Ferdinand Frobenius

Ferdinand Frobenius (1849–1917) was a German mathematician with a rare double gift: he did first-rate work in both the abstract world of group theory and the very practical world of solving differential equations. A demanding, old-school Berlin professor who liked his mathematics pure and exact.

The masterstroke

When a differential equation misbehaves at a point and ordinary tricks fail, the Frobenius method comes to the rescue — a clever recipe for building power series solutions even around awkward "singular" points. His name is also stamped across algebra: Frobenius groups, the Frobenius endomorphism, and theorems about matrices and characters that students meet again and again.

Frobenius was a proud defender of "pure" mathematics done for its own sake, and he could be sniffy about work aimed at applications — he reportedly worried that his beloved Berlin would slide toward being a mere "technical school" if it chased too much practical science. The irony is delicious: his own methods for solving differential equations, and his results on matrices, turned out to be exactly the sort of tools engineers and physicists now can't live without. Pure maths has a funny habit of becoming useful whether its inventor likes it or not.