Frank Nelson Cole

Frank Nelson Cole (September 20, 1861 – May 26, 1926) was an American mathematician, born in Ashland, Massachusetts, and educated at Harvard, where he lectured on mathematics from 1885 to 1887.

Later, he was employed at the University of Michigan and Columbia University.[1] Professor Cole became secretary of the American Mathematical Society in 1895 and an editor of its Bulletin in 1897.

Cole published a number of important papers, including The Diurnal Variation of Barometric Pressure (1892).[1] In 1893 in Chicago, his paper On a Certain Simple Group (the group is PSL(2,8)) was read (but not by him) at the International Mathematical Congress held in connection with the World's Columbian Exposition.[2][3][4]

On October 31, 1903, Cole famously made a presentation to a meeting of the American Mathematical Society where he identified the factors of the Mersenne number 267 − 1, or M67.[5] Édouard Lucas had demonstrated in 1876 that M67 must have factors (i.e., is not prime), but he was unable to determine what those factors were. During Cole's so-called "lecture", he approached the chalkboard and in complete silence proceeded to calculate the value of M67, with the result being 147,573,952,589,676,412,927. Cole then moved to the other side of the board and wrote 193,707,721 × 761,838,257,287, and worked through the tedious calculations by hand. Upon completing the multiplication and demonstrating that the result equaled M67, Cole returned to his seat, not having uttered a word during the hour-long presentation. His audience greeted the presentation with a standing ovation. Cole later admitted that finding the factors had taken "three years of Sundays."[6]

Cole died alone in New York City, aged 64. The American Mathematical Society's Cole Prize was named in his honor.

Frank Nelson Cole
Frank Nelson Cole
BornSeptember 20, 1861
Ashland, Massachusetts, United States
DiedMay 26, 1926 (aged 64)
New York City, New York, United States
Scientific career
InstitutionsHarvard University
University of Michigan
Columbia University
American Mathematical Society
Doctoral advisorFelix Klein
Doctoral studentsEric Temple Bell
George Abram Miller


  1. ^ a b Fiske, T. S. (1927). "Frank Nelson Cole". Bull. Amer. Math. Soc. 33 (6): 773–777. doi:10.1090/s0002-9904-1927-04477-9. MR 1561460.
  2. ^ "On a Certain Simple Group by F. N. Cole". Mathematical papers read at the International Mathematical Congress held in connection with the World's Columbian Exposition. NY: Macmillan as publisher for the AMS. 1896. pp. 40–43.
  3. ^ Case, Bettye Anne, ed. (1996). "Come to the Fair: The Chicago Mathematical Congress of 1893 by David E. Rowe and Karen Hunger Parshall". A Century of Mathematical Meetings. American Mathematical Society. pp. 67–68.
  4. ^ Gallian, Joseph A. (September 1976). "The Search for Finite Simple Groups" (PDF). Mathematics Magazine. 49 (4): 163–174. doi:10.2307/2690115.
  5. ^ Cole, F. N. (1903), "On the factoring of large numbers", Bull. Amer. Math. Soc., 10: 134–137, doi:10.1090/S0002-9904-1903-01079-9, JFM 34.0216.04
  6. ^ Gridgeman, N (1963), "The search for perfect numbers", New Scientist (334): 86–88

External links


1903 (MCMIII)

was a common year starting on Thursday of the Gregorian calendar and a common year starting on Wednesday of the Julian calendar, the 1903rd year of the Common Era (CE) and Anno Domini (AD) designations, the 903rd year of the 2nd millennium, the 3rd year of the 20th century, and the 4th year of the 1900s decade. As of the start of 1903, the Gregorian calendar was

13 days ahead of the Julian calendar, which remained in localized use until 1923.

1903 in science

The year 1903 in science and technology involved some significant events, listed below.

1903 in the United States

Events from the year 1903 in the United States.

1926 in the United States

Events from the year 1926 in the United States.

Andrei Suslin

Andrei Suslin (Russian: Андре́й Алекса́ндрович Су́слин, sometimes transliterated Souslin) was a Russian mathematician who contributed to algebraic K-theory and its connections with algebraic geometry. He was a Trustee Chair and Professor of mathematics at Northwestern University.He was born on 27 December 1950 in St. Petersburg, Russia. He received his PhD from Leningrad University in 1974; his thesis was titled Projective modules over polynomial rings.In 1976 he and Daniel Quillen independently proved Serre's conjecture about the triviality of algebraic vector bundles on affine space.

