Ferdinand Joachimsthal attended school at Liegnitz (now Legnica, Poland) where he was taught by Kummer. In 1836 he entered the University of Berlin where he was taught by Dirichlet and Steiner.
From 1838 he studied at the University of Königsberg where his teachers included Jacobi and Bessel. After taking his first degree he went to Halle to undertake research and obtained a doctorate from there in 1840.
From 1844 Joachimsthal taught in Berlin at the Konigliche Realschule. From 1847 he taught at the Collège Royal Français in Berlin where he was appointed a professor in 1852. He also taught at the University of Berlin from 1845.
At the University of Berlin Joachimsthal taught courses on analytic geometry and calculus, giving more advanced courses on the theory of surfaces, the calculus of variations, statics and analytic mechanics. His is famed for the high quality of his lectures. His colleagues included many famous mathematicians who all contributed to his development of mathematical ideas, in particular Eisenstein, Dirichlet, Jacobi, Steiner and Borchardt.
Joachimsthal was appointed to a chair in Halle in 1853, then he became Kummer's successor at Breslau in 1855 where again he acquired a high reputation for teaching. His high quality teaching extended to the textbooks which he wrote, these are famed for their clarity of exposition.
Influenced by the work of Jacobi, Dirichlet and Steiner, Joachimsthal wrote on the theory of surfaces where he made substantial contributions, particularly to the problem of normals to conic sections and second degree surfaces.
Joachimsthal applied the theory of determinants to geometry. He made the important step of introducing oblique coordinates. Joachimsthal surfaces are named after him, these have a family of plane lines of curvature within the plane of a pencil. He has a theorem named after him which concerns the intersection of surfaces. He is also remembered for another theorem on the four normals to an ellipse from a point inside it.
Of course his determination that his works should be of the very highest standard meant there was a price to pay. As stated in :-
His marked predilection for mature, polished exposition was expressed in constant recasting, revising and rewriting, so that many planned works never reached completion.
Article by: J J O'Connor and E F Robertson