Profession: mathematician

As a young unknown whose work made advances on their own, Jacobi wrote to Gauss and Legendre; both were strongly impressed. He met Legendre in Paris (also Fourier and Poisson), and visited Gauss along the way. Jacobi, recovering from a breakdown, and his close lifelong friend Dirichlet led a posse of mathematician friends (Steiner, Jacobi’s former student Borchardt, with Schläfli as interpreter), on a long recuperative visit to Italy; Humboldt made it financially possible. Hesse was another student, Neumann and Bessel colleagues in Könbigsberg, while Hamilton and Babbage were met in Manchester.

Ohm taught him at school. Studying in Paris, he came into contact with Biot, Legendre, Laplace and Hachette, while meeting Fourier and Poisson stimulated his interest in mathematical physics. Fourier, Humboldt (who encouraged him to return to Germany) and Gauss (whom he eventually succeeded) all helped him in his career. He was Jacobi’s great friend, and Babbage’s guide in Berlin. Riemann (who revered him, and became his colleague) was among his students, who often spent afternoons at ‘Kaffeehaus Dirichlet’. He married the Mendelssohns’ sister and adopted Fanny’s son; Joachim and Scumann played at their parties.

Bossut was taught by d’Alembert, and also encouraged by Clairaut; he collaborated with d’Alembert on mathematical entries for Diderot’s Encyclopédie. Monge, Borda and Coulomb were among his students at the engineering school at Mézières (Monge in particular his protégé). Condorcet worked closely with him, and may have helped get him appointed to a newly-created chair in hydrodynamics, one of his specialisms — research on water-resistance he did with Condorcet and d’Alembert was applied by Fulton, whose steam-boat demonstration on the Seine involved Bossut and others being towed behind — a great success.

Disbarred as a woman from formal study, Germain sent Lagrange a term-paper under a male pseudonym. Greatly impressed by it, he asked to meet its author, was duly astonished to discover her gender, and took her on as his protégée. Cauchy and (especially) Fourier became supportive friends, not least in the face of deliberate frostiness from Poisson and his allies. She wrote to Legendre about number-theory, the ensuing correspondence amounting to a full collaboration. She and Gauss corresponded for some years; she helped ensure his safety, while he proposed her for an honorary degree, the first to a woman.