Johann Friedrich Pfaff (1765-1825), German mathematician, was born on the 22nd of December 1765 at Stuttgart. He received his early education at the Carlsschule, where he met F. Schiller, his lifelong friend. His mathematical capacity was early noticed; he pursued his studies at Gottingen under Abraham Gotthelf Kastner (1719-1800), and in 1787 he went to Berlin and studied practical astronomy under E. Bode. In 1788 Pfaff became professor of mathematics in Helmstedt, and so continued until that university was abolished in 1810. From that time till his death on the 21st of April 1825 he held the chair of mathematics at Halle. Pfaff's researches bore chiefly on the theory of series, to which he applied the methods of the so-called combinatorial school of German mathematicians, and on the solution of differential equations. His two principal works are Disquisitiones analyticae maxime ad calculum integralem et doctrinam serierum pertinentes (4to., vol. i., Helmstedt, 1797) and "Methodus generalis, aequationes differentiarum particularum, necnon aequationes differentiates vulgares, utrasque primi ordinis inter quotcumque variabiles, complete integrandi" in Abh. d. Berl. Acad. (1814-1815). The former work contains Pfaff's discussion of a certain differential equation which generally bears his name, but which had originally been treated in a less complete manner by L. Euler (see Differential Equations). The latter work contains an important addition to the theory of partial differential equations as it had been left by J. L. Lagrange.
His brother, Johann Wilhelm Andreas Pfaff (1774-1835), was professor of pure and applied mathematics successively at Dorpat, Nuremberg, Wurzburg and Erlangen. Another brother, Christian Heinrich Pfaff (1773-1852), graduated in medicine at Stuttgart in 1793, and from 1801 till his death was professor of medicine, physics and chemistry at the university of Kiel.
