Mathematics Genealogy Project
Frank Nelson Cole
BiographyMathSciNet
Advisor: C. Felix (Christian) Klein
Students:
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According to our current on-line database, Frank Cole has 3 students and descendants.
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Factors of Mersenne Number M67/Historical Note
Historical Note on Factors of Mersenne Number $M_{67}$
While François Édouard Anatole Lucas had demonstrated in $$ that $M_{67}$ is composite, he had not established what its divisors are.
The Factors of Mersenne Number $M_{67}$ were demonstrated by Frank Nelson Cole in a famously dramatic presentation On The Factorization of Large Numbers to a meeting of the American Mathematical Society in October $$.
When called to give his lecture, he walked to the blackboard, and worked out the calculation, longhand, of $2^{67}$. Then he carefully subtracted $1$.
Moving to another area of the board, he then multiplied out $, , \times , , , $.
The numbers matched.
Cole returned to his seat to thunderous applause, having delivered the only lecture in history in which not a word was spoken.
When asked how long it had taken him to find these factors, he reportedly replied:
- Three years of Sundays.
It is noted that Marin Mersenne had originally listed $M_{67}$ as one of the integers of the form $2^p - 1$ to be prime.
Sources
Who was Frank Nelson Cole?
Frank Nelson Cole, Ph.D. was an American mathematician, born in Ashland, Massachusetts, and educated at Harvard, where he lectured on mathematics from to
Later, he was employed at the University of Michigan and Columbia University. Professor Cole becamesecretary of the AmericanMathematicalSociety in and an editor of its Bulletin in
Cole published a number of important papers, including The Diurnal Variation of Barometric Pressure.
In 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. Édouard Lucas had demonstrated in that M₆₇ must have factors, 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 ,,,,,, Cole then moved to the other side of the board and wrote ,, × ,,,, and worked through the tedious calculations by hand.
- Born
- Sep 20,
Ashland - Also known as
- Nationality
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- Education
- Employment
- University of Michigan
- Columbia University
- Harvard University
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Frank Nelson Cole
Quick Info
- Born
- 20 September
Ashland, Massachusetts, USA- Died
- 26 May
New York, USA- Summary
- Frank Cole was an American mathematician whose main research contributions are to number theory, in particular to prime numbers, and to group theory.
Biography
Frank Cole's parents were Frances Maria Pond and Otis Cole who came from a family which had been living in Rehoboth, Massachusetts, since the 17th century. Otis Cole was a farmer, a dealer in lumber having an involvement in manufacturing, who also had an interest in mathematics. After Frank graduated from High School in Marlboro, Massachusetts, he was privately tutored before he entered Harvard University in 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 , but also a Parker Travelling Fellowship which paid for him to visit Leipzig during when he studied under Klein. The period spent with Klein was very profitable despite Klein's health being poor during this time when he suffered badly from depression. Cole also spent some time at Göttingen during these years spent in Germany and met there his futur
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