The unreasonable efficiency of mathematics in science is a gift we neither understand nor deserve.

The unreasonable efficiency of mathematics in science is a gift we neither understand nor deserve.

~Eugene Paul Wigner

The 321st day of the year. 321 is the number of partitions of 13 into at most 4 parts. (7+3+2+1 would be one such)

321 is a Central Delannoy number. The Delannoy numbers are the number of lattice paths from (0, 0) to (b, a) in which only east (1, 0), north (0, 1), and northeast (1, 1) steps are allowed. Central Delannoy numbers are paths to (a,a). [Delannoy numbers are named for Henri Auguste Delannoy (1833–1915) who was a friend and correspondent of Edouard Lucas, editor of Récréations Mathématiques.]

321 = 161^2 - 160^2 = 55^2 - 52^2

321 is a Central Delannoy number. The Delannoy numbers are the number of lattice paths from (0, 0) to (b, a) in which only east (1, 0), north (0, 1), and northeast (1, 1) steps are allowed. Central Delannoy numbers are paths to (a,a). [Delannoy numbers are named for Henri Auguste Delannoy (1833–1915) who was a friend and correspondent of Edouard Lucas, editor of Récréations Mathématiques.]

321 = 161^2 - 160^2 = 55^2 - 52^2

**EVENTS**

**1717**While making his rounds a gendarme found an infant on the steps of the Church of Saint Jean-le-Rond in Paris. The child was christened Jean-le-Rond. Later, for unknown reasons, he added the surname d’Alembert. Jean le Rond D'Alembert (1717 1783) was abandoned by his mother on the steps of Saint Jean le Rond, which was the baptistery of Notre-Dame. Foster parents were found and he was christened with the name of the saint. When he became famous, his mother attempted to reclaim him, but he rejected her. His father, we now know, was an artillery officer, Louis-Camus Destouches. His natural father did not want his paternity known, but paid for his education in secret. D'Alembert was a pioneer in the study of differential equations and their use of in physics. He studied the equilibrium and motion of fluids.

*Pastel portrait of d'Alembert by Maurice Quentin de La Tour, 1753:*

**1767**At the commencement, the College of Philadelphia bestowed on David Rittenhouse, then present, the honorary degree of Master of Arts, Dr. William Smith, the Provost, addressing him as follows:

Sir,--The trustees of this College (the faculty of professors cheerfully concurring), being ever desirous to distinguish real merit, especially in the natives of this province,--and well-assured of the extraordinary progress and improvement which you have made, by a felicity of natural genius, in mechanics, mathematics, astronomy, and other liberal arts and sciences, all which you have adorned by singular modesty and irreproachable morals,--have authorized and required me to admit you to the honorary degree of Master of Arts, in this seminary: I do therefore, by virtue of this authority, most cheerfully admit, &c.*U Penn Library web site

One admirer and colleague of Rittenhouse, Francis Hopkinson, was on the Navy Board that wrote the Flag Act of 1777, which defined the Flag of the United States of America and explained the blue field of stars as a representation of "a new constellation." This is thought by some to be a direct tribute to Rittenhouse. Biographer Brooke Hindle wrote, "Few admired Rittenhouse more unrestrainedly than Francis Hopkinson."

**In 1797**, the first patent in the U.S. for a clock was issued to Eli Terry of East Windsor, Conn. for an equation clock.The patent was signed by President John Adams. The clock had two minute hands, one of which showed the mean or true time, while the other "together with the striking part and hour hand showed the apparent time, as divided by the sun according to the table of variation of the sun and clock for each day of the year." He began making clocks in 1793, in Plymouth, Conn. Terry introduced wooden geared clocks using the ideas of Eli Whitney's new armory practice to produce interchangeable gears (1802) and mass production of very inexpensive household clocks. Terry developed ways to produce wooden clock works by machine. *TIS

*Eight-day weight-powered wood movement, Eli Terry, Plymouth – Connecticut Historical Society*

**1834**Astronomer Royal Airy receives suggestion to begin mathematical search for undiscovered planet that would be Neptune by the Reverend T.J. Hussey.

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

**1921**Fisher reads his famous Royal Society paper, On the Mathematical Foundations of Theoretical Statistics. Statistical Historian, Steven Stigler writes that, “in 1921 Fisher presented a major pathbreaking memoir to the Royal Society of London, a memoir that more than any other single work gave the framework and direction to twentieth century statistical theory.”

