Johann Friedrich Pfaff
Johann Friedrich Pfaff
Born	(1765-12-22)22 December 1765 Stuttgart, Holy Roman Empire
Died	21 April 1825(1825-04-21) (aged 59) Halle, Germany
Nationality	German
Alma mater	University of Göttingen
Known for	Pfaffians Pfaffian constraint Pfaffian function Pfaffian system Pfaffian orientation
Scientific career
Fields	Mathematics
Institutions	University of Helmstedt Halle University
Doctoral advisor	Abraham Kästner Johann Elert Bode
Doctoral students	Carl Friedrich Gauss August Möbius Karl Mollweide
Other notable students	Johann Christian Martin Bartels

Johann Friedrich Pfaff (sometimes spelled Friederich; 22 December 1765 – 21 April 1825) was a German mathematician. He was described as one of Germany's most eminent mathematicians during the 19th century. He was a precursor of the German school of mathematical thinking, under which Carl Friedrich Gauss and his followers largely determined the lines on which mathematics developed during the 19th century.

They asked Laplace who, in his opinion, was the greatest mathematician of Germany. "It's Pfaff," he answered. - "I thought," the questioner replied, "that Gauss was superior to him." - "But," exclaimed Laplace, "you're asking me who is the greatest mathematician of Germany, and Gauss is the greatest mathematician of Europe."

— Nouvelle Biographie Générale, volume 19, page 686.

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 continued his work as a professor until that university was abolished in 1810. After this event, 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, Christoph Heinrich Pfaff, was a professor of medicine, physics and chemistry.

Works

• Commentatio de ortibus et occasibus siderum apud auctores classicos commemoratis (in Latin). Göttingen: Johann Christian Dieterich. 1786.