"As a fencer, if you are going to make a guess about an opponent, then it's best to use a math-type skill," said Dr. John Heil, a sports psychologist and the chairman of the Sports Science, Safety and Technology Committee for the U.S. Fencing Association. "You think of your body as a box. You're very much visualizing lines in space."
Fencing in particular teaches students about center of gravity, force, motion and other mathematical principles by experiencing them physically, according to Dr. Penny Hammrich, founder of Sisters/Brothers in Sports Science.
Frank Mustilli, who has coached fencers for more than 40 years, teaches his pupils to count the seconds of an attack in their heads, to form letters and numbers with their weapons to defend and attack, and to mentally divide the remaining match time on the clock to strategize.