# 1911 Encyclopædia Britannica/Pfaff, Johann Friedrich

**PFAFF, JOHANN FRIEDRICH** (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 Göttingen under Abraham
Gotthelf Kästner (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 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., Helmstädt, 1797) and “Methodus
generalis, aequationes differentiarum particularum, necnon
aequationes differentiales 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, Würzburg 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.