Profession: mathematician

Abel, who died at 26, was one of the most significant mathematicians of the 19th C. In Berlin, he helped inspire the founding of Crelle’s journal, and contributed several papers. Gauss dismissed the proof he sent, and they never met. In Paris, Abel met Hachette and Dirichlet, and in particular Legendre and Cauchy; Legendre (who liked him) described a paper of his as monumental, but passed it to Cauchy, who lost it (Abel considered him mad and bigoted). Jacobi was a mathematical rival. Abel’s friend Crelle tried hard to find a university post for him, succeeding only when he was terminally ill.

Dedekind made notable contributions to set theory and number theory. Gauss’s last student, he was was also taught by Weber. Riemann was a fellow-student, lifelong friend and professional colleague; visiting Berlin together, they met Borchardt, Kummer and Weierstrass. Gauss’s successor Dirichlet also became a close friend as well as professional colleague; Dedekind published the work of both, and of Riemann, posthumously. Cantor was met on holiday in Switzerland; they became correspondents and friends for life, although it has been suggested that latterly they were unnecessarily reserved about sharing ideas with one another.

Gauss and Weber taught Riemann, one of the most important mathematicians of the 19thC, Gauss encouraging his famous work on the foundations of geometry. He also studied with Dirichlet and Eisenstein (both influential), and with Steiner and Jacobi. As Weber’s assistant, he helped with his and Kohlrausch’s research. Listing influenced his ideas about topology. Dedekind, a friend from student days, went to the Harz with him, and edited his work for publication after his early death. He met Kummer and Weierstrass in Berlin, Hermite and Bertrand in Paris, and stayed with Betti in Italy. Borchardt was his greatest correspondent.

Taurinus, who had studied law not mathematics, developed ideas with (but also beyond) his young uncle F. K. Schweikart; though little-known, he is a significant figure in the development of non-Euclidean geometry, a subject of mutual interest that he discussed with his correspondent Gauss. Though Gauss encouraged Taurinus in his work (while claiming to have developed similar ideas years previously), he also asked him not to reveal their discussions. Taurinus did however do so when he published his book; it was nevertheless a flop, with Taurinus having all unsold copies burned.

Bolyai and Gauss met as students in Göttingen. Bolyai had gone to Germany to study; they became lifelong friends. After Bolyai returned home, his life had few consolations other than his own work and his continuing correspondence with Gauss, even his relationship with his mathematician son János being a difficult one; he spoke about a “permanently overcast sky” after the promise of “beautiful days” in Germany.