In 1982 he and Alexander Merkurjev proved the famous Merkurjev–Suslin theorem on the norm residue homomorphism in Milnor K2-theory, with applications to the Brauer group.

Suslin was an invited speaker at the International Congress of Mathematicians in 1978 and 1994, and he gave a plenary invited address at the Congress in 1986. He was awarded the Frank Nelson Cole Prize in Algebra in 2000 by the American Mathematical Society for his work on motivic cohomology.In 2010 special issues of Journal of K-theory

and of Documenta Mathematica

have been published in honour of his 60th birthday.

He died on 10 July 2018.

Cole Prize

The Frank Nelson Cole Prize, or Cole Prize for short, is one of two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to number theory. The prize is named after Frank Nelson Cole, who served the Society for 25 years. The Cole Prize in algebra was funded by Cole himself, from funds given to him as a retirement gift; the prize fund was later augmented by his son, leading to the double award.To be eligible for the Cole prize, the author must be a member of the American Mathematical Society or the paper should appear in a recognized North American journal. The first award for algebra was made in 1928 to L. E. Dickson, while the first award for number theory was made in 1931 to H. S. Vandiver.

Don Zagier

Don Bernard Zagier (born 29 June 1951) is an American mathematician whose main area of work is number theory. He is currently one of the directors of the Max Planck Institute for Mathematics in Bonn, Germany. He was a professor at the Collège de France in Paris, France from 2006 to 2014. Since October 2014, he is also a Distinguished Staff Associate at ICTP.

George Abram Miller

George Abram Miller (31 July 1863 – 10 February 1951) was an early group theorist.

At age 17 Miller began school-teaching to raise funds for higher education. In 1882 he entered Franklin and Marshall Academy, and progressed to Muhlenberg College in 1884. He received his B.A. in 1887 and M.A. in 1890. While a graduate student, Miller was Principal of schools in Greeley, Kansas and then professor of mathematics as Eureka College in Eureka, Illinois. He corresponded with Cumberland University in Lebanon, Tennessee for his Ph.D. in 1892. He then joined Frank Nelson Cole at University of Michigan and began to study groups. In 1895 he went to Europe where he heard Sophus Lie lecture at Leipzig and Camille Jordan at Paris. In 1897 he went to Cornell University as an assistant professor, and in 1901 to Stanford University as associate professor. In 1906 he went to University of Illinois where he taught until retirement in 1931.Miller helped in the enumeration of finite groups of order 8, 9, and 10. Arthur Cayley had listed 198 groups of order 8 in 1891, and Miller found two more making the total 200 in 1893. Camille Jordan had given a list for order 9 in 1872, re-examined by Cole, and brought up to 258 groups by Miller. In 1894 Miller produced a list of 294 intransitive groups of degree 10. In consequence, the Academy of Science of Cracow awarded a prize and "Miller came to prominence in the mathematical world abruptly."Miller was president of the Mathematical Association of America 1921–1922 and gave a plenary address at the International Congress of Mathematicians in 1924 in Toronto. Miller's Collected Works were edited by Henry Roy Brahana and published by University of Illinois Press, the first two volumes appearing in 1935 and 1939. The final three volumes were published in 1946, 1955, and 1959. His doctoral students include H. L. Rietz.

Harry Vandiver

Harry Schultz Vandiver (21 October 1882 – 9 January 1973) was an American mathematician, known for work in number theory.

He was born in Philadelphia, Pennsylvania to John Lyon and Ida Frances (Everett) Vandiver. He did not complete a formal education, choosing instead to leave school at an early age to work for his father's firm, although he did attend some graduate classes at the University of Pennsylvania in 1904–5.

From 1917 to 1919 he was a member of the United States Naval Reserve, and in 1919 became an instructor of mathematics at Cornell University, where he taught for five years before becoming an associate professor of pure mathematics at the University of Texas in 1924. He was made a full professor the following year, and named distinguished professor of applied mathematics and astronomy in 1947. He remained at Texas until his retirement in 1966.

