**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 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.

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

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

- 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

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

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

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

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

**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

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