany) Schwarz worked on the conformal mapping of polyhedral surfaces onto the spherical surface and on a problem of the calculus of variation, namely surfaces of least area. In 1870 he produced work related to the Riemann mapping theorem. Although Riemann had given a proof of the theorem that any simply connected region of the plane can be mapped conformally onto a disc, his proof involved using the Dirichlet problem. Weierstrass had shown that Dirichlet's solution to this was not rigorous, see for details. Schwarz's gave a method to conformally map polygonal regions to the circle. Then, by approximating an arbitrary simply connected region by polygons he was able to give a rigorous proof of the Riemann mapping theorem. Schwarz also gave the alternating method for solving the Dirichlet problem which soon became a standard technique.
His most important work is a Festschrift for Weierstrass's 70th birthday. Schwarz answered the question of whether a given minimal surface really yields a minimal area. An idea from this work, in which he constructed a function using successive approximations, led Émile Picard to his existence proof for solutions of differential equations. It also contains the inequality for integrals now known as the 'Schwarz inequality', *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

Friday, 29 November 2019

On This Day in Math - November 29

I did try to make things clear, first to myself and then to my students,

and somehow to make these dry bones live.

~Horace Lamb

The 333rd day of the year; There are 333 possible hexagonal polyominoes with seven cells.

333 is a base ten palindrome, and also a palindrome in base 8, $ 515_8 \equiv 333_{10} $

If you add the smallest primes containing each of the digits 0 to 9, the sum is 333. 101 + 11 + 2 + 3 + 41 + 5 + 61 + 7 + 83 + 19=333

Of course you know that 3² + 4² = 5², but did you know that 333² + 444² = 555².... and the magic doesn't end there.

EVENTS

1114 An Earthquake devastated the town of Antioch in Turkey. In the suburb of Mamistra, the young mathematician, Adelard of Bath, freshly to the Middle East to study the wisdom of the Arabs, clung to a stone bridge in fear for his life. *Jonathan Lyons, The House of Wisdom: How the Arabs Transformed Western Civilization

1813 Iodine was discovered on this date. The discovery was made during the process of producing potassium nitrate for gunpowder and was made public in a meeting of the Imperial Institute of France. Its name is derived from the Greek 'iodes' meaning violet. *.rsc.org

1877 It was on this day, November 29, 1877, that Thomas Edison demonstrated his hand-cranked phonograph. *Thomas Robb

1907 Florence Nightingale was presented with the Order of Merit. *@EnglishHeritage (Thony Christie ‏@rmathematicus advised me that, "One is not presented with the Order of Merit one is appointed to it; it's a membership." )

In 1932, a U.S. patent was issued for the first card game table with an automatic dealing device, to Laurens Hammond of Chicago, Ill. (No. 1,889,729), who later invented the Hammond organ. When cards were played in a recessed tray, four shuffled 13-card bridge hands were delivered to the players. A rotary mechanism built within the square game table had an arm with a rubber tip to pick up and carry cards from the deck to the player. The destination hand was controlled by a serrated wheel with varied notch depths in 52 positions. A deal took about one minute. Marketed for a few years from 1932, the invention was an attempt to diversify Hammond's declining clock business during the depression-era, but sold poorly.*TIS

1960 Digital Equipment Company (DEC) announces the PDP-1, the ﬁrst computer with a video display terminal. *VFR

1972 Atari Corporation announces Pong, an early video game popular both at home and at video arcades. In Pong, players were represented by paddles that could move up and down to try to deflect a ball and keep it from passing into their goal. Despite simplistic graphics, Pong started a craze. Atari, founded by Nolan Bushnell, sold video games as well as computers on which to play the games. (Oh for the days of REAL video games!")*TIS

BIRTHS

1803 Christian Doppler (29 Nov 1803; 17 Mar 1853) Austrian physicist who first described how the observed frequency of light and sound waves is affected by the relative motion of the source and the detector, known as the Doppler effect. In 1845, to test his hypothesis, Doppler used two sets of trumpeters: one set stationary at a train station and one set moving on an open train car, all holding the same note. As the train passed the station, it was obvious that the frequency of the notes from the two groups didn't match. Sound waves would have a higher frequency if the source was moving toward the observer and a lower freqency if the source was moving away from the observer. Edwin Hubble used the Doppler effect of light from distant stars to determine that the universe is expanding.*TIS

1849 Sir John Ambrose Fleming (29 Nov 1849; 18 Apr 1945) English engineer who made numerous contributions to electronics, photometry, electric measurements, and wireless telegraphy. In 1904, he discovered the one directional current effect between a positively biassed electrode, which he called the anode, and the heated filament in an evacuated glass tube; the electrons flowed from filament to anode only. Fleming called the device a diode because it contained two electrodes, the anode and the heated filament. He noted that when an alternating current was applied, only the positive halves of the waves were passed - that is, the wave was rectified (from a.c. to d.c.). It would also take a radio frequency wave and produce d.c.corresponding to the on and off of the Morse code transmitted signals.*TIS

1847 Alfred George Greenhill (29 Nov 1847 in London, England - 10 Feb 1927 in London, england) graduated from Cambridge and became Professor of Mathematics at the Royal Military Academy at Woolwich. His main work was on Elliptic Functions but he published widely on applications of mathematics to practical problems. He became an honorary member of the EMS in 1908. *SAU

1849 Horace Lamb (29 Nov 1849 in Stockport, England - 4 Dec 1934 in Cambridge, England) wrote important texts and made important contributions to applied mathematics, in particular to acoustics and fluid dynamics. Describing his own teaching at the celebrations for his eightieth birthday, Lamb said, "I did try to make things clear, first to myself (an important point) and then to my students, and somehow to make these dry bones live." *SAU

1866 Ernest (William) Brown (29 Nov 1866; 22 July 1938) was a British astronomer who devoted his career to the theory of the Moon's motion and constructing accurate lunar tables. His theory took account of "the gravitational action of every particle of matter which can have a sensible effect on the Moon's motion," some 1500 terms. He then determined the numerical values of the constants by analyzing 150 years of Greenwich observations, and computed tables accurate to 0.01 arcsec. After 30 years of work, Brown published his lunar tables Tables of the Motion of the Moon in 1919. In 1926 Brown published a paper in which he ascribed fluctuations in the Moon's motion to irregular changes in the Earth's period of rotation, which has subsequently proved correct.*TIS

1879 Nikolai Mitrofanovich Krylov (29 Nov 1879 in St Petersburg, Russia - 11 May 1955 in Moscow, USSR) was a Russian mathematician who published over 200 papers on analysis and mathematical physics. *SAU

1892 Dr. Gustav Doetsch (November 29, 1892 – June 9, 1977) was a German mathematician, aviation researcher, decorated war veteran, and became a enthusiastic Nazi supporter. The modern formation and permanent structure of the Laplace transform is found in Doetsch's 1937 work Theorie und Anwendung der Laplace-Transformation, which was well-received internationally. He dedicated most of his research and scientific activity to the Laplace transform, and his books on the subject became standard texts throughout the world, translated into several languages. His texts were the first to apply the Laplace transform to engineering. *Wik

1952 John David Barrow FRS (29 November 1952 – 26 September 2020) is an English cosmologist, theoretical physicist, and mathematician. He is currently Research Professor of Mathematical Sciences at the University of Cambridge. Barrow is also a writer of popular science and an amateur playwright.
In 1981 he joined the University of Sussex and rose to the rank of Professor and Director of the Astronomy Centre. In 1999, he became Professor in the Department of Applied Mathematics and Theoretical Physics and a fellow in Clare Hall at Cambridge University. He is Director of the Millennium Mathematics Project. From 2003–2007 he was Gresham Professor of Astronomy at Gresham College, London, and he has been appointed as Gresham Professor of Geometry from 2008–2011; only one person has previously held two different Gresham chairs. In 2008, the Royal Society awarded him the Faraday Prize.

Barrow died on 27 September 2020 from colon cancer at the age of 67. *Wik

1959 Richard Ewen Borcherds (29 Nov 1959, ) British mathematician who won the Fields Medal in 1998 for his for his work in the fields of algebra and geometry, in particular for his proof of the so-called Moonshine conjecture. This conjecture had been formulated at the end of the '70s by the British mathematicians John Conway and Simon Norton and presents two mathematical structures in such an unexpected relationship that the experts gave it the name "Moonshine." In 1989, Borcherds was able to cast some more light on the mathematical background of this topic and to produce a proof for the conjecture. The Moonshine conjecture provides an interrelationship between the so-called "monster group" and elliptic functions. *TIS

DEATHS

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.)

