The Mysteries of 26

My entry of May 26, 2003 —

Many Dimensions — Why 26? —

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

26 Implies the Bimonster 

(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.