In August of last year, mathematician Shinichi Mochizuki reported that he had solved one of the great puzzles of number theory: the ABC conjecture (previously on Metafilter). Almost a year later, no one else knows whether he has succeeded. No one can understand his proof.
Crispin Sartwell is a cryptic and sensational man. The Chair of Humanities and Sciences at the Maryland Institute College of Art, he has translated the Tao Te Ching, published philosophy papers and books, maintained pages on hip hop, founded the American Nihilist Party (and gave a speech to young Democrats urging them to reconsider their votes for John Kerry), taught courses on conjuring and illusion, etc. etc. See also his essay on the pagan cult of mathematics and his thought experiment on music.