1872 Mary Fairfax Greig Somerville (26 Dec 1780 in Jedburgh, Roxburghshire, Scotland
- 29 Nov 1872 in Naples, Italy) Somerville wrote many works which influenced Maxwell. Her discussion of a hypothetical planet perturbing Uranus led Adams to his investigation. Mary Somerville was a strong supporter of women's education and women's suffrage. When John Stuart Mill, the British philosopher and economist, organised a massive petition to parliament to give women the right to vote, he had Mary put her signature first on the petition.Somerville College in Oxford was named after her.*SAU

1920 Thomas Bond Sprague (29 March 1830 in London, England - 29 Nov 1920 in Edinburgh, Scotland) studied at Cambridge and went on to become the most important actuary of the late 19th Century. He wrote more than 100 papers including many in the Proceedings of the EMS. *SAU

1953 Ernest Barnes (1 April 1874 in Birmingham, England - 29 Nov 1953 in Sussex, England) In all, Barnes wrote 29 mathematical papers during the years 1897-1910. His early work was concerned with various aspects of the gamma function, including generalisations of this function given by the so-called Barnes G-function, which satisfies the equation G(z+1)=G(z)Γ(z) and to the double gamma function. Barnes next turned his attention to the theory of integral functions, where, in a series of papers, he investigated their asymptotic structure. He also considered second-order linear difference equations connected with the hypergeometric functions. In the last five of his papers dealing with the hypergeometric functions, Barnes made extensive use of the integrals studied by Mellin in which the integral. *SAU

1992 Jean Dieudonné (1 Jul 1906, 29 Nov 1992) French mathematician and educator known for his writings on abstract algebra, functional analysis, topology, and his theory of Lie groups. Dieudonné was one of the two main contributors to the Bourbaki series of texts. He began his mathematical career working on the analysis of polynomials. He worked in a wide variety of mathematical areas including general topology, topological vector spaces, algebraic geometry, invariant theory and the classical groups. *TIS

*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

Thursday, 28 November 2019

On This Day in Math - November 28

Newton is, of course, the greatest of all Cambridge professors; he also happens to be the greatest disaster that ever befell not merely Cambridge mathematics in particular, but British mathematical science as a whole.
~Leonard Roth
(This quote probably needs a brief explanation for young readers. The conflict between Newton and Leibniz over the discovery of Calculus isolated England from the more rapidly developing function notations used in Europe. It would not be until the mid 19th century that young British Intellectuals would press to adopt the continental ideas.)

The 332nd day of the year; 332 is the number of ways to partition 47 into non-zero triangular numbers. (36 + 10 + 1 would be one such way)

The sum of the first 332 primes is a prime.

As numbers get larger and larger, it would seem that there would be fewer and fewer primes in each century of them, such as from 100 to 199. But there seem to be a large number of centuries with only six primes. There are only five year days such that between 100*n and 100*n+99 there are exactly six primes. 332 is one of them. (there are exactly six primes between 33200 and 33299)

EVENTS
In 2348 BC, a supposed comet under divine guidance passed near Earth, causing the Great Flood, in the opinion of Anglican priest and mathematician, William Whiston. In his time, the water composition of comets was known. He said the forty days of rain resulted from the Earth's travel through the comet's tail. The body's gravity stretched and cracked the earth's brittle crust, and waters arose from the "fountains of the great deep." He explained this in his popular treatise New Theory of the Earth (1696), describing the Book of Genesis in terms of physics based on the Principia written by his mentor, Isaac Newton. Whiston succeeded Newton and became the third Lucasian Professor of Mathematics at Cambridge University (May 1702)*TIS

1660 After attending a lecture by Christopher Wren, a group gathered to discuss the founding of “a college for the promoting of physico-mathematical experimental learning.” The result was to become the Royal Society of London. *VFR The Society subsequently petitioned King Charles II to recognise it and to make a royal grant of incorporation. The Royal Charter, which was passed by the Great Seal on 15 Jul 1662, created the Royal Society of London.*TIS
Memorandum November 28 1660: "These persons following according to the usual custom of most of them, met together at Gresham College to hear Mr Wren's lecture, viz. The Lord Brouncker, Mr Boyle, Mr Bruce, Sir Robert Moray, Sir Paule Neile, Dr Wilkins, Dr Goddard, Dr Petty, Mr Ball, Mr Rooke, Mr Wren, Mr Hill. And after the lecture was ended they did according to the usual manner, withdraw for mutual converse."

1679 Newton writes the Royal Society to suggest that if falling objects were studied, they would find a consistent deviation east due to the rotation of the earth.*VFR (Hook will later experiment and observe motion both to the west and the south. (see 6 Jan, 1680))

1772 At the Board meeting of 28 November 1772 Nevil Maskelyne, Astronomer Royal, presented the other astronomer's suggestions 'for improving (Tobias) Mayer's (Lunar) Tables by lessening the Errors in the method of calculation which he had perfected under the encouragement of the Board ; and at the same time reported that he has reduced the Errors of those Tables to about one half'.
Maskelyne is often viewed as an opponent of computing longitude by clock, but as early as 1765 he was quoted as saying, "the calculations would be always somewhat conciser in the method by the watch than in that by the Moon" *Board of Longitude project, Royal Museums Greenwich

1889 The Gilbert Club was officially formed on 28 November 1889. Advertised by a specially printed circular sent to select scientists, engineers, and other enthusiasts, the proposed association was also mentioned in the Times and in the leading British and American scientific weeklies, Nature and Science. By the time of the inaugural meeting, eighty-seven members had already signed up, many of whom were gathered in the chambers of the Society of Arts that afternoon to hear Silvanus Phillips Thompson describe the eminence and importance of William Gilbert of Colchester (1544-1603), the doctor whose early experimental investigations "constituted the absolute starting-point of the science of electricity."
The Gilbert Club counted among its first members numerous Fellows of the Royal Society and other prominent scientists in all fields, including Lord Rayleigh, John Tyndall, John Lubbock, Oliver Lodge, and the Presidents of the Physical Society and the Royal College of Surgeons. Leading these luminaries at the inaugural meeting was the most famous living British physicist and current President of the Institution of Electrical Engineers, Sir William Thomson (later Lord Kelvin). *Canadian Journal of History, 2003

1895 The day (I suspect) that the term "Octonions" was introduced into mathematical vocabulary. On this day a paper from Alex McAuley of the Univ of Tasmania was read to the Royal Society of London by Rev N. M. Ferrers with the title Octonions. The first sentence says, "Octonions is a name adapted for various reasons in place of Clifford's Bi-quaternions." Hamilton had already used the latter term in an altogether different sense. *Proceedings of the Royal Society of London, Volume 59

1936 This is the earliest exact date I can find where L. R. Ford presented information about his ideas on Ford Circles. He presented his idea at a meeting of the American Mathematical Society at Lawrence Kansas. (If someone knows dates of presentations at Rice, Univ of Texas, etc I would love to have those dates and any information on which parts were presented). *Am Mathematical Monthly, 1938.

In 1967, the first pulsating radio source (pulsar) was detected by an alert graduate student, Jocelyn Bell (see 15 July, 1943), then working under the direction of Prof. A. Hewish at the Mullard Radio Astronomy Observatory, Cambridge, England. They were using a special radio telescope, a large array of 2,048 aerials covering an area of 4.4 acres. The discovery of these fascinating objects opened new horizons in studies as diverse as quantum-degenerate fluids, relativistic gravity and interstellar magnetic fields. Under extraordinary physical conditions, radiation is generated and appears pulsed with a clock-like precision synchronously with the pulsar rotational period. These periods range from 1.57 milliseconds to 5.1 sec. *TIS

BIRTHS
1700 Nathaniel Bliss (28 Nov 1700; 2 Sep 1764) Britain's fourth Astronomer Royal, though only for the two years before his death. In 1736, Bliss became rector of St Ebbe's Oxford, and in 1742, he followed Halley as Savilian Professor of Geometry. Bliss occasionally assisted James Bradley, third A.R. In 1761, he made observations of the transit of Venus when Bradley was unable to do so due to poor health. Bliss succeeded Bradley in 1762. On 1 Apr 1764 Bliss published his observations of the annular eclipse visible from Greenwich. Besides his Observatory work, Bliss also worked for and with the Earl of Macclesfield, on astronomical problems. This work included making meridian observations of a comet approaching the Sun around 1744 at Shirburn Castle and at Greenwich.*TIS

