September 19, 2003
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The Mysteries of 26
My entry of May 26, 2003 —
dealt with the question of whether this number, said to be of significance (as a number of dimensions) in theoretical physics, has any purely mathematical properties of interest.
That entry contained the above figure, a so-called Levi graph illustrating point/line incidence in the finite projective plane with 13 points and 13 lines, PG(2,3).
It turns out that in a paper of April 7, 2000, John H. Conway and Christopher S. Simons discussed a close connection between this plane and the Monster group. See
(Journal of Algebra. Vol. 235, no. 2.
MR 2001k:20028).
Conway had written about such a connection as early as 1985.
I apologize for not knowing about this sooner, and so misleading any mathematical readers about the number 26, which it seems does have considerable purely mathematical significance.
