Daniel Bernoulli was one of the founders of mathematical physics. His father Johann taught him, but (over-competitive and jealous) tried to claim the honours for Daniel’s work on hydrodynamics. Goldbach, Clairaut, Maupertuis and Euler were all close mathematical friends of Bernoulli’s, living fruitfully intertwined lives. Euler, a friend from youth, lodged and worked with him in St Petersburg (he was asked to bring tea, coffee and brandy from Switzerland). Goldbach helped him get an early paper published, and like Lagrange and Clairaut, kept up an important correspondence. König was one of his students.
Tait worked across boundaries, and is especially known for his work on the mathematics of knots and a book written with Thomson. He and his friend from schooldays on, Maxwell, lived intertwined lives, with their friend Thomson often a third strand. Dewar was another collaborator. Hamilton, correspondent and friend, was an important influence. Inclined to let heart rule head, Tait got into unwinnable arguments with Cayley, Tyndall, Heaviside and (in print) Clausius. He played golf with Helmholtz (baffled by it), and with Huxley and Crum Brown (whose hand got burned by their phosphorescent night-time ball).
Thomson’s importance lay in his attempts to unify electromagnetic and thermodynamic theory, and to apply theory to practice. As a young graduate he worked in Regnault’s lab, as Foucault also did, and met with Biot, Cauchy, Liouville (an especially encouraging friend) and Sturm for good stimulating mathematical/scientific discussion. Stokes (met like Cayley at Cambridge) and Joule were long-term friends and collaborators of Thomson’s, while both Maxwell and Faraday did notable work stimulated by him. Tesla (whom he greatly admired), Edison and Westinghouse were all met in New York, while Helmholtz, a good friend, visited Thomson in Scotland.