**I have made this letter longer than usual, because I lack the time to make it short.**

~ Blaise Pascal, (my favorite Pascal Quote)

**The 310th day of the year**; 310 = 1234 in base six. In base 2 it repeats one period, 100,110,110

(1!)²+(2!)²+...+(310!)² is prime. *Math Year-Round @MathYearRound

The four possible 3 digit permutations of 310 all use the same digits in their squares as well, 130

^{2}= 16900, 310

^{2}= 96100, 103

^{2}= 10609,and 301

^{2}= 90601. (Are there numbers with a digit greater than three for which this is true? With or without a 0.)

310 is a magnanimous number. A number (which we assume of at least 2 digits) such that the sum obtained inserting a "+" among its digit in any position gives a prime. 31+0 is prime and 3+10 is prime

1500 Nicholas Copernicus observes a deep (85%) partial eclipse of the Moon from Rome. *David Dickinson @Astroguyz 4m:

**EVENTS**

1500 Nicholas Copernicus observes a deep (85%) partial eclipse of the Moon from Rome. *David Dickinson @Astroguyz 4m:

**1572,**a supernova was first noted by Wolfgang Schuler of Wittenberg in the W-shaped constellation of Cassiopeia but was seen by many observers throughout Europe and in the Far East. It appeared as a new star, adjacent to the fainter star seen just northwest of the middle of the "W." Tycho Brahe first noticed this new star on 11 Nov 1572, and he began to meticulously record its appearance. Although he was not the first to see it, he gained fame from his book Stella Nova (Latin: "new star"). For two weeks it was brighter than any other star in the sky and visible in daytime. By month's end, it began to fade and change color, from bright white to yellow and orange to faint reddish light. It was visible to the naked eye for about 16 months until Mar 1574 *TISDe Stella Nova opened to display image with the Supernova located in the foot of the serpent bearer

*Wik |

**1766**Lagrange welcomed, at age 30, to the Berlin Academy by Frederick the Great. “The greatest king in Europe” wished to have at his court “the greatest mathematician of Europe.” *VFR

By March 1766 d'Alembert knew that Euler was returning to St Petersburg and wrote again to Lagrange to encourage him to accept a post in Berlin. Full details of the generous offer were sent to him by Frederick II in April, and Lagrange finally accepted. Leaving Turin in August, he visited d'Alembert in Paris, then Caraccioli in London before arriving in Berlin in October. Lagrange succeeded Euler as Director of Mathematics at the Berlin Academy on 6 November 1766.

**1780**Aloisio Galvani discovers the famous "twitch" in a frog's leg. *A history of physics in its elementary branches By Florian Cajori

During the 1780's, biologist Luigi Galvani performed experiments at the University of Bologna involving frogs. While cutting a frog’s leg, Galvani's steel scalpel touched a brass hook that was holding the leg inplace. The leg twitched. Further experiments confirmed this effect, and Galvani was convinced that he was seeing the effects of what he called animal electricity. *batteryfacts

**1869**The first game of intercollegiate "football" between two colleges from the United States was an unfamiliar ancestor of today's college football, as it was played under 99-year-old soccer-style Association rules. The game was played between teams from Rutgers University and Princeton University, which was called the College of New Jersey at the time. It took place on November 6, 1869 at College Field, which is now the site of the College Avenue Gymnasium at Rutgers University in New Brunswick, New Jersey. Rutgers won by a score of 6 "runs" to Princeton's 4 *Wik

**1936**Problem number 153 was entered into the Scottish Book by Stanislaw Mazur. The problem asked (although not in these words) about the existence of Schauder bases in separable Banach spaces. As with many of the problems in the Scottish Book the proposer would offer a prize for their solution. Prizes offered included wine, spirits, or a meal in Cambridge but Mazur offered a live goose as the prize for this particular problem. Per Enflo showed in 1972 that the problem had a negative solution and, while in Warsaw lecturing on his solution, Mazur presented him with his prize, the live goose! The ceremony was broadcast throughout Poland. *SAU

1960 The New York Times picked up an Associated Press story about a Catholic Church near Cologne, Germany which had decided to put a modern touch to the new church bell, so they ordered Einstein's famous equation to be engraved on the bell. Unfortunately, someone miss engraved the bell, replacing the C with an R. Unfortunately, when the story ran in the press, another adjustment to the Professor's great equation had occurred... read it for yourself.

