Joseph Plateau

1801 (Brussels) – 1883 (Ghent, Belgium)

Plateau is known for his research into vision and into the mathematics of soap-film surfaces, and for the development of early cinematic devices. Quetelet taught and befriended him, drew him into his scientific circle, and was generally strongly influential. Plateau met Arago in France, while sourcing good laboratory equipment (he probably met his fellow-researcher into colour, Chevreul, on the same trip). He adapted ideas of Faraday’s and Roget’s, Faraday — a friend — writing sympathetically in his blindness. Despite Plateau’s staring into the sun for experimental purposes, his eventual blindness probably had other primary causes.

John Herschel

1792 (Slough, England) – 1871 (Hawkhurst)

Herschel, the first to properly map the southern hemisphere stars, also gave the world clear photographic terminology and a number of significant processes. His father William and aunt Caroline were both important influences. He studied alongside Babbage (a close friend and fellow-worker for life), Peacock and Whewell. Darwin, Sedgwick, Lyell and Cameron were all good friends. He showed another friend, Talbot, whom he’d met while both were visiting Fraunhofer, how to fix his pioneering images. Faraday and he, Royal Society colleagues, were warm to one another, while Wollaston helped him find his real métier.

Mary Somerville

1780 (Jedburgh, Scotland) – 1872 (Naples)

Somerville’s importance is as a connectionist and interpreter of maths and science, and as a trailblazer for other women. Nasmyth taught her painting; a chance comment of his set her off studying geometry. Brewster, Scott and Playfair (who encouraged her) were close Edinburgh friends. In London, she introduced Lovelace to Babbage, was strongly supported by John Herschel, and met Arago and Biot (who introduced her to leading colleagues in Paris). Laplace, whose work she translated and elucidated, said she was one of only two women to understand it. She had an extensive circle of friends from Italy to America.

Niels Abel

1802 (Nedstrand, Norway) – 1829 (Froland)

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.

Richard Dedekind

1831 (Braunschweig, Germany) – 1916 (Braunschweig)

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.

Richard Dedekind knew…

Bernhard Riemann

Bernard Riemann

1826 (Breselenz, Germany) – 1866 (Selasca, Italy)

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.

Bernhard Riemann knew…

August Möbius

August Ferdinand Möbius;August Moebius

1790 (Schulpforta, Germany) – 1868 (Leipzig)

Möbius made significant contributions to the then-young field of topology. Although he was primarily a mathematician, his two most influential teachers were both in astronomy; of them Mollweide’s interests overlapped sympathetically with those of Möbius, while the other — Gauss — was quite simply the greatest mathematician of his time. Grassmann submitted work to Möbius for his doctorate, but Möbius failed to understand its implications; however he later awarded Grassmann a prize (from a field of one).

August Möbius knew…

Franz Taurinus

Franz Adolph Taurinus

1794 (Bad König, Germany) – 1874 (Köln)

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.

Franz Taurinus knew…

Farkas Bolyai

Wolfgang Bolyai

1775 (Bolya, Hungary, now Buia, Romania) – 1856 (Marosvásáhrely, now Târgu Mureş)

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.

Farkas Bolyai knew…

August Leopold Crelle

1780 (Eichwerder, Germany) – 1855 (Berlin)

Crelle’s genius was as a mathematical talent-spotter and disseminator of others’ work. Abel was a particular protégé, who with Steiner helped inspire the publication of Crelle’s important journal. Others he took up personally were Eisenstein and Plücker, while the likes of Möbius, Lobachevsky, Grassmann, Weierstrass and Hesse all had important early exposure through his efforts. Jacobi was also very close. Humboldt was a strong supporter, and invited him to breakfast when Gauss wanted to meet Babbage. Ampère, Legendre and Talbot were all correspondents. Poncelet called him “honourable and knowledgeable.”