1772 Luke Howard, FRS (28 November 1772 – 21 March 1864) was a British manufacturing chemist and an amateur meteorologist with broad interests in science. His lasting contribution to science is a nomenclature system for clouds, which he proposed in an 1802 presentation to the Askesian Society.
He has been called "the father of meteorology" because of his comprehensive recordings of weather in the London area from 1801 to 1841 and his writings, which transformed the science of meteorology. *Wik

1898 John Wishart FRSE (28 November 1898 – 14 July 1956) was a Scottish mathematician and agricultural statistician.
He worked successively at University College London with Karl Pearson, at Rothamsted Experimental Station with Ronald Fisher, and then as a reader in statistics in the University of Cambridge where he became the first Director of the Statistical Laboratory in 1953. He was elected a Fellow of the Royal Society of Edinburgh in 1931, and edited Biometrika from 1937. The Wishart distribution is named after him.
Wishart died at age 57 in a bathing accident in Acapulco while representing the Food and Agriculture Organization on a mission to set up a research centre.*Wik

1905 Albert William Tucker (28 November 1905 – 25 January 1995) was a Canadian-born American mathematician who made important contributions in topology, game theory, and non-linear programming.In the 1960s, he was heavily involved in mathematics education, as chair of the AP Calculus committee for the College Board (1960–1963), through work with the Committee on the Undergraduate Program in Mathematics (CUPM) of the MAA (he was president of the MAA in 1961–1962), and through many NSF summer workshops for high school and college teachers.
In the early 1980s, Tucker recruited Princeton history professor Charles Gillispie to help him set up an oral history project to preserve stories about the Princeton mathematical community in the 1930s. With funding from the Sloan Foundation, this project later expanded its scope. Among those who shared their memories of such figures as Einstein, von Neumann, and Gödel were computer pioneer Herman Goldstine and Nobel laureates John Bardeen and Eugene Wigner.
Albert Tucker noticed the leadership ability and talent of a young mathematics graduate student named John G. Kemeny, whose hiring Tucker suggested to Dartmouth College. Following Tucker's advice, Dartmouth recruited Kemeny, who became Chair of the Mathematics Department and later College President. Years later, Darthmouth College recognized Albert Tucker with an honorary degree. Tucker died in Highstown, N.J. in 1995 at age 89. *Wik

1950 Russell Alan Hulse (28 Nov 1950, )American physicist who in 1993 shared the Nobel Prize for Physics with his former teacher, the astrophysicist Joseph H. Taylor, Jr., for their joint discovery of the first binary pulsar (1974). This is an astronomical system of two celestial bodies so close they are separated by only several times the distance between the moon and the earth. Their findings, first reported in 1978, constitute the first indirect proof of the existence of the gravitational waves predicted by Albert Einstein in his theory of relativity. *TIS

DEATHS 1821 Samuel Vince (6 April 1749; Fressingfield – 28 November, 1821; Ramsgate) was an English clergyman, mathematician and astronomer at the University of Cambridge.
The son of a plasterer, Vince was admitted as a sizar to Caius College, Cambridge in 1771. In 1775 he was Senior Wrangler, and Winner of the Smith Prize at Cambridge. Migrating to Sidney Sussex College in 1777, he gained his M.A. in 1778 and was ordained a clergyman in 1779.
He was awarded the Copley Medal in 1780 and was Plumian Professor of Astronomy and Experimental Philosophy at Cambridge from 1796 until his death.
As a mathematician, Vince wrote on many aspects of his expertise, including logarithms and imaginary numbers. His Observations on the Theory of the Motion and Resistance of Fluids and Experiments upon the Resistance of Bodies Moving in Fluids had later importance to aviation history. He was also author of the influential A Complete System of Astronomy (3 vols. 1797-1808).
Vince also published the pamphlet The Credibility of Christianity Vindicated, In Answer to Mr. Hume's Objections; In Two Discourses Preached Before the University of Cambridge by the Rev. S. Vince. In this work, Vince made an apology of the Christian religion and, like Charles Babbage, sought to present rational arguments in favor of the belief in miracles, against David Hume's criticism. *Wik

1914 Johann Wilhelm Hittorf (27 Mar 1824, 28 Nov 1914) German physicist who was a pioneer in electrochemical research. His early investigations were on the allotropes (different physical forms) of phosphorus and selenium. He was the first to compute the electricity- carrying capacity of charged atoms and molecules (ions), an important factor in understanding electrochemical reactions. He investigated the migration of ions during electrolysis (1853-59), developed expressions for and measured transport numbers. In 1869, he published his laws governing the migration of ions. For his studies of electrical phenomena in rarefied gases, the Hittorf tube has been named for him. Hittorf determined a number of properties of cathode rays, including (before Crookes) the deflection of the rays by a magnet. *TIS

1943 Eduard Helly (1 June 1884 in Vienna, Austria - 28 Nov 1943 in Chicago, Illinois, USA) Helly worked on functional analysis and proved the Hahn-Banach theorem in 1912 fifteen years before Hahn published essentially the same proof and 20 years before Banach gave his new setting. *SAU

1952 Fritz Carlson (23 July 1888 in Vimmerby, Sweden - 28 Nov 1952 in Stockholm, Sweden) His main work focused on the theory of analytic functions. Some of his most well-known contributions are a theorem connected to the Phragmén-Lindelöf principle, a theorem about the zeros of the V-function and several theorems about power series with integer coefficients. Such names as Carlson inequality, Carlson - Levin constants, Carlson theorem in complex analysis, Pólya - Carlson theorem on rational functions and Carlson theorem on Dirichlet series are well-known in mathematics. *SAU

1954 Enrico Fermi (29 Sep 1901, 28 Nov 1954) Italian-born American physicist who was awarded the Nobel Prize for physics in 1938 as one of the chief architects of the nuclear age. He was the last of the double-threat physicists: a genius at creating both esoteric theories and elegant experiments. In 1933, he developed the theory of beta decay, postulating that the newly-discovered neutron decaying to a proton emits an electron and a particle he called a neutrino. Developing theory to explain this decay later resulted in finding the weak interaction force. He developed the mathematical statistics required to clarify a large class of subatomic phenomena, discovered neutron-induced radioactivity, and directed the first controlled chain reaction involving nuclear fission. *TIS Emilio Segre tells this story in his biography of Fermi: "Fermi told me that one of his great intellectual efforts was his attempt to understand - at the age of ten- what was meant by the statement that the equation x² + y² = z² represents a circle. Someone must have stated the fact to him, but he had to discover the meaning by himself."
Fermi, while working in Los Alamos once calculated very high odds that the Earth should have been visited by aliens repeatedly over history. He sometimes would call out, "Where are they?"
Once, it was said, Fermi uttered his famous question in the presence of Lio Szilard, who responded, "They are among us, but they call themselves Hungarians." *P Ballew "Where are They?".... We are here!

1954 Herbert Bright, developer of one of the first FORTRAN user programs (and consequently, the first error message), dies at 67. Bright had been a promoter of security through data encryption, as well as a research engineer at AT&T Laboratories. He also held various executive offices in the Association for Computing Machinery (ACM).*CHM

1968 Jean Frédéric Auguste Delsarte (October 19, 1903, Fourmies – November 28, 1968, Nancy) was a French mathematician known for his work in mathematical analysis, in particular, for introducing mean-periodic functions and generalized shift operators. He was one of the founders of the Bourbaki group.*Wik

1968 Leonard Roth (29 August 1904 Edmonton, London, England – 28 November 1968 Pittsburgh, Pennsylvania) was a mathematician working in the Italian school of algebraic geometry. He introduced an example of a unirational variety that was not rational (though his proof that it was not rational was incomplete).*Wik

1969 Elbert Frank Cox (December 5, 1895–November 28, 1969) was an American mathematician who became the first black person in the world to receive a Ph.D. in mathematics. He spent most of his life as a professor at Howard University in Washington, D.C., where he was known as an excellent teacher. During his life, he overcame various difficulties which arose because of his race. In his honor, the National Association of Mathematicians established the Cox-Talbot Address, which is annually delivered at the NAM's national meetings. The Elbert F. Cox Scholarship Fund, which is used to help black students pursue studies, is named in his honor as well.*Wik

Wednesday, 27 November 2019

I'm sure I'm not that clever so ??????

I recently came across this problem in the first Irish Mathematics Olympiad. I thought I figured it out mentally, but then realized, if it is an olympiad problem, it is probably not that transparent. Soo....... I'm posting it and going to think more deeply about my attempt, and the solution, but encourage you to comment with your solution, and I will make sure all of them are added to the post. And the question is.... Drum Roll Please:

5. A person has seven friends and invites a different subset of three friends to dinner every night for
one week (seven days). In how many ways can this be done so that all friends are invited at least
once?

