John Howard Redfield

John Howard Redfield (1879–1944) was an American mathematician, best known for discovery of what is now known as Pólya enumeration theorem (PET) in 1927, ten years ahead of similar but independent discovery made by George Pólya. John Howard Redfield was a great-grandson of William Charles Redfield, one of the founders and the first president of AAAS.

During much of his life John Howard Redfield earned his living as an engineer but his main interests lay elsewhere. He performed and wrote music and was a gifted linguist, familiar with almost all European languages, as well as with some African and Asian tongues. In middle age he turned his attention towards combinatorial mathematics but it was not until many years after his death that the mathematical world realized that he had obtained significant results.cite journal | last = Lloyd | first = E. Keith | title = J. Howard Redfield 1879-1944 | journal = Journal of Graph Theory | volume = 8 | year = 1984 | issue = 2 | pages = 195-203 | url = http://doi.wiley.com/10.1002/jgt.3190080203 | doi = 10.1002/jgt.3190080203]

Solution to MacMahon's conjecture

Redfield's ability can be esteemed from the letter exchange between Redfield, Percy MacMahon, and Sir Thomas Muir, 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. [cite journal| author=MacMahon, P. A. |title=The Structure of a Determinant| journal=Journal London Mathematical Society |year=1927 |volume=s1-2 |issue=4 |pages=273-286|url=http://intl-jlms.oxfordjournals.org/cgi/reprint/s1-2/4/273.pdf] 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 [2] .

Redfield's contemporaries on him

A letter from Professor Cletus Oakley to Frank Harary, 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, 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

# cite journal
last = Redfield
first = J. Howard
title = The Theory of Group-Reduced Distributions
journal = American Journal of Mathematics
volume = 49
year = 1927
issue = 3
pages = 433–455
url = http://www.jstor.org/stable/2370675
doi = 10.2307/2370675
id = MathSciNet | id = 1506633
# cite journal
last = Redfield
first = J. Howard
title = Enumeration by frame group and range groups
journal = Journal of Graph Theory
volume = 8
year = 1984
issue = 2
pages = 205-223
url = http://doi.wiley.com/10.1002/jgt.3190080204
doi = 10.1002/jgt.3190080204 : Publication [2] 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 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. [cite journal | author = Frank Harary and Robert W. Robinson | title = The rediscovery of Redfield's papers | journal = Journal of Graph Theory | volume = 8 | year = 1984 | issue = 2 | pages = 191-193 | url = http://doi.wiley.com/10.1002/jgt.3190080202 | doi = 10.1002/jgt.3190080202]

References