Vandiver won the Frank Nelson Cole Prize of the American Mathematical Society for his paper on Fermat's Last Theorem in 1931. In 1952 he used a computer to study it, proving the result for all primes less than 2000.A question he frequently asked about the class group of cyclotomic fields, and now known as Vandiver's conjecture, was first posed in an 1849 letter from Ernst Kummer to Leopold Kronecker.

For the academic year 1927–1928 Vandiver received a Guggenheim Fellowship. In 1934 he was elected to the National Academy of Sciences. In 1945 the U. of Pennsylvania gave him an honorary doctoral degree.

Henry Mann

Henry Berthold Mann (27 October 1905, Vienna – 1 February 2000, Tucson)

was a professor of mathematics and statistics at Ohio State University. Mann proved the Schnirelmann-Landau conjecture in number theory, and as a result earned the 1946 Cole Prize. He and his student developed the ("Mann-Whitney") U-statistic of nonparametric statistics. Mann published the first mathematical book on the design of experiments Mann (1949).

Henryk Iwaniec

Henryk Iwaniec (born October 9, 1947) is a Polish-American mathematician, and since 1987 a professor at Rutgers University.

James Ax

James Burton Ax (10 January 1937 – 11 June 2006) was an American mathematician who proved several results in algebra and number theory by using model theory. He shared, with Simon B. Kochen, the seventh Frank Nelson Cole Prize in Number Theory, which was awarded for a series of three joint papers on Diophantine problems.

John R. Stallings

John Robert Stallings Jr. (July 22, 1935 – November 24, 2008) was a mathematician known for his seminal contributions to geometric group theory and 3-manifold topology. Stallings was a Professor Emeritus in the Department of Mathematics at the University of California at Berkeley where he had been a faculty member since 1967. He published over 50 papers, predominantly in the areas of geometric group theory and the topology of 3-manifolds. Stallings' most important contributions include a proof, in a 1960 paper, of the Poincaré Conjecture in dimensions greater than six and a proof, in a 1971 paper, of the Stallings theorem about ends of groups.

List of Cole Prize winners affiliated with the Institute for Advanced Study

This is a comprehensive list of Cole Prize winners affiliated with the Institute for Advanced Study (IAS) in Princeton, New Jersey as current and former faculty members, visiting scholars, and other affiliates. Of the fifty-six mathematicians who have received the Cole Prize as of 2016, thirty-nine have been affiliated with the IAS at some point in their career.The Cole Prize is one of two prizes awarded to mathematicians by the American Mathematical Society.

Peter Scholze

Peter Scholze (born 11 December 1987) is a German mathematician known for his work in algebraic geometry. He has been a professor at the University of Bonn since 2012, and director at the Max Planck Institute for Mathematics since 2018. He has been called one of the leading mathematicians in the world. He won the Fields Medal in 2018, which is regarded as the highest professional honor in mathematics.

Robert Guralnick

Robert Michael Guralnick (born 10 July 1950) is an American mathematician. He works as a Professor of Mathematics at the University of Southern California.Guralnick was elected a Fellow of the American Mathematical Society in 2012, and was awarded the Cole Prize in 2018.

Serge Lang

Serge Lang (French: [lɑ̃ɡ]; May 19, 1927 – September 12, 2005) was a French-American mathematician and activist who taught at Yale University for most of his career. He is known for his work in number theory and for his mathematics textbooks, including the influential Algebra. He received the Frank Nelson Cole Prize in 1960 and was a member of the Bourbaki group. As an activist, he campaigned successfully against the nomination of the political scientist Samuel P. Huntington to the National Academies of Science, and later descended into AIDS denialism, claiming that HIV had not been proven to cause AIDS and protesting Yale's research into HIV/AIDS.

Simon B. Kochen

Simon Bernhard Kochen (; born 14 August 1934, Antwerpen) is a Canadian mathematician, working in the fields of model theory, number theory and quantum mechanics.

Wolfgang M. Schmidt

Wolfgang M. Schmidt (born 3 October 1933, Vienna, Austria) is a mathematician working in the area of number theory. He studied mathematics at the University of Vienna, where he received his PhD, which was supervised by Edmund Hlawka, in 1955. Wolfgang Schmidt is professor at the University of Colorado at Boulder and a member of the Austrian Academy of Sciences and the Polish Academy of Sciences.

This page is based on a Wikipedia article written by authors (here).
Text is available under the CC BY-SA 3.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.