Your answer goes here........

On This Day in Math - November 26

One of the chief duties of a mathematician in acting as an advisor to scientists is to discourage them from expecting too much of mathematicians.
~Norbert Wiener

The 330th day of the year; if all the diagonals of an eleven sided regular polygon were drawn, they would have 330 internal intersections.

330 is the last year day which is a pentagonal number. It is the sum of fifteen consecutive integers starting with the integer 15. (All Pentagonal numbers follow a similar pattern) The average of all the pentagonal numbers up to 330 is the 15th triangular number.

A set of 11 points around a circle provide the vertices for 330 quadrilaterals.

330 is the sum of five consecutive squares, or of six consecutive primes.

EVENTS
1607 John Harvard, founder of Harvard College, born in London. Harvard, the oldest university in the U.S., was named for him in 1639. *VFR (The college was actually founded almost two years before Harvard made his deathbed bequest to fund it. The grateful colony changed the name of the college to honor its benefactor.)

1750 Euler presents his famous “Gem”; Vertices + Faces -2 = Edges, in two papers Euler presented several results relating the number of plane angles of a solid to the number of faces, edges, and vertices (he referred to “solid angles”). Euler also classified polyhedra by the number of solid angles they had. According to C. G. J. Jacobi, a treatise with this title was read to the Berlin Academy on November 26, 1750. The proofs were contained in a second paper. According to C. G. J. Jacobi, it might have been read to the Berlin Academy on September 9, 1751. According to the records there, it was presented to the St. Petersburg Academy on April 6, 1752. (There seems to be some question as to whether or not this theorem appears in Descartes. There is no question, it seems that he made statements that directly lead to the theorem, but Polya, Lakatos, and many others don't find an actual statement of the theorem in his work. I leave this question to the knowledgeable historians of the period to work out the intricacies .)

1789 President George Washington proclaimed Thanksgiving day the ﬁrst national holiday, acknowledging the nation’s “many and signal favors of Almighty God.” *VFR Washington declared the holiday in an Oct 3 declaration. Other Presidents throughout the years up to the civil war declared days of thanksgiving, not always in the fall. By 1858 proclamations appointing a day of thanksgiving were issued by the governors of 25 states and two territories. President Abraham Lincoln, prompted by a series of editorials written by Sarah Josepha Hale(she is known also as the author of "Mary Had a Little Lamb"), proclaimed a national Thanksgiving Day, to be celebrated on the final Thursday in November 1863. *Wik

1857 An amendment to the Sadlerian Chair to allow teaching of other modern topics beyond Algebra led to an application the same day for the position form Arthur Cayley. His Quickly published resume for the job included 318 of his publications. *A. J. Crilly, Arthur Cayley: Mathematician Laureate of the Victorian Age

1864 Charles Dodgson gives Alice Liddell (rhymes with “ﬁddle”) a hand-printed copy of Alice’s Adventures under Ground, a work he wrote for her. This was reproduced by Dover in 1965. See 4 July 1862. *VFR

In 1885, the first meteor trail was photographed in Prague, Czechoslovakia. This was part of the Andromedid meteor shower also known as the Bielids because they were caused by Comet Biela. William F. Denning (Bristol, England) noted the activity with rates averaging 100 per hour. On the next evening, 27 Nov, he declared "meteors were falling so thickly as the night advanced that it became almost impossible to enumerate them." Observers with especially clear skies had rates of about one meteor/second or 3600/hour. Meteor showers are produced by small fragments of cosmic debris entering the earth's atmosphere at extremely high speed. The debris originates from the intersection between a planet's orbit and a comet's orbit. *TIS If someone can supply a digital copy of this first photo, I would be greatly pleased.

1885 Smith Prize winners under new regulations announced in Nature Magazine. A. N. Whitehead gets only honorable mention in the new essay-based Smith's Prize.
And the winners are...."awarded to two essays declared equal in merit, viz. that of Mr. H. E. G. Gallop, Fellow of Trinity College, Second Wrangler in 1883, 1st Division in Part III., 1884, subject, “The Distribution of Electricity on the Circular Disk and Spherical Bowl”; and that of Mr. R. Lachlan, Fellow of Trinity College, 3rd Wrangler, 1883, 1st Division in Part III., 1884, subject “Systems of Circles.” It is further announced that the essay by Mr. C. Chree, Fellow of King’s College, on “Elastic Solids,” and that of Mr. A. N. Whitehead, Fellow of Trinity College, on the “General Equations of Hydrodynamics,” deserved honourable mention." *nature.com

BIRTHS
1894 Norbert Wiener (26 Nov 1894; 18 Mar 1964) U.S. mathematician, who established the science of cybernetics, a term he coined, which is concerned with the common factors of control and communication in living organisms, automatic machines, and organizations. He attained international renown by formulating some of the most important contributions to mathematics in the 20th century. His work on generalised harmonic analysis and Tauberian theorems won the Bôcher Prize in 1933 when he received the prize from the American Mathematical Society for his memoir Tauberian theorems published in Annals of Mathematics in the previous year. His extraordinarily wide range of interests included stochastic processes, quantum theory and during WW II he worked on gunfire control. *TIS Cybernetics, published in 1948, was a major influence on later research into artificial intelligence. In the book, Wiener drew on World War II experiments with anti-aircraft systems that anticipated the course of enemy planes by interpreting radar images. Wiener also did extensive analysis of brain waves and explored the similarities between the human brain and a modern computing machine capable of memory association, choice, and decision making.*CHM (Wiener is somewhat revered as the ultimate absent-minded professor. An anecdote, almost certainly exaggerated, I used to share with my classes went something like this: Wiener had moved to a new address, and his wife knowing of his forgetfulness wrote a note with his new address and put it in his coat pocket. During the day struck by a mathematical muse he whipped out the piece of paper and scribbled notes on the back, then realizing his idea had been wrong, he tossed the piece of paper away and went about his day. In the afternoon he returned to his old house out of habit and coming up to the empty house remembered that he had moved, but not where. As he started to leave a young girl walked up and he stopped here. "Young lady, I am the famous mathematician Wiener. Do you know where I live?" The lass replied, "Yes, father, I'll show you the way home."... )

1895 Bertil Lindblad (26 Nov 1895; 26 Jun 1965) Swedish astronomer who contributed greatly to the theory of galactic structure and motion and to the methods of determining the absolute magnitude (true brightness, disregarding distance) of distant stars. He theorized that the areas around the center of a galaxy revolve and this is why it was flattened. Oort later proved that does indeed happen. He studied the structure and dynamics of star clusters, estimated the Milky Way's galactic mass, the period of our Sun's orbit, confirmed Harlow Shapley's direction and approximate distance to the center of the Galaxy, and developed spectroscopic means of distinguishing between giant and main sequence stars.*TIS

1940 Enrico Bombieri (26 Nov 1940, )Italian mathematician who was awarded the Fields Medal in 1974 for his major contributions to the study of the prime numbers, to the study of univalent functions and the local Bieberbach conjecture, to the theory of functions of several complex variables, and to the theory of partial differential equations and minimal surfaces. "Bombieri's mean value theorem", which concerns the distribution of primes in arithmetic progressions which is obtained by an application of the methods of the large sieve. Between 1979 and 1982 Bombieri served on the executive committee of the International Mathematical Union. Bombieri now works in the United States. In 1996 Bombieri was elected to membership of the National Academy of Sciences.*TIS

DEATHS
1896 Benjamin Apthorp Gould (27 Sep 1824, 26 Nov 1896) American astronomer whose star catalogs helped fix the list of constellations of the Southern Hemisphere Gould's early work was done in Germany, observating the motion of comets and asteroids. In 1861 undertook the enormous task of preparing for publication the records of astronomical observations made at the US Naval Observatory since 1850. But Gould's greatest work was his mapping of the stars of the southern skies, begun in 1870. The four-year endeavor involved the use of the recently developed photometric method, and upon the publication of its results in 1879 it was received as a signicant contribution to science. He was highly active in securing the establishment of the National Academy of Sciences. *TIS

1965 Zoárd Geöcze (1873–1916) was a Hungarian mathematician famous for his theory of surfaces (Horváth 2005:219ff). He was born August 23, 1873 in Budapest, Hungary and died November 26, 1916 in Budapest. *Wik

