  We establish a precise correspondence between the ABC Conjecture and N=4
super-Yang-Mills theory.
  This is achieved by combining three ingredients: (i) Elkies' method of
mapping ABC-triples to elliptic curves in his demonstration that ABC implies
Mordell/Faltings; (ii) an explicit pair of elliptic curve and associated Belyi
map given by Khadjavi-Scharaschkin; and (iii) the fact that the bipartite
brane-tiling/dimer model for a gauge theory with toric moduli space is a
particular dessin d'enfant in the sense of Grothendieck.
  We explore this correspondence for the highest quality ABC-triples as well as
large samples of random triples. The Conjecture itself is mapped to a statement
about the fundamental domain of the toroidal compactification of the string
realization of N=4 SYM.