The paper begins with a list of definitions that, while almost unheard of before that paper, have become standard in even elementary statistics courses. Terms like estimation, likelihood, optimum, and not defined, but actually used in the descriptions of other terms was Fisher’s first public use of “parameter”. *Stigler, Fisher in 1921

At right the Fisher window from from the Greatroom at Caius College., Cambridge

**1921**lN the issue of NATURE of November 17, p. 381, it is stated that "in 1861 telegraphy, the only practical application of electricity, was in private hands. The earliest telegraph was erected on the London and North-Western Railway between Euston and Chalk Farm so far back as 1837 by Cooke and Wheatstone, " It is strange that no mention is made of the completely equipped reciprocal working electrical telegraph eight miles long (both above and below ground) erected by Francis Ronalds in his garden at Hammersmith in 1816, and fully described bv him in a most interesting book published in 1823 (" Description of an Electrical Telegraph and of some other Electrical Apparatus," R. Hunter, 72 St. Paul's Churchyard).

I _thought the story of his treatment by the ~Admiralty in 1816, when he asked for inspection of

his telegraph with a view to its substitution in place of the semaphores then (and for years afterwards) in use between London and Portsmouth, was well known. He was informed that "telegraphs of any kind are now wholly unnecessary. *Nature Magazine

The following print shows the Admiralty building in Whitehall. On the roof at the rear of the building, a tall post can be seen with two arms. This was the London end of the chain of stations between London and Portsmouth.

**1930**Kurt Godel’s “On formally undecidable propositions of Principia Mathematica and related systems ” was received for publication. It contained the amazing result that there are true but unprovable statements in arithmetic.

**In 1970**, a U.S. patent was issued for the computer mouse - an "X-Y Position Indicator for a Display System" (No. 3541541). The inventor was Doug Engelbart. In the lab, he and his colleagues had called it a "mouse," after its tail-like cable. The first mouse was a simple hollowed-out wooden block, with a single push button on top. Engelbart had designed this as a tool to select text, move it around, and otherwise manipulate it. It was a key element of his larger project - the NLS (oN Line System), a computer he and some colleagues at the Stanford Research Institute had built. The NLS also allowed two or more users to work on the same document from different workstations.*TIS

**2011**French law allows the ﬁrst taste of Beaujolais Nouveau on this date each year. In 1985 the law was changed to the third Thursday in November. Also permission was given to ship wine ahead of time to bonded warehouses outside of France. Thus in the US we can drink the Nouveau on the same day as the French. Get out now and buy several bottles for the holidays. *VFR

**2023**The maximum of the Leonid activity in 2023 is expected during the night of the 18th November. The Leonids are a prolific meteor shower. It tends to peak around November 17-19, but some are spread through several days on either side and the specific peak changing every year. *Cute-Calendar.com

Image of 1833 Leonid shower |

**BIRTHS**

**1597 Henry Gellibrand**was an English clergyman who worked on magnetic declination and who made mathematical contributions to navigation.*SAU He discovered that magnetic declination – the angle of dip of a compass needle – is not constant but changes over time. He announced this in 1635, relying on previous observations by others, which had not yet been correctly interpreted.

He also devised a method for measuring longitude, based on eclipses. The mathematical tables of Henry Briggs, consisting of logarithms of trigonometric functions, were published by Gellibrand in 1633 as Trigonometria Britannica.

He was Professor at Gresham College, succeeding Edward Gunter in 1626. He was buried in St Peter Le Poer. (London, demolished in 1907) *Wik

**1790 August Möbius**(17 Nov 1790; 26 Sep 1868)August Ferdinand Möbius was a German astronomer, mathematician and author. He is best known for his work in analytic geometry and in topology, especially remembered as one of the discoverers of the Möbius strip, which he had discovered in 1858. A Möbius strip is a two-dimensional surface with only one side. It can be constructed in three dimensions as follows. Take a rectangular strip of paper and join the two ends of the strip together so that it has a 180 degree twist. It is now possible to start at a point A on the surface and trace out a path that passes through the point which is apparently on the other side of the surface from A. Although his most famous work is in mathematics, Möbius did publish important work on astronomy.*TIS