1968 Georgii Nikolaevich Polozii (23 April 1914 in Transbaikal, Russia - 26 Nov 1968 in Kiev, Ukraine) Georgii Polozii studied at Saratov University which had been founded in 1919. He graduated in 1937 and then was appointed to the teaching staff of the university. In 1949 Polozii was appointed to the University of Kiev and he remained at Kiev until his death in 1968.
Polozii's major pure mathematical contributions were to the theory of functions of a complex variable, approximation theory, and numerical analysis. He also made major contributions to mathematical physics and applied mathematics in particular working on the theory of elasticity. *SAU

1977 Ruth Moufang (10 Jan 1905 in Darmstadt, Germany - 26 Nov 1977 in Frankfurt, Germany) Moufang studied projective planes, introducing Moufang planes and non-associative systems called Moufang loops. *SAU

1981 Machgielis Euwe (20 May 1901 in Watergraafsmeer, near Amsterdam, Netherlands
- 26 Nov 1981 in Amsterdam, Holland) Machgielis Euwe is better known by the name Max Euwe, and he is better known as the world chess champion from 1935 to 1937 than as a mathematician. However, Euwe was indeed a very fine mathematician who concentrated more on his mathematics throughout his life than on his chess. In 1929 he published a mathematics paper in which he constructed an infinite sequence of 0's and 1's with no three identical consecutive subsequences of any length. He then used this to show that, under the rules of chess that then were in force, an infinite game of chess was possible. It had always been the intention of the rules that this should not be possible, but the rule that a game is a draw if the same sequence of moves occurs three times in succession was not, as Euwe showed, sufficient. *SAU

1990 Richard Alan Day (9 Oct 1941 in Sault Ste Marie, Ontario, Canada - 26 Nov 1990 in Thunder Bay, Ontario, Canada) He spent his whole career at Lakeland University in Thunder Bay, being promoted to Associate Professor in 1975 and to full professor five years later.
Day made many major contributions to lattice theory. One of the first was in the paper A simple solution to the word problem for lattices (1970) where he gave a simple solution to the word problem in free lattices. This paper introduced Day famous doubling construction. *SAU

2015 Amir D. Aczel (November 6, 1950 – November 26, 2015) was an Israeli-born American lecturer in mathematics and the history of mathematics and science, and an author of popular books on mathematics and science.
Aczel was born in Haifa, Israel. Aczel's father was the captain of a passenger ship that sailed primarily in the Mediterranean Sea. When he was ten, Aczel's father taught his son how to steer a ship and navigate. This inspired Aczel's book The Riddle of the Compass.
When Aczel was 21 he studied at the University of California, Berkeley. He graduated with a BA in mathematics in 1975, and received a Master of Science in 1976. Several years later Aczel earned a Ph.D. in statistics from the University of Oregon.
Aczel taught mathematics at universities in California, Alaska, Massachusetts, Italy, and Greece. He married his wife Debra in 1984 and has one daughter, Miriam, and one stepdaughter. He accepted a professorship at Bentley College in Massachusetts where he taught classes on the history of science and the history of mathematics. While teaching at Bentley, Aczel wrote several non-technical books on mathematics and science, as well as two textbooks. His book, Fermat's Last Theorem (ISBN 978-1-56858-077-7), was a United States bestseller and was nominated for a Los Angeles Times Book Prize. Aczel appeared on CNN, CNBC, The History Channel, and Nightline. Aczel was a 2004 Fellow of the John Simon Guggenheim Memorial Foundation and Visiting Scholar in the History of Science at Harvard University (2007). In 2003 he became a research fellow at the Boston University Center for Philosophy and History of Science, and in Fall 2011 was teaching mathematics courses at University of Massachusetts Boston.
He died of cancer on Nov. 26, 2015 in Nîmes, in the south of France. He was 65. *Wik, *Obit
His most recent book was Finding Zero: A Mathematician's Odyssey to Uncover the Origins of Numbers

On This Day in Math - November 27

Mathematics education is much more complicated than you expected, even though you expected it to be more complicated than you expected.
~ Edward Griffith Begle

The 331st day of the year; 31, 331, 3331, 33331 are all prime. What percentage of the numbers 33....331 are prime? Is there a pattern? A nice symmetric pic from Jim Wilder@wilderlab:

331 is also the sum of five consecutive primes. It is both a centered Pentagonal number and a centered Hexagonal number.

EVENTS
1727 Isaac Greenwood began his “private” lectures as Hollis Professor of Mathematics and Natural Philosophy at Harvard. These lectures were given to selected students and required parental permission, probably to insure payment of the attendance fee of forty shillings. [I. B. Cohen, Some Early Tools of American Science, p. 35]. *VFR

1783 John Michell made the first proposal of what would come to be called black holes, which he called "dark stars" in a paper read on this day in the Philosophical Transactions of the Royal Society of London. During the chaotic wars over President Banks in January of 1784, the only papers interrupting the partisan bickering was the continuation of the reading of Mtchell's paper. *Wik , *Cavendish by Christa Jungnickel, Russell McCormmac

In 1826, John Walker (1781-1859), an English pharmacist from Stockton-on-Tees, invented the first practical, strike-anywhere, friction match, but refused to patent his creation. He used three-inch splints of wood, tipped with potassium chlorate, antimony sulphide, and gum arabic. The match head was ignited by drawing it through a fold of fine glasspaper. By 1829, similar matches called "Lucifers" were sold throughout London. Their difference was added sulphur to aid combustion, and white phosphorus. Matchmaking workers quickly developed a bone disease called "phossy jaw" from the phosphorus. Phosphorus sesquisulphide replaced the deadly white phosphorus in the strike-anywhere match during the early twentieth century.*TIS

1839 "On November 27, 1839, five men held a meeting in the rooms of the American Education Society at No. 15 Cornhill in Boston, Massachusetts, to organize a statistical society. Its purpose, as stated in the society's first constitution, was to "collect, preserve, and diffuse statistical information in the different departments of human knowledge." Originally called the American Statistical Society, the organization's name was changed to the American Statistical Association (ASA) at its first annual meeting, held in Boston on February 5, 1840. " *Robert L. Mason, ASA: The First 160 Years
The five men were "William Cogswell, teacher, fund-raiser for the ministry, and genealogist; Richard Fletcher, lawyer and U.S. Congressman; John Dix Fisher, physician and pioneer in medical reform; Oliver Peabody, lawyer, clergyman, poet, and editor; and Lemuel Shattuck, statistician, genealogist, publisher, and author of perhaps the most significant single document in the history of public health to that date. " *ASA

1875 Johns Hopkins University offered J. J. Sylvester 5000 dollars a year plus moving expenses to assume the mathematics professorship. He set three conditions under which he would accept: The sum be paid in gold, the university provide a residence, and that he be allowed to appropriate student fees. Only the ﬁrst was acceptable to the university, but Sylvester agreed when the offer was increased to 6000 in gold. Shortly after arriving he founded the American Journal of Mathematics. In 1883 he left to become Savilian professor of geometry at Oxford. *VFR

In 1895, Alfred Nobel had his will drawn up in Paris, then deposited in a bank in Stockholm. In it, he provided for most of his fortune to be put in trust to establish the Nobel Prizes. As the inventor of new, more powerful explosives used in the weapons of war, he left a legacy to reward those persons who provided benefits to mankind. Prizes were to be established in the fields of physics, chemistry, physiology, literature and a prize for peace. He died a year later, 10 Dec 1896, of a cerebral hemorrhage at his villa in San Remo, Italy, leaving this surprise at the opening of his will. *TIS

1979 The New York Times in an article entitled “Soviet mathematician is obscure no more,” reported on Leonid Khachiyan, the 27-year-old discoverer of a polynomial-time algorithm for linear programming. *Mathematics Magazine 53 (1980), p 119.

