Fuchs was born in Moschin, Germany (now part of Poland). Little is documented about his earlier life, but it is his contribution to mathematics for which he is best remembered. He was first educated in Berlin at the Friedrich Wilhelm Gymnasium, later studying at the University of Berlin. It was from this point that mathematics was identified as Fuchs’s greatest ability, and his main passion.
While at University Fuchs was taught by Weierstrass, one of the leaders in mathematics at the time, and who was to be an inspiration in Fuchs’s study of function theory. Weierstrass also assisted Fuchs with his degree which he received in 1858.
It was over the next few years that Fuchs’s long-term ambition of becoming a university professor began to be realised, firstly teaching at a Gymnasium, and moving next to the Friedrich Werderschen Trade School. His university teaching career began as an unpaid lecturer (a Privatdozen) in Berlin, and he achieved a full professorship in 1866, staying until 1868. Fuchs also held a second appointment during this time in Berlin, again teaching mathematics, at the Artillery and Engineering School.
After holding posts at Göttingen and Heidelberg, he returned to Berlin in 1884 to take the ‘chair’ of Kummer, another former teacher, upon his retirement. Fuchs was to remain in this post until his death in 1902.
Fuchs lasting contribution to mathematics came in the form of Fuchsian equations and equations of the Fuchsian class, these terms were first used by Poincaré which was of significant importance to his work on automorphic functions.