**1865 John Stanley Plaskett**(17 Nov 1865; 17 Oct 1941) Canadian astronomer known for his expert design of instruments and his extensive spectroscopic observations. He designed an exceptionally efficient spectrograph for the 15-inch refractor and measured radial velocities and found orbits of spectroscopic binary stars. He designed and supervised construction of the 72-inch reflector built for the new Dominion Astrophysical Observatory in Victoria and was appointed its first director in 1917. There he extended the work on radial velocities and spectroscopic binaries and studied spectra of O and B-type stars. In the 1930s he published the first detailed analysis of the rotation of the Milky Way, demonstrating that the sun is two-thirds out from the center of our galaxy about which it revolves once in 220 million years. *TIS

**1902 Eugene Paul Wigner**(17 Nov 1902; 1 Jan 1995) Hungarian-born American physicist who was the joint winner of the 1963 Nobel Prize for Physics (with Maria Goeppert Mayer and Johannes Hans Jensen) for his insight into quantum mechanics, for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles. He made many contributions to nuclear physics and played a prominent role in the development of the atomic bomb and nuclear energy. *TIS I love this story about Wigner as a child, "When he was ten years old ... he was told that he had tuberculosis. The cure was to be found in sending him to a sanatorium in Breitenstein in Austria and he spent six weeks there before being told that the diagnosis had been wrong and that he had never had tuberculosis. However, one advantage of his six weeks was that he began to think about mathematical problems "I had to lie on a deck chair for days on end, and I worked terribly hard on constructing a triangle if the three altitudes are given." *SAU

**1917 Ruth Aaronson Bari**(November 17, 1917 – August 25, 2005) was an American mathematician known for her work in graph theory and homomorphisms. The daughter of Polish-Jewish immigrants to the U.S., she was a professor at George Washington University beginning in 1966. She was the mother of environmental activist Judi Bari, science reporter Gina Kolata and art historian Martha Bari.*Wik

**1704 Valentin Heins**(May 15th 1637 in Hamburg - November 17 1704 ) was a German arithmetician (Reckoner)

The son of a linen weaver, the source of his education is unknown. From 1651 Heins was licensed to provide instruction in commercial computing (accounting, bookkeeping, arithmetic, etc). In the years 1658 and 1659 Heins studied theology for several semesters at the universities of Jena and Leipzig , but then returned to Hamburg. There he married and had a vicariate (financial endoument) in 1661 at the Cathedral. Whether Heins performed for a service is not known.

In 1670 he became writing and arithmetic master of the German Church School St. Michaelis . He was also from 1663-1672 accountant of the Guinean-African Company.

He wrote several textbooks, which made him known beyond national boundaries. They were reprinted up to the beginning of the 19th Century. Particularly popular was his tyrocinium mercatorio arithmeticum, a commercial arithmetic and accounting book.

Heins founded in 1690, with the calculation of the parish school master of St. Jacobi Henry Meissner , the art-loving Societät billing. This later became the Mathematical Society of Hamburg, the worlds oldest existing mathematical society. *Wik

**1929 Herman Hollerith**(29 Feb 1860, 17 Nov 1929) American inventor of a tabulating machine that was an important precursor of the electronic computer. For the 1890 U.S. census, he invented several punched-card machines to automate the sorting of data. The machine which read the cards used a pin going through a hole in the card to make an electrical connection with mercury placed beneath. The resulting electrical current activated a mechanical counter. It saved the United States 5 million dollars for the 1890 census by completing the analysis of the data in a fraction of the time it would have taken without it and with a smaller amount of manpower than would have been necessary otherwise. In 1896, he formed the Tabulating Machine Company, a precursor of IBM. *TIS

**1953 Pierre Humbert (**13 June 1891 in Paris, France, 17 Nov 1953 in Paris, France) graduated from the École Polytechnique in Paris and then moved to Edinburgh to do research under Whittaker. He spent most of his career in the University of Montpellier. He specialized in the history of the seventeenth century he wrote particularly on the French astronomers of that period.

He also made contributions to mathematics, in particular he wrote on elliptic functions, Lamé functions, and Mathieu functions. His main mathematical work from the mid 1930s onwards was in developing the symbolic calculus. He also wrote on applications of the symbolic calculus to mathematical physics.

*SAU**1954 Tadeusz Banachiewicz**(13 February 1882, Warsaw, Congress Poland, Russian Empire – 17 November 1954, Kraków) was a Polish astronomer, mathematician and geodesist.