1984 Binion’s Horseshoe Casino announced that a Texan, known only as “Tom,” lost 1 million dollars on a single roll of the dice and “acted like it was nothing.” He won 770,000 on a single roll in 1980 and 538,000 earlier this year, so he is still ahead. Is this a good way to gamble? [AP Press Release] *VFR

1995 Microsoft Corp. shipped its Internet Explorer 2.0, starting a browser war with the popular Netscape Navigator. Netscape Communications Corp. had had a virtual monopoly on World Wide Web browsers since the infancy of the web. The Netscape Navigator and Communicator browsers serve as a format for viewing and creating World Wide Web pages, as well as participating in newsgroups and sending e-mail. Microsoft promotes its Internet Explorer with specific mention of its privacy and encryption.*CHM

In 2001, sodium was detected in the atmosphere of an extrasolar planet by the Hubble Space Telescope. The planetary atmosphere of HD 209458b was the first outside our solar system to be measured. The planet, informally known as Osiris, was the first transiting planet discovered (5 Nov 1999). It orbits the sun-like star designated HD 209458. Later measurements with the Hubble Space Telescope Imaging Spectrograph (2003-4), found an enormous ellipsoidal envelope of hydrogen, carbon and oxygen around the planet with a temperature that reaches 10,000°C, resulting in a significant "tail" of atoms moving at speeds greater than the escape velocity.*TIS

BIRTHS
1701 Birthdate of the Swedish astronomer Anders Celsius (27 November 1701 – 25 April 1744). In 1742 he popularized a thermometer with a 100-degree scale. As ﬁxed points he chose the freezing and boiling points of water, calling them 100 and 0 respectively. In 1747 the present system with the scale reversed was introduced. Around 1800 people started calling this the Celsius Thermometer. *VFR Celsius was born in Uppsala where he succeeded his father as professor of astronomy in 1730. It was there also that he built Sweden's first observatory in 1741. He and his assistant Olof Hiortner discovered that aurora borealis influence compass needles.*TIS

1848 Henry Augustus Rowland (27 Nov 1848; 16 Apr 1901)American physicist who invented the concave diffraction grating, which replaced prisms and plane gratings in many applications, and revolutionized spectrum analysis--the resolution of a beam of light into components that differ in wavelength. His first major research was an investigation of the magnetic permeability of iron, steel and nickel, work which won the praise of Maxwell. Another experiment was the first to conclusively demonstrate that the motion of charged bodies produced magnetic effects. In the late 1870s, he established an authoritative figure for the absolute value of the ohm, and redetermined the mechanical equivalent of heat in the early 1880s, demonstrating that the specific heat of water varied with temperature. *TIS

1849 Sir Horace Lamb (27 Nov 1849; 4 Dec 1934) English mathematician who contributed to the field of mathematical physics. Topics he worked on include wave propagation, electrical induction, earthquakes, and the theory of tides. He wrote important papers on the oscillations of a viscous spheroid, the vibrations of elastic spheres, waves in elastic solids, electric waves and the absorption of light. In a famous paper in the Proceedings of the London Mathematical Society he showed how Rayleigh's results on the vibrations of thin plates fitted with the general equations of the theory. Another paper reported on his study of the propagation of waves on the surface of an elastic solid where he tried to understand the way that earthquake tremors are transmitted around the surface of the Earth. *TIS

1867 Arthur Lee Dixon FRS (27 November 1867 — 20 February 1955) was a British mathematician and holder of the Waynflete Professorship of Pure Mathematics at the University of Oxford. The younger brother of Alfred Cardew Dixon, he was educated at Kingswood School and Worcester College, Oxford, becoming a Tutorial Fellow at Merton College in 1898 and the Waynflete Professor in 1922. Dixon was the last mathematical professor at Oxford to hold a life tenure, and although he was not particularly noted for his mathematical innovations he did publish many papers on analytic number theory and the application of algebra to geometry, elliptic functions and hyperelliptic functions. Elected a Fellow of the Royal Society in 1912 and serving as President of the London Mathematical Society from 1924 to 1926, *Wik

1871 Giovanni Giorgi (27 Nov 1871; 19 Aug 1950) Italian physicist who proposed a widely used system for the definition of electrical, magnetic, and mechanical units of measurement. He developed the Giorgi International System of Measurement (also known as the mksa system) in 1901. Originally, he suggested that the basic units of scientific measurement be the metre, kilogram, second, and joule. With the the ampere replacing the joule as a basic unit, this system was subsequently endorsed by the General Conference of Weights and Measures (1960). Giorgi also worked in hydroelectric power, electricity distribution networks, and urban trolley systems.*TIS

1914 Edward Griffith Begle (27 Nov 1914; 2 Mar 1978) American mathematician, a topologist, who led development of "new math." When the Soviet Union launched the Sputnik satellite (1957), beating the U.S. into space, the effectiveness of science and mathematics education in American schools came under scrutiny. Begle's idea was to replace the traditional focus on mathematics as memorization and algorithmic computation. Instead, he designed a program to emphasise the fundamental importance of understanding the principles of mathematics. He directed (1958-72) the School Mathematics Study Group, funded by the National Science Foundation. SMSG produced teaching materials for all grade levels with this approach. Ultimately, initiating lasting reform through teachers was unsuccessful.*TIS

1923 J. Ernest Wilkins, Jr. (27 Nov 1923, ) African-American physicist, mathematician, and engineer (chemical/nuclear). He entered the University of Chicago at age 13, and by age 19, in 1942, he became the seventh African American to obtain a Ph.D. in Mathematics. His career achievement has been to develop radiation shielding against gamma radiation, emitted during electron decay of the Sun and other nuclear sources. He developed mathematical models to calculate the amount of gamma radiation absorbed by a given material. This technique of calculating radiative absorption is widely used among researcher in space and nuclear science projects. His was also a joint owner of a company which designed and developed nuclear reactors for electrical power generation.*TIS

DEATHS
1680 Athanasius Kircher (2 May 1601, 27 Nov 1680) German Jesuit priest and scholar, sometimes called the last Renaissance man. Kircher's prodigious research activity spanned a variety of disciplines including geography, astronomy, physics, mathematics, language, medicine, and music. He made an early, though unsuccessful attempt to decipher hieroglyphics of the Coptic language. During the pursuit of experimental knowledge, he once had himself lowered into the crater of Vesuvius to observe its features soon after an eruption. He made one of the first natural history collections. Kircher studied animal luminescence, writing two chapters of his book Ars Magna Lucis et Umbrae to bioluminescence, and debunked the idea that that an extract made from fireflies could be used to light houses. *TIS

1754 Abraham de Moivre,(26 May 1667 in Vitry-le-François , Champagne , France — 27 November 1754 in London, England) the mathematics tutor, succumbed at the age of 87, to lethargy. He was sleeping twenty hours a day, and it became a joke that he slept a quarter of an hour more every day and would die when he slept the whole day through. *VFR French mathematician who was a pioneer in the development of analytic trigonometry and in the theory of probability. He published The Doctrine of Chance in 1718. The definition of statistical independence appears in this book together with many problems with dice and other games. He also investigated mortality statistics and the foundation of the theory of annuities. He died in poverty, and correctly predicted the day of his own death. (more myth than fact, but in his weakened state he was sleeping most of his days away at the end.) He found that he was sleeping 15 minutes longer each night and from this the arithmetic progression, calculated that he would die on the day that he slept for 24 hours. *TIS

1849 Ruan Yuan was a Chinese scholar who wrote biographies of astronomers and mathematicians.*SAU

1852 Countess Augusta Ada King Lovelace (10 Dec 1815, 27 Nov 1852) (countess of Lovelace) English mathematician, the legitimate daughter of Lord Byron, was educated privately, studying mathematics and astronomy in addition to the more traditional topics. She seems to have developed an early ambition to be a famous scientist. After she met Charles Babbage in 1833, she began to assist in the development of his analytical engine and published notes on the work. She was one of the first to recognize the potential of computers and has been called the first computer programmer. (The programming language Ada is named after her.) Her other plans, such as a Calculus of the Nervous System, failed to mature - the obstacles in her way were simply too great. As a woman, for example, she was denied access to the Royal Society Library.*TIS (In 2009 and 2010, 24 March was commemorated by some as Ada Lovelace Day, a day to celebrate the achievements of women in technology and science. The 2011 Ada Lovelace Day was on 7 October)

1873 Auguste-Arthur de La Rive (9 Oct 1801, 27 Nov 1873) Swiss physicist who was one of the founders of the electrochemical theory of batteries. He began experimenting with the voltaic cell (1836) and supported the idea of Michael Faraday that the electricity was the result of chemical reactions in the cell. He invented a prize-winning electroplating method to apply gold onto brass and silver. He determined the specific heat of various gases, examined the temperature of the Earth's crust, and made ozone from electrical discharge through oxygen gas. He was a contemporary of Faraday, Ampere and Oersted, with whom he exchanged correspondence on electricity.*TIS

1904 Paul Tannery (20 Dec 1843 in Mantes-la-Jolie, Yvelines, France - 27 Nov 1904 in Pantin, Seine-St Denis, France) His main contributions were to the history of Greek mathematics and to the philosophy of mathematics. He published a history of Greek science in 1887, a history of Greek geometry in the same year, and a history of ancient astronomy in 1893.
Tannery did work of great importance as an editor of famous mathematics texts. He edited the work of Fermat in three volumes (jointly with C Henry) between 1891 and 1896. In addition he edited the work of Diophantus in two volumes (1893-95). He was an editor of the twelve volume complete works of Descartes Oeuvres de Descartes (1897-1913).
Tannery became so skilled in using Greek numerals in his historical work that he believed that they had certain advantages over our present system. *SAU

1998 Moshé Flato (17 Sept 1937 in Tel Aviv, Israel (under British mandate)
- 27 Nov 1998 in Paris, France) was a colorful mathematical physicist, with interests in groups, deformation theory and latterly, *-products. He pushed for the establishment of a European association of mathematical physics, which was never founded, but the momentum he created led to the foundation of the International Association of Mathematical Physics, IAMP. He also started the journal, Letters in Mathematical Physics, which is now well-established with a good reputation for the quality of its papers. I must admit that at the time, I was against founding a letters journal for mathematical physics, since the subject should not involve hasty publication of ideas so simple that they can be explained in a short article. However, I now think that it was a good idea, and leads to speedy progress in our subject. *Ray Streater

Monday, 25 November 2019

On This Day in Math - November 25

The capacity to blunder slightly is the real marvel of DNA.
Without this special attribute, we would still be anaerobic bacteria
and there would be no music.

