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Encyclopedia Britannica



PFAFF, JOHANN FRIEDRICH (17651825)

This article appears in Volume V21, Page 340 of the Encyclopedia Britannica.

Encyclopedia Britannica - Main :: PER-PIG
PFAFF, JOHANN FRIEDRICH (17651825) , 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 (17191800), 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. (18141815). 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 (17741835), 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
 .


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