JOHANN

FRIEDRICH

See also:

• JOHANN FRIEDRICH PFAFF (1765–1825)

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 J . E . Bode . In 1788 Pfaff became professor of mathematics in Helmstedt, and so continued until that university was abolished in 181o . 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 caleulum integralem et doctrinam serierum pertinentes (4to., vol. i., Helmstedt, 1797) and " Methodus generalis, aequationes differentiarum particularum, necnon aequationes differentiales vulgares, utrasque primi ordinis inter quotcumque variabiles, complete integrandi " in Abb. 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 DIFFE 2ENTIAL 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 18o1 till his death was professor of medicine, physics and chemistry at the university of Kiel .