He was educated at Warsaw University and his thesis was on "reduction constants of the Repsold heliometer". In 1905, after the closure of the University by the Russians, he moved to Göttingen and in 1906 to the Pulkowa Observatory. He also worked at the Engel'gardt Observatory at Kazan University from 1910–1915.

In 1919, after Poland regained her independence, Banachiewicz moved to Kraków, becoming a professor at the Jagiellonian University and the director of Kraków Observatory. He authored approximately 180 research papers and modified the method of determining parabolic orbits. In 1925, he invented a theory of "cracovians" — a special kind of matrix algebra — which brought him international recognition. This theory solved several astronomical, geodesic, mechanical and mathematical problems.

In 1922 he became a member of PAU (Polska Akademia Umiejętności) and from 1932 to 1938 was the vice-president of the International Astronomical Union. He was also the first President of the Polish Astronomical Society, the vice-president of the Geodesic Committee of The Baltic States and, from 1952 to his death, a member of the Polish Academy of Sciences. He was also the founder of the journal Acta Astronomica. He was the recipient of Doctor Honoris Causa titles from the University of Warsaw, the University of Poznań and the University of Sofia in Bulgaria.[citation needed]

Banachiewicz invented a chronocinematograph. The lunar crater Banachiewicz is named after him. He wrote over 230 scientific works. *Wik

**1956 John Evershed**(26 Feb 1864, 17 Nov 1956) English astronomer who discovered (1909) the Evershed effect - the horizontal motion of gases outward from the centres of sunspots. While photographing solar prominences and sunspot spectra, he noticed that many of the Fraunhofer lines in the sunspot spectra were shifted to the red. By showing that these were Doppler shifts, he proved the motion of the source gases. This discovery came to be known as the Evershed effect. He also gave his name to a spectroheliograph, the Evershed spectroscope.*TIS

**1958 Yutaka Taniyama**(November 12, 1927, Kisai near Tokyo – November 17, 1958, Tokyo) was a Japanese mathematician known for the Taniyama-Shimura conjecture.

Taniyama was best known for conjecturing, in modern language, automorphic properties of L-functions of elliptic curves over any number field. A partial and refined case of this conjecture for elliptic curves over rationals is called the Taniyama-Shimura conjecture or the modularity theorem whose statement he subsequently refined in collaboration with Goro Shimura. The names Taniyama, Shimura and Weil have all been attached to this conjecture, but the idea is essentially due to Taniyama.

In 1986 Ribet proved that if the Taniyama-Shimura conjecture held, then so would Fermat's last theorem, which inspired Andrew Wiles to work for a number of years in secrecy on it, and to prove enough of it to prove Fermat's Last Theorem. Due to the pioneering contribution of Wiles and the efforts of a number of mathematicians the Taniyama-Shimura conjecture was finally proven in 1999. The original Taniyama conjecture for elliptic curves over arbitrary number fields remains open, and the method of Wiles and others cannot be extended to provide its proof.*Wik

**1990 Robert Hofstadter**(5 Feb 1915, 17 Nov 1990) American scientist who was a joint recipient of the Nobel Prize for Physics in 1961 for his investigations in which he measured the sizes of the neutron and proton in the nuclei of atoms. He revealed the hitherto unknown structure of these particles and helped create an identifying order for subatomic particles. He also correctly predicted the existence of hte omega-meson and rho-meson. He also studied controlled nuclear fission. Hofstadter was one of the driving forces behind the creation of the Stanford Linear Accelerator. He also made substantial contributions to gamma ray spectroscopy, leading to the use of radioactive tracers to locate tumors and other disorders.*TIS

He is the father of Godel, Escher, Bach author Douglas Hofstadter and cousin of famous Columbia University historian Richard Hofstadter. (*HT to John McGowan)

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

Credits :

*CHM=Computer History Museum

*FFF=Kane, Famous First Facts

*NSEC= NASA Solar Eclipse Calendar

*RMAT= The Renaissance Mathematicus, Thony Christie

*SAU=St Andrews Univ. Math History

*TIA = Today in Astronomy

*TIS= Today in Science History

*VFR = V Frederick Rickey, USMA

*Wik = Wikipedia

*WM = Women of Mathematics, Grinstein & Campbell

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