Johann Friedrich Pfaff - Biography

Biography

He received his early education at the Carlsschule, where he met Friedrich Schiller, his lifelong friend. His mathematical capacity was noticed during his early years. He pursued his studies at Göttingen under Abraham Gotthelf Kästner, and in 1787 he went to Berlin and studied practical astronomy under J. E. Bode. In 1788 Pfaff became professor of mathematics in Helmstedt, and so continued until that university was abolished in 1810, when he became professor of mathematics at the University of Halle, where he stayed for the rest of his life.

He studied mathematical series and integral calculus, and is noted for his work on partial differential equations of the first order (Pfaffian systems as they are now called) which became part of the theory of differential forms; and as Carl Friedrich Gauss's formal research supervisor. He knew Gauss well, when they both lived together in Helmstedt in 1798. August Möbius was later his student.

His two principal works are Disquisitiones analyticae maxime ad calculum integralem et doctrinam serierum pertinentes (4to., vol. i., Helmstädt, 1797) and “Methodus generalis, aequationes differentiarum particularum, necnon aequationes differentiales vulgares, utrasque primi ordinis inter quotcumque variabiles, complete integrandi” in Abhandlungen der Königlichen Akademie der Wissenschaften zu Berlin (1814-1815).

His brother Johann Wilhelm Andreas Pfaff was a professor of pure and applied mathematics. Another brother, Christian Heinrich Pfaff, was a professor of medicine, physics and chemistry.