Frank Nelson Cole

Life and works[edit]

Cole was born in Ashland, Massachusetts. When he was very young, the family moved to Marlborough, Massachusetts where he attended school and graduated from Marlborough High School. He was then educated at Harvard, where he lectured on mathematics from 1885 to 1887.


Later, he was employed at the University of Michigan (from 1888 to 1895) and Columbia University^[1] (from 1895 until his death in 1926). Professor Cole became the Secretary of the American Mathematical Society in 1895 and an editor of the Bulletin of the AMS 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 in New York City, aged 64. The American Mathematical Society's Cole Prizes in Algebra and Number Theory are named in his honor.