*J F PTAK

**1980**Microsoft signs a contract with IBM to create an operating system for the new IBM PC. The PC ignited the personal computer market, making home computers popular among more than just hobbyists. Microsoft cofounders Bill Gates and Paul Allen developed the Microsoft Disk Operating System, commonly known as MS-DOS, using existing software from a Seattle company as a foundation. *CHM

**2002**A group of Australian scientists published a paper in Applied Ergonomics with the title, "An Analysis of the Forces Required to Drag Sheep over Various Surfaces." *sciencedirect abstract

**BIRTHS**

**1638 James Gregory**(6 Nov 1638; Oct 1675) Scottish mathematician, astronomer and inventor of a type of reflecting telescope, born in Aberdeen. He was the first to investigate converging number series, which have an infinite number of terms but a finite sum.

Gregory published Vera Circuli et Hyperbolae Quadratura (1667) in which he approximated the areas of the circle and hyperbola with convergent series:

[James Gregory] cannot be denied the authorship of many curious theorems on the relation of the circle to inscribed and circumscribed polygons, and their relation to each other. By means of these theorems he gives with infinitely less trouble than by the usual calculations, … the measure of the circle and hyperbola (and consequently the construction of logarithms) to more than twenty decimal places. Following the example of Huygens, he also gave constructions of straight lines equal to the arcs of the circle, and whose error is still less.

"The first proof of the fundamental theorem of calculus and the discovery of the Taylor series can both be attributed to him.

He made important contributions to the development of the calculus, although some of his best work remained virtually unknown until long after his death. In 1660 he published his Optica Promota, in which he described the first practical reflecting ("Gregorian") telescope. Light reflected from a concave elliptical secondary mirror is brought to a focus just behind a hole in the primary mirror. It was superceded by the Newtonian and Cassegrain telescopes. Gregory also introduced estimation of stellar distances by photometric methods. *TIS (For more on the origin of reflecting telescopes see this blog by the Renaissance Mathematicus.)

*Wik |

**1781 Giovanni Antonio Amedeo Plana**(6 November 1781 – 20 January 1864) was an Italian astronomer and mathematician. In 1800 he entered the École Polytechnique, and was one of the students of Joseph Lagrange. Jean Fourier, impressed by Plana's abilities, managed to have him appointed to the chair of mathematics in a school of artillery in Piedmont in 1803, which came under the control of the French in 1805. In 1811 he was appointed to the chair of astronomy at the University of Turin thanks to the influence of Lagrange. He spent the remainder of his life teaching at that institution.

His contributions included work on the motions of the Moon, as well as integrals, elliptic functions, heat, electrostatics, and geodesy. In 1820 he was one of the winners of a prize awarded by the Académie des Sciences in Paris based on the construction of lunar tables using the law of gravity. In 1832 he published the Théorie du mouvement de la lune. In 1834 he was awarded with the Copley Medal by the Royal Society for his studies on lunar motion. He became astronomer royal, and then in 1844 a Baron. At the age of 80 he was granted membership in the prestigious Académie des Sciences. He died in Turin. He is considered one of the premiere Italian scientists of his age. *Wik

**1906 Emma Markovna Lehmer**(née Trotskaia) (November 6, 1906 – May 7, 2007) was a mathematician known for her work on reciprocity laws in algebraic number theory. She preferred to deal with complex number fields and integers, rather than the more abstract aspects of the theory. At UC Berkeley, she started out in engineering in 1924, but found her niche in mathematics. One of her professors was Derrick N. Lehmer, the number theorist well known for his work on prime number tables and factorizations. While working for him at Berkeley finding pseudosquares, she met her future husband Derrick H. Lehmer. Upon her graduation summa cum laude with a B.A. in Mathematics (1928), Emma married the younger Lehmer. They moved to Brown University, where Emma received her M.Sc., and Derrick his Ph.D., both in 1930. Emma did not obtain a Ph.D. herself. Most universities had nepotism rules which prevented husband and wife from both holding teaching positions, although Emma claimed there were many advantages to not holding a Ph.D.

