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Frank Cole's father was a farmer who was interested in mathematics. After Frank graduated from High School he was privately tutored before he entered Harvard in 1878. There his ability was recognised at once and he was awarded scholarships which not only helped him while studying for his A.B., awarded in 1882, but also paid for him to visit Leipzig during 1883-85 when he studied under Klein.
Cole returned to Harvard and wrote a thesis on the general equation of the 6 th degree which he presented for his Ph.D. which was awarded in 1886. While writing his doctoral thesis Cole had already begun to lecture at Harvard and he continued to lecture there until 1887. In 1888 he was appointed instructor at the University of Michigan, soon being promoted to assistant professor.
In 1895 Cole was appointed professor at Columbia University, a post which he held until his death. Soon after he arrived at Columbia University he was appointed as Secretary of the American Mathematical Society and he held this post from 1896 until 1920. This was not his only work for the American Mathematical Society for in 1897 he was appointed as Editor-in Chief of the Bulletin of the American Mathematical Society, holding this position until just before his death.
His main research contributions are to number theory, in particular to prime numbers, and to group theory. In number theory he achieved the distinction of being the first to factor 2 - 1 and he did this using quadratic remainders. In fact
2 - 1 = 147573952589676412927= 761838257287 * 193707721
which a computer will compute in a few seconds today.
He established the Frank Nelson Cole Prizes in algebra and number theory and today these are highly prestigious awards. Cole is described by David Eugene Smith in  as follows:-
As a man Cole was admired by all who penetrated a certain reserve that was natural to him, as an executive he was faithful to every duty, as a teacher he was lavish of the time that he would give to those who proved their worth, and as a friend he was loyal to the last. He loved to take long walks in the country studying trees and wild flowers.In fact Cole took his love of trees and wild flowers from his father, and in fact inherited his love of mathematics from the same source.
Osgood and M Bôcher were among his students.
References (4 books/articles)
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