James Garfield. A former professor of ancient languages, literature, and mathematics who had paid for his first year of college by working as a carpenter, Garfield’s interests and abilities were as deep as they were broad. In fact, so detailed was his interest in mathematics, and so acute his understanding, that he had recently written an original proof of the Pythagorean theorem during a free moment at the Capitol. The New England Journal of Education had published the proof just the month before, transparently astonished that a member of Congress had written it.