The Lehmers had two children, Laura (1932) and Donald (1934). Emma did independent mathematical work, including a translation from Russian to English of Pontryagin's book Topological Groups. She worked closely with her husband on many projects; 21 of her 60-some publications were joint work with him. Her publications were mainly in number theory and computation, with emphasis on reciprocity laws, special primes, and congruences. *Wik

Photo by Paul Halmos

*SAU |

**1960 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

**1966 Laurent Lafforgue**(born 6 November 1966, in Antony, Hauts-de-Seine) is a French mathematician.

He won 2 silver medals at International Mathematical Olympiad (IMO) in 1984 and 1985. He entered the École Normale Supérieure in 1986. In 1994 he received his Ph.D. under the direction of Gérard Laumon in the Arithmetic and Algebraic Geometry team at the Université de Paris-Sud. Currently he is a research director of CNRS, detached as permanent professor of mathematics at the Institut des Hautes Études Scientifiques (I.H.E.S.) in Bures-sur-Yvette, France.

In 2002 at the 24th International Congress of Mathematicians in Beijing, China he received the Fields Medal together with Vladimir Voevodsky. Lafforgue made outstanding contributions to Langlands' program in the fields of number theory and analysis, and in particular proved the Langlands conjectures for GLn of a function field. The crucial contribution by Lafforgue to solve this question is the construction of compactifications of certain moduli stacks of shtukas. The monumental proof is the result of more than six years of concentrated efforts.

He received the Clay Research Award in 2000. His younger brother Vincent Lafforgue is also a notable mathematician.*Wik

**DEATHS**

**1656 Jean-Baptiste Morin**was a French astrologer and astronomer who attempted to solve the longitude problem using lunar observations. He was certainly not the first to propose the method but he did add one important new piece of understanding, namely he took lunar parallax into account.

Since Morin put forward his method for a longitude prize, a committee was set up by Cardinal Richelieu to evaluate it. Étienne Pascal, Mydorge, Beaugrand, Hérigone, J C Boulenger and L de la Porte served on the committee and they were in dispute with Morin for the five years after he made his proposal.

Morin realized that instruments had to be improved, improved methods of solving spherical triangles had to be found and better lunar tables were needed. He made some advances in these areas but his method, although theoretically sound, could not achieve either the computational or observational accuracy to succeed. Morin refused to listen to objections to his proposal.

Even while the dispute was going on, in 1638, Morin attacked Descartes saying that he had realized as soon as they met how bad his philosophy was. These disputes alienated Morin from the scientific community. He was to spend the latter part of his life isolated from other scientists although Cardinal Richelieu's successor Cardinal Mazarin did award him a pension for his work on the longitude in 1645. *SAU

**1790 James Bowdoi**n (7 Aug 1726, 6 Nov 1790) American founder and first president of the American Academy of Arts and Sciences (1780). He was a scientist prominent in physics and astronomy, and wrote several papers including one on electricity with Benjamin Franklin, a close friend. In one of his letters to Franklin, Bowdoin suggested the theory, since generally accepted, that the phosphorescence of the sea, under certain conditions, is due to the presence of minute animals. Bowdoin was also a political leader in Massachusetts during the American revolution (1775-83), and governor of Massachusetts (1785-87). His remarkable library of 1,200 volumes, ranged from science and math to philosophy, religion, poetry, and fiction. He left it in his will to the Academy.*TIS

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

Bellavitis anticipated the idea of a Euclidean vector with his notion of

**equipollence**. Two line segments*AB*and*CD*are equipollent if they are parallel and have the same length and direction. The relation is denoted In modern terminology, this relation between line segments is an example of an equivalence relation. The concept of vector addition was written by Bellavitis as: According to Laissant, Bellavitis published works in "arithmetic, algebra, geometry, infinitesimal calculus, probability, mechanics, physics, astronomy, chemistry, mineralogy, geodesy, geography, telegraphy, social science, philosophy, and literature. *Wik**1913 Sir William Henry Preece**(15 Feb 1834, 6 Nov 1913) Welsh electrical engineer who was a major figure in the development and introduction of wireless telegraphy and the telephone in Great Britain. Preece's interest in applied electricity and telegraphic engineering was developed as a graduate student under Michael Faraday. For 29 years, from 1870, he was an engineer with the Post Office telegraphic system and contributed many inventions and improvements, including a railroad signaling system that increased railway safety. An early pioneer in wireless telegraphy, he originated his own system in 1892. He encouraged Guglielmo Marconi by obtaining assistance from the Post Office for his work. Preece also introduced into Great Britain the first Bell telephones. Preece was knighted in 1899. *TIS