— Lewis Thomas

The 329th day of the year; 329 is the sum of three consecutive primes. 329 is the number of forests (trees and disconnected trees) possible with ten vertices.

329 is also a happy number, since the iteration of the sums of the squares of its digits includes 1, $3^2 + 2^2 + 9^2 = 94, 9^2 + 4^2 = 97, 9^2 + 7^2 = 130, 1^2 +3^2+0^2 = 10, and 1^2 + 0^2 = 1 $

EVENTS
1658 The prize committee for Pascal’s cycloid problems (see 1 October 1658) decided not to give the prize of sixty Spanish gold doubloons to anyone. [DSB 7, 583] *VFR
In 1658, four years after renouncing mathematics as a vainglorious pursuit, Pascal found himself one day suffering from a painful toothache, and in desperation began to think about the cycloid to take his mind off the pain. Quickly the pain abated, and Pascal interpreted this as a sign from the Almighty that he should proceed to study the cycloid, which he did intensively for the next eight days. During this period he rediscovered most of what had already been learned about the cycloid, and several results that were new. Pascal decided to propose a set of challenge problems, with the promise of a first and second prize to be awarded for the best solutions. Roberval was named as one of the judges. Only two sets of solutions were received, one from Antoine de Lalouvere and another from John Wallis, but Pascal and Roberval decided that neither of the entries merited a prize, so no prizes were awarded. Instead, Pascal published his own solutions, along with an essay on the "History of the Cycloid". *www.mathpages.com

1731 A letter from Euler to Goldbach on this day includes the first use by Euler of continued fractions. Prior to his use continued fractions had made only scattered appearences. In the same letter he introduced the letter e as the base for the natural logarithms, "(e denotat hic numerum, cujus logarithmus hyperbolicus est=1.)," which Google translates as "(e denotes here the number of out of which the hyperbolic logarithm is equal to 1.)"
According to Maor's book e: The story of a number,:

Euler had already used the letter e to represent the number 2.71828... in one of his earliest works, a manuscript entitled "Meditation upon Experiments made recently on the firing of Cannon," written in 1727 when he was only twenty years old (it was not published until 1862, eighty years after his death). In a letter written in 1731 the number e appeared again in connection with a certain differential equation; Euler defines it as "that number whose hyperbolic logarithm is=1." The earliest appearance in a published work was in Euler's Mechanica (1736), in which he laid the foundations of analytical mechanics.

(My thanks to Dave Richeson who provided resources and tied all this information together for me.)

1804 Gauss, in a letter to his close friend Farkas Bolyai, explains that he does not agree with Bolyai's claim that he had put Euclidean Geometry on Solid Ground, "Bolyai has communicated to Gauss his claim that he has put Euclidean geometry on solid ground."

You desire only my careful and unfettered judgment: it is that your explanation does not satisfy me. I will try to explain the issue (it belongs to the same set of reefs on which my attempts have run aground) with as much clarity as possible. To be sure, I still have hope that, before my time is up, these reefs will permit passage. For the time being I have so many other tasks at hand that I cannot think about this; believe me, it would really make me happy if you were to pull ahead of me and overcome all obstacles. I would then undertake with the greatest joy, with all that is in my power, to defend your accomplishment and bring it to the light of day.

*Stan Burris, Notes on Non-Euclidean Geometry

1901 Richardson's law; Owen Willans Richardson read a paper before the Cambridge Philosophical Society which first announced his work on thermionic emission (the release of electrons from hot metals) and in particular a law which mathematically described how the amount of electron current increased as the temperature of the hot surface was raised. (He had been working at the Cavendish Laboratory only one year since his graduation from Cambridge University.) As recorded in the published Proceedings, in Richardson's words: "If then the negative radiation is due to the corpuscles coming out of the metal, the saturation current s should obey the law s = AT^1/2e^-b/T." The discovery of Richardson's law earned him the 1928 Nobel Prize for Physics.*TIS

1906 First Audion tube. The first triode was ordered by Lee de Forest who instructed the New York automobile lamp maker, H. W. Candless, to make a glass bulb containing a "grid" wire between a filament and an electrode plate. These specifications extended the Fleming two-element diode valve design previously published in the Proceedings of the Royal Society. The third element - the grid wire - regulated the flow of electrons between the filament and the anode plate, producing an amplification of the variations in a signal voltage applied to the grid. De Forest named his invention the "Audion." Within a few years (1913-1917) he was able to profit from his patents that he sold to AT&T for a total of $390,000.*TIS

1907 First general meeting of the Warsaw Scientiﬁc Society. Among the 14 founders of the Society were the two mathematicians Samuel Dickstein (1851–1939) and WLladysLlaw Gosiewski (1844– 1911). [Kuratowski, A Half Century of Polish Mathematics, p. 17] *VFR

1915 Albert Einstein completed his general theory of relativity. [A. Hellemans and B. Bunch, The Timetables of Science, p 429].*VFR

1952 Portugal issued two stamps commemorating the centenary of the birth of the mathematician Francisco Gomes Teixeira (1851-1932). [Scott #751-2]. *VFR

1997 Pixar’s A Bug’s Life and Geri’s Game is released. Pixar Animation Studio released their second feature-length animated film, “A Bug’s Life,” on this day in 1997, preceding it with a computer animated short, “Geri’s Game.” A Bug’s Life, following on the success of Pixar’s Toy Story, was the story of a rag-tag group of bugs who band together to defeat a group of invading grasshoppers. The film would make more than $160 million in its initial US release. Geri’s Game would go on to win the Academy Award for Best Animated Short Film. *CHM

BIRTHS
1783 Claude-Louis Mathieu (25 Nov 1783; 5 Mar 1875) French astronomer and mathematician who worked particularly on the determination of the distances of the stars. He began his career as an engineer, but soon became a mathematician at the Bureau des Longitudes in 1817 and later professor of astronomy in Paris. For many years Claude Mathieu edited the work on population statistics L'Annuaire du Bureau des Longitudes produced by the Bureau des Longitudes. His work in astronomy focussed on determining the distances to stars. He published L'Histoire de l'astronomie au XVIII siècle in 1827. *TIS

1814 (Julius) Robert Mayer (25 Nov 1814; 20 Mar 1878) a German physicist. While a ship's doctor sailing to Java, he considered the physics of animal heat. In 1842, he measured the mechanical equivalent of heat. His experiment compared the work done by a horse powering a mechanism which stirred paper pulp in a caldron with the temperature rise in the pulp. He held that solar energy was the ultimate source of all energy on earth, both living and nonliving. Mayer had the idea of the conservation of energy before either Joule or Helmholtz. The prominence of these two scientists, however, diminished credit for Mayer's earlier insights. James Joule presented his own value for the mechanical equivalent of heat. Helmhotlz more systematically presented the law of conservation of energy. *TIS

1816 Lewis Morris Rutherfurd (25 Nov 1816; 30 May 1892) American spectroscopist, astrophysicist and photographer, born in Morrisania, NY, who made the first telescopes designed for celestial photography. He produced a classification scheme of stars based on their spectra as similarly developed by the Italian astronomer. Rutherfurd spent his life working in his own observatory, built in 1856, where he photographed (from 1858) the Moon, Jupiter, Saturn, the Sun, and stars down to the fifth magnitude. While using photography to map star clusters, he devised a new micrometer to measure distances between stars with improved accuracy. When Rutherford began (1862) spectroscopic studies, he devised highly sophisticated diffraction gratings.*TIS

