John Lewis Selfridge (February 17, 1927 in Ketchikan, Alaska – October 31, 2010 in DeKalb, Illinois), was an American mathematician who contributed to the fields of analytic number theory, computational number theory, and combinatorics. He co-authored 14 papers with Paul Erdős (giving him an Erdős number of 1).Selfridge received his Ph.D. in 1958 from the University of California, Los Angeles under the supervision of Theodore Motzkin.In 1962, he proved that 78,557 is a Sierpinski number; he showed that, when k=78,557, all numbers of the form k2n + 1 have a factor in the covering set {3, 5, 7, 13, 19, 37, 73}. Five years after, he and Sierpiński proposed (but could not prove) the conjecture that 78,557 is the smallest Sierpinski number, and thus the answer to the Sierpinski problem. A distributed computing project called Seventeen or Bust is currently trying to prove this statement, as of January 2011 only six of the original seventeen possibilities remain.In 1975 John Brillhart, Derrick Henry Lehmer and Selfridge developed a method of proving the primality of p given only partial factorizations of p − 1 and p + 1. Together with Samuel Wagstaff they also all participated in the Cunningham project.Together with Paul Erdős, Selfridge solved a 250 year old problem, proving that the product of consecutive numbers is never a power. It took them many years to find the proof and John made extensive use of computers, but the final version of the proof requires only a modest amount of computation, namely evaluating a function f(n) for 30,000 values of n. Selfridge suffered from Writer's block and paid a former student to write up the result, even though it is only two pages long.As a mathematician, Selfridge was one of the most effective number theorists with a computer. He also had a way with words and coined a useful phrase to describe the exploratory phase of a computer investigation. On the occasion that Samuel Wagstaff, another very effective number theorist when using a computer, was lecturing at the annual Bloomington Illinois Number Theory Conference on the early stages of his now well known computer investigations into Fermat's Last Theorem, at question time someone asked a little too pointedly what methods Wagstaff had used and kept insisting on an answer. Wagstaff stood there like a deer blinded in headlights, totally at a loss what to say, until Selfridge helped him out. "He used the principle of computer fooling-aroundedness," Selfridge said. Selfridge also developed the Selfridge–Conway discrete procedure for creating an envy-free division of a resource among three people. Selfridge developed this in 1960, and John Conway independently discovered it in 1993. Neither of them ever published the result, but Richard Guy told many people Selfridge's solution in the 60s, and it was eventually attributed to them in a number of books. Selfridge served on the faculties of the University of Illinois at Urbana-Champaign and Northern Illinois University from 1971 to 1991 (retirement), chairing the Department of Mathematical Sciences 1972–1976 and 1986–1990.He was executive editor of Mathematical Reviews from 1978 to 1986, overseeing the computerization of its operations [1]. He was a founder of the Number Theory Foundation [2], which has named its Selfridge prize in his honour.
Fecha de nacimiento
1927-02-17
Año de nacimiento
1927
Fecha de defunción
2010-10-31
Año de defunción
2010
Comentar
0