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, mathematical structure, structure, space, Mathematica ...

. He is most famous for discovering 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 17t ...

2⁶⁷ − 1.

Life and works

Cole was born in Ashland,

Massachusetts Massachusetts ( ; ), officially the Commonwealth of Massachusetts, is a U.S. state, state in the New England region of the Northeastern United States. It borders the Atlantic Ocean and the Gulf of Maine to its east, Connecticut and Rhode ...

. 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 Harvard University is a private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher lear ...

, where he lectured on

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

from 1885 to 1887. Later, he was employed at the

University of Michigan The University of Michigan (U-M, U of M, or Michigan) is a public university, public research university in Ann Arbor, Michigan, United States. Founded in 1817, it is the oldest institution of higher education in the state. The University of Mi ...

(from 1888 to 1895) and

Columbia University Columbia University in the City of New York, commonly referred to as Columbia University, is a Private university, private Ivy League research university in New York City. Established in 1754 as King's College on the grounds of Trinity Churc ...

(from 1895 until his death in 1926). Professor Cole became the 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 the Bulletin of the AMS 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 from May 5 to October 31, 1893, to celebrate the 400th anniversary of Christopher Columbus's arrival in the New World in 1492. The ...

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

where he identified the factors of the

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 Luc ...

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 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 in

New York City New York, often called New York City (NYC), is the most populous city in the United States, located at the southern tip of New York State on one of the world's largest natural harbors. The city comprises five boroughs, each coextensive w ...

, aged 64. The American Mathematical Society's Cole Prizes in Algebra and Number Theory are named in his honor.

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* * * {{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

Life and works

Notes

See also

External links