1946 Dunham Jackson (July 24, 1888, Bridgewater, Massachusetts – November 6, 1946) was a mathematician who worked within approximation theory, notably with trigonometrical and orthogonal polynomials. He is known for Jackson's inequality. He was awarded the Chauvenet Prize in 1935. His book Fourier Series and Orthogonal Polynomials (dated 1941) was reprinted in 2004.

Harold Bacon recalls that Jackson was an inspired writer of limericks. When Bacon purchased Jackson's "The Theory of Approximations" he took it to Jackson's office and requested he sign it, suggesting a limerick. Without any visible prethought Jackson wrote on the flyleaf:

There was a young fellow named Bacon*Steven Krantz, Mathematical Apocrypha Redux

Whose judgement of books was mistaken

In a moment too rash

He relinquished some cash

And his faith in the Author was shaken

*Wik |

**1966 Frieda Nugel**(18 June 1884 in Cottbus, Brandenburg, Germany

- 6 Nov 1966 in Bad Godesberg, Bonn, Germany) was a German mathematician who was one of the first women to receive a doctorate in Germany. *SAU

**1975**

**Samuel Stephens Kistler**(March 26, 1900 – November 6, 1975) was an American scientist and chemical engineer, best known as the inventor of aerogels, one of the lightest known solid materials.

The exact circumstances of the creation of the first aerogels are not well recorded. A popular story is that they resulted from a competition between Kistler and one Charles Learned "to see if they could replace the liquid inside of a jelly jar without causing any shrinkage". Whether these experiments were performed at the College of the Pacific, still with limited facilities following the move in 1923 to the new Stockton campus, or at Stanford, where Kistler began pursuing a doctorate in 1927, is a source of some confusion. Either way, in 1931 Kistler published a paper in Nature (vol. 127, p. 741) titled "Coherent Expanded Aerogels and Jellies".

He died in Salt Lake City in November 1975, shortly before the resurgence of interest in aerogels caused by the discovery of a less time-consuming method of manufacture by researchers led by Stanislaus Teichner in France.

**1979 Alexander Weinstein**(21 Jan 1897 in Saratov, Russia

- 6 Nov 1979 in Washington DC, USA)Weinstein's research covered a wide range of topics. He is famed for solving a variety of boundary value problems. For example he solved Helmholtz's problem for jets, giving the first uniqueness and existence theorems for free jets in a series of papers from 1923 to 1929. He examined boundary problems in an infinite strip, giving hydrodynamic and electromagnetic applications.

Weinstein's method was developed to give accurate bounds for eigenvalues of plates and membranes. In examining singular partial differential equations he introduced a new branch of potential theory and applied the results to many different situations including flow about a wedge, flow around lenses and flow around spindles. *SAU

**1928 Laszlo Belady**,( April 29, 1928 in Budapest - November 6, 2021) creator of the Belady algorithm (used in optimizing the performance of computers), is born. Belady worked at IBM for 23 years in software engineering before joining the Mitsubishi Electronics Research Laboratory in the mid-1980s. He wins numerous awards, including the J.D. Warnier Prize for Excellence in Information and an IEEE fellowship. *CHM

Credits

*CHM=Computer History Museum

*FFF=Kane, Famous First Facts

*NSEC= NASA Solar Eclipse Calendar

*SAU=St Andrews Univ. Math History

*TIA = Today in Astronomy

*TIS= Today in Science History

*VFR = V Frederick Rickey, USMA

*Wik = Wikipedia

*WM = Women of Mathematics, Grinstein & Campbell

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