John Howard Redfield

John Howard Redfield (June 8, 1879 – April 17, 1944) 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.

Redfield's ability is evident in letters exchanged among Redfield, Percy MacMahon, and Sir Thomas Muir, following the publication of Redfield's 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far as is known, Redfield did not follow up this suggestion, but the proof of MacMahon's conjecture was included in an unpublished manuscript which appears to be a sequel to the paper [3].

A letter from Professor Cletus Oakley to Frank Harary, 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):

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