J. H. Redfield
Encyclopedia
John Howard Redfield was an American
mathematician
, best known for discovery of what is now called Pólya enumeration theorem
(PET) in 1927, ten years ahead of similar but independent discovery made by George Pólya
. Redfield was a great-grandson of William Charles Redfield
, one of the founders and the first president of AAAS
.
, followed publication of Redfield paper [1] in 1927. Apparently Redfield sent a copy of his paper to MacMahon. In reply (letter of November 19, 1927), MacMahon expresses the view that Redfield has made a valuable contribution to the subject and goes on to mention a conjecture which he himself made in his recently delivered Rouse-Ball memorial lecture. He also says that it is probable that Redfield's work would lead to a proof of it. Such was the case: in a draft reply dated December 26, 1927, Redfield writes:
MacMahon, who had failed to prove it himself and then put the matter before men at both Cambridge and Oxford "without effect", delightedly wrote to Redfield (letter of January 9, 1928):
MacMahon urged Redfield to publish his new results and also informed Muir about them. In a letter to Redfield dated December 31, 1931, Muir also encourages him to publish his verification "without waiting for MacMahon's executors" and suggests the Journal of the London Mathematical Society as an appropriate medium. As far as is known, Redfield did not follow up this suggestion, but the proof of MacMahon's conjecture was included in an unpublished manuscript which appears to be a sequel to the paper [3].
, dated December 19, 1963, reads in part:
Redfield's brother, Alfred, a marine biologist-oceanographer and former Associate Director of the Woods Hole Oceanographic Institution
, wrote (letter to E. Keith Lloyd, September 8, 1976):
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, best known for discovery of what is now called Pólya enumeration theorem
Pólya enumeration theorem
The Pólya enumeration theorem , also known as the Redfield–Pólya Theorem, is a theorem in combinatorics that both follows and ultimately generalizes Burnside's lemma on the number of orbits of a group action on a set. The theorem was first published by John Howard Redfield in 1927...
(PET) in 1927, ten years ahead of similar but independent discovery made by George Pólya
George Pólya
George Pólya was a Hungarian mathematician. He was a professor of mathematics from 1914 to 1940 at ETH Zürich and from 1940 to 1953 at Stanford University. He made fundamental contributions to combinatorics, number theory, numerical analysis and probability theory...
. Redfield was a great-grandson of William Charles Redfield
William Charles Redfield
William Charles Redfield was one of the founders and the first President of the American Association for the Advancement of Science formed in 1848....
, one of the founders and the first president of AAAS
American Association for the Advancement of Science
The American Association for the Advancement of Science is an international non-profit organization with the stated goals of promoting cooperation among scientists, defending scientific freedom, encouraging scientific responsibility, and supporting scientific education and science outreach for the...
.
Solution to MacMahon's conjecture
Redfield's ability can be esteemed from the letter exchange between Redfield, Percy MacMahon, and Sir Thomas MuirThomas Muir (mathematician)
Sir Thomas Muir FRS was a Scottish mathematician, remembered as an authority on determinants. He was born in Stonebyres in South Lanarkshire, and brought up in the small town of Biggar. At the University of Glasgow he changed his studies from classics to mathematics after advice from the future...
, followed publication of Redfield paper [1] in 1927. Apparently Redfield sent a copy of his paper to MacMahon. In reply (letter of November 19, 1927), MacMahon expresses the view that Redfield has made a valuable contribution to the subject and goes on to mention a conjecture which he himself made in his recently delivered Rouse-Ball memorial lecture. He also says that it is probable that Redfield's work would lead to a proof of it. Such was the case: in a draft reply dated December 26, 1927, Redfield writes:
- "I am now able to demonstrate your conjectured expression...".
MacMahon, who had failed to prove it himself and then put the matter before men at both Cambridge and Oxford "without effect", delightedly wrote to Redfield (letter of January 9, 1928):
- "when you first wrote to me I formed the opinion that with your powerful handling of the theory of substitutions it would be childs play to you and I was right. I congratulate you and feel sure that your methods will carry you far."
MacMahon urged Redfield to publish his new results and also informed Muir about them. In a letter to Redfield dated December 31, 1931, Muir also encourages him to publish his verification "without waiting for MacMahon's executors" and suggests the Journal of the London Mathematical Society as an appropriate medium. As far as is known, Redfield did not follow up this suggestion, but the proof of MacMahon's conjecture was included in an unpublished manuscript which appears to be a sequel to the paper [3].
Redfield's contemporaries on him
A letter from Professor Cletus Oakley to Frank HararyFrank Harary
Frank Harary was a prolific American mathematician, who specialized in graph theory. He was widely recognized as one of the "fathers" of modern graph theory....
, dated December 19, 1963, reads in part:
- "I knew him from about 1938-1944. Indeed in 1940 he came to Haverford College and gave us some lectures on 'Electronic Digital Computers' (this was slightly before Eckert-Mauchly). Knowing him as I did in those later years, I could well understand how he would not make a great teacher. He was completely off in the clouds at all times. He never looked at you, he spoke softly with his eyes on the floor, he worked with his back to you and wrote on the board. His board work, however, was impeccable. It could have been photographed and printed by photo offset it was so perfect."
- "He came to Haverford to talk to our math club many times and always had something new to say..."
Redfield's brother, Alfred, a marine biologist-oceanographer and former Associate Director of the Woods Hole Oceanographic Institution
Woods Hole Oceanographic Institution
The Woods Hole Oceanographic Institution is a private, nonprofit research and higher education facility dedicated to the study of all aspects of marine science and engineering and to the education of marine researchers. Established in 1930, it is the largest independent oceanographic research...
, wrote (letter to E. Keith Lloyd, September 8, 1976):
- "During the later years of his life, he turned to mathematics and I usually found him working at it when I called on him. It was evident that this was his true love."
Publications
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- This publication is based on a manuscript discovered in Redfield's legacy by his daughter. The correspondence found with the manuscript revealed that it had been submitted for publication in the American Journal of MathematicsAmerican Journal of MathematicsThe American Journal of Mathematics is a bimonthly mathematics journal published by the Johns Hopkins University Press.- History :The American Journal of Mathematics is the oldest continuously-published mathematical journal in the United States, established in 1878 at the Johns Hopkins University...
on October 19, 1940 and was rejected by the editors in a brief letter of January 7, 1941. Redfield answered the objections of the referee in great detail ten days later and asked specific questions, but he never received a reply to his rebuttal. Apparently it was not subsequently resubmitted elsewhere. The significance of this paper is discussed in.
- This publication is based on a manuscript discovered in Redfield's legacy by his daughter. The correspondence found with the manuscript revealed that it had been submitted for publication in the American Journal of Mathematics
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- This publication represents a typescript of a lecture delivered by Redfield in 1937. According to Lloyd, “The text of Redfield's lecture is very readable, and anyone wishing to study his work would be well advised to read the lecture before passing on to his 1927 and 1940 papers.”
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