1841 Friedrich Wilhelm Karl Ernst Schröder (25 Nov 1841 in Mannheim, Germany - 16 June 1902 in Karlsruhe, Germany) His important work is in the area of algebra, set theory and logic. His work on ordered sets and ordinal numbers is fundamental to the subject. *SAU

1913 Lewis Thomas (25 Nov 1913; 3 Dec 1993) American physician, researcher, author, and teacher best known for his reflective essays on a wide range of topics in biology. While his specialities are immunology and pathology, in his book, Lives of a Cell, his down-to-earth science writing stresses that what is seen under the microscope is similar to the way human beings live, and he emphasizes the interconnectedness of life. As a research scientist, Thomas made an impact by suggesting that an immunosurveillance mechanism protects us from the possible ravages of mutant cells, an idea later championed by Macfarlane Burnett. He also proposed that viruses have played a major role in the evolution of species by their ability to move pieces of DNA from one individual or species to another. *TIS

1987 Evelyn Merle Nelson (November 25, 1943 – August 1, 1987), born Evelyn Merle Roden, was a Canadian mathematician. Nelson made contributions to the area of universal algebra with applications to theoretical computer science. Nelson's teaching record was, according to one colleague, "invariably of the highest order". However, before earning a faculty position at McMaster, prejudice against her lead to doubts about her teaching ability. Nelson published over 40 papers during her 20-year career before she died from cancer in 1987.
She, along with Cecilia Krieger, is the namesake of the Krieger–Nelson Prize, awarded by the Canadian Mathematical Society for outstanding research by a female mathematician. *Wik

DEATHS
1694 Ismael Boulliau (28 Sept 1605 , 25 Nov 1694) was a French clergyman and amateur mathematician who proposed an inverse square law for gravitation before Newton. Boulliau was a friend of Pascal, Mersenne and Gassendi and supported Galileo and Copernicus. He claimed that if a planetary moving force existed then it should vary inversely as the square of the distance (Kepler had claimed the first power), "As for the power by which the Sun seizes or holds the planets, and which, being corporeal, functions in the manner of hands, it is emitted in straight lines throughout the whole extent of the world, and like the species of the Sun, it turns with the body of the Sun; now, seeing that it is corporeal, it becomes weaker and attenuated at a greater distance or interval, and the ratio of its decrease in strength is the same as in the case of light, namely, the duplicate proportion, but inversely, of the distances that is, 1/d². *SAU

1913 Sir Robert Stawell Ball (1 July 1840 – 25 November 1913) was an Irish astronomer. He worked for Lord Rosse from 1865 to 1867. In 1867 he became Professor of Applied Mathematics at the Royal College of Science in Dublin. In 1874 Ball was appointed Royal Astronomer of Ireland and Andrews Professor of Astronomy in the University of Dublin at Dunsink Observatory. In 1892 he was appointed Lowndean Professor of Astronomy and Geometry at Cambridge University at the same time becoming director of the Cambridge Observatory.[(not exactly at the same time)In 1892 John Couch Adams, the Lowndean Professor of Astronomy and Geometry at Cambridge and the director of the Cambridge Observatory, died. Ball applied ... and was appointed as Lowndean Professor of Astronomy and Geometry but disputes with the university meant that he had to wait a year before he was appointed director of the Cambridge Observatory.*SAU] His lectures, articles and books (e.g. Starland and The Story of the Heavens) were mostly popular and simple in style. However, he also published books on mathematical astronomy such as A Treatise on Spherical Astronomy. His main interest was mathematics and he devoted much of his spare time to his "Screw theory". He served for a time as President of the Quaternion Society. His work The Story of the Heavens is mentioned in the "Ithaca" chapter of James Joyce's Ulysses. *Wik

1936 Édouard (-Jean-Baptiste) Goursat (21 May 1858, 25 Nov 1936) French mathematician and theorist whose contribution to the theory of functions, pseudo- and hyperelliptic integrals, and differential equations influenced the French school of mathematics. The Cauchy-Goursat theorem states the integral of a function round a simple closed contour is zero if the function is analytic inside the contour. Cauchy had established the theorem with the added condition that the derivative of the function was continuous. In 1891, he wrote Leçons sur l'intégration des équations aux dérivées partielles du premier ordre. Goursat's best known work is Cours d'analyse mathématique (1900-10) which introduced many new analysis concepts. *TIS
It is almost certain that l'Hôpital's rule, for finding the limit of a rational function whose numerator and denominator tend to zero at a point, is so named because Goursat named the rule after de l'Hôpital in his Cours d'analyse mathématique . Certainly the rule appears in earlier texts (for example it appears in the work of Euler), but Goursat is the first to attach de l'Hôpital's name to it.*SAU

1937 Alessandro Padoa (14 October 1868 – 25 November 1937) was an Italian mathematician and logician, a contributor to the school of Giuseppe Peano. He is remembered for a method for deciding whether, given some formal theory, a new primitive notion is truly independent of the other primitive notions. There is an analogous problem in axiomatic theories, namely deciding whether a given axiom is independent of the other axioms.*Wik

1952 Edward Vermilye Huntington (April 26 1874, Clinton, New York, USA -- November 25, 1952, Cambridge, Massachusetts, USA) was an American mathematician.
Huntington's primary research interest was the foundations of mathematics. He was one of the "American postulate theorists" (the term is Scanlan's), American mathematicians active early in the 20th century (including E. H. Moore and Oswald Veblen) who proposed axiom sets for a variety of mathematical systems. In so doing, they helped found what are now known as metamathematics and model theory.
Huntington was perhaps the most prolific of the American postulate theorists, devising sets of axioms (which he called "postulates") for groups, abelian groups, geometry, the real number field, and complex numbers. His 1902 axiomatization of the real numbers has been characterized as "one of the first successes of abstract mathematics" and as having "filled the last gap in the foundations of Euclidean geometry". Huntington excelled at proving axioms independent of each other by finding a sequence of models, each one satisfying all but one of the axioms in a given set. His 1917 book The Continuum and Other Types of Serial Order was in its day "...a widely read introduction to Cantorian set theory." (Scanlan 1999) Yet Huntington and the other American postulate theorists played no role in the rise of axiomatic set theory then taking place in continental Europe.
In 1904, Huntington put Boolean algebra on a sound axiomatic foundation. He revisited Boolean axiomatics in 1933, proving that Boolean algebra required but a single binary operation (denoted below by infix '+') that commutes and associates, and a single unary operation, complementation, denoted by a postfix prime. The only further axiom Boolean algebra requires is: (a '+b ')'+(a '+b)' = a, now known as Huntington's axiom.
Revising a method from Joseph Adna Hill, Huntington is credited with the Method of Equal Proportions or Huntington-Hill method of apportionment of seats in the U.S. House of Representatives to the states, as a function of their populations determined in the U.S. census. This mathematical algorithm has been used in the U.S. since 1941 and is currently the method used.
In 1919, Huntington was the first President of the Mathematical Association of America, which he helped found. He was elected to the American Academy of Arts and Sciences in 1913, and to the American Philosophical Society in 1933.*Wik

1978 Eduard L. Stiefel (21 April 1909, Zürich – 25 November 1978, Zürich) was a Swiss mathematician. Together with Cornelius Lanczos and Magnus Hestenes, he invented the conjugate gradient method, and gave what is now understood to be a partial construction of the Stiefel–Whitney classes of a real vector bundle, thus co-founding the study of characteristic classes.
Stiefel achieved his full professorship at ETH Zurich in 1948, the same year he founded the Institute for Applied Mathematics. The objective of the new institute was to design and construct an electronic computer (the Elektronische Rechenmaschine der ETH, or ERMETH). *Wik

1988 Dmitrii Evgenevich Menshov (18 April 1892 in Moscow, Russia - 25 Nov 1988)
For his work on the representation of functions by trigonometric series, Menshov was awarded a State Prize in 1951. He was then elected a Corresponding Member of the USSR Academy of Sciences in 1953. In 1958 Menshov attended the International Congress of Mathematicians in Edinburgh and he was invited to address the Congress with his paper On the convergence of trigonometric series. *SAU

2008 Beno Eckmann (March 31, 1917, Bern – November 25, 2008, Zurich) was a Swiss mathematician who was a student of Heinz Hopf.
Born in Bern, Eckmann received his master's degree from Eidgenössische Technische Hochschule Zürich (ETH) in 1931. Later he studied there under Heinz Hopf, obtaining his Ph.D. in 1941. Eckmann was the 2008 recipient of the Albert Einstein Medal.
Calabi–Eckmann manifolds, Eckmann–Hilton duality, the Eckmann–Hilton argument, and the Eckmann–Shapiro lemma are named after Eckmann.*Wik

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