Frank Nelson Cole (September 20, 1861 – May 26, 1926) was an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

Life and works

Cole was born in Ashland,

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. When he was very young, the family moved to Marlborough, Massachusetts where he attended school and graduated from

Marlborough High School Marlborough High School is a secondary school in Zimbabwe which is located in a Harare suburb called Marlborough. Marlborough is to the north of Harare City Centre and lies between the roads leading to Chinhoyi and Bindura from Harare. Marlboroug ...

. He was then educated at Harvard, where he lectured on mathematics from 1885 to 1887. Later, he was employed at the

University of Michigan , mottoeng = "Arts, Knowledge, Truth" , former_names = Catholepistemiad, or University of Michigania (1817–1821) , budget = $10.3 billion (2021) , endowment = $17 billion (2021)As o ...

and

Columbia University Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhatt ...

. Professor Cole became secretary of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

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). 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 The World's Columbian Exposition (also known as the Chicago World's Fair) was a world's fair held in Chicago in 1893 to celebrate the 400th anniversary of Christopher Columbus's arrival in the New World in 1492. The centerpiece of the Fair, hel ...

. On October 31, 1903, Cole famously made a presentation to a meeting of the

where he identified the factors of the

Mersenne number In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th ...

2⁶⁷ − 1, or M₆₇.

Édouard Lucas __NOTOC__ François Édouard Anatole Lucas (; 4 April 1842 – 3 October 1891) was a French mathematician. Lucas is known for his study of the Fibonacci sequence. The related Lucas sequences and Lucas numbers are named after him. Biography 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".. Cole died alone in

New York City New York, often called New York City or NYC, is the most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the most densely populated major city in the Un ...

, aged 64. The American Mathematical Society's Cole Prize was named in his honor.

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External links

* * * {{DEFAULTSORT:Cole, Frank Nelson 1861 births 1926 deaths 19th-century American mathematicians 20th-century American mathematicians Columbia University faculty Harvard College alumni People from Ashland, Massachusetts University of Michigan faculty