Carl Gustav Jacob Jacobi

Carl Gustav Jacob Jacobi (1804–1851) was a German mathematician bursting with energy, wit, and opinions. He worked ferociously, produced ideas faster than most people could read them, and turned Königsberg into a buzzing hub of research. His motto for how to make discoveries was gloriously blunt: "Man muss immer umkehren" — "you must always invert" — meaning, when a problem is stuck, flip it around and look from the other side.

The lasting legacy

Jacobi's name is scattered across maths like confetti. In number theory he generalised Legendre's notation into the Jacobi symbol, which extends the "is it a square?" question to any odd modulus and makes computations wonderfully quick. Elsewhere you meet the Jacobian matrix and determinant in calculus, Jacobi's elliptic functions, and the Jacobi method for solving equations — a suspicious number of things named after one man.

When a government official grumbled that Jacobi's pure mathematics was useless compared to practical science, Jacobi shot back that the true glory of the human spirit is to seek knowledge for its own honour — a chemist should not sneer at a number theorist any more than the reverse. He also famously teased that Fourier thought the whole point of maths was public usefulness, when really "the honour of the human mind" was reason enough. Jacobi never lacked a sharp reply.