Johann Friedrich Pfaff (sometimes spelled Friederich; 22 December 1765 – 21 April 1825) was a German mathematician. He is best known for his work on differential equations and as Carl Friedrich Gauss's doctoral advisor.
Biography
Johann Friedrich Pfaff was born 22 December 1765 to Friedrich Burkhard Pfaff (1738-1817) and Mary Magdalena Pfaff (née Brand) in Stuttgart. He was one of seven sons and five daughters. there he completed his first notable mathematical work, on series summation. While in Berlin, Pfaff joined Friedrich Nicolai's circle of enlighteners.
In 1788, on the recommendation of Georg Christoph Lichtenberg, Pfaff became professor of mathematics at the University of Helmstedt. His inaugural dissertation investigates the calculation of differentials. His subsequent mathematical work at Helmstedt included: nine articles in Carl Hindenburg's journals, notably two linking arithmetic and analysis, his treatise on analysis, a paper independently deriving Vandermonde's identity and proving Saalschütz's theorem, and a paper solving for the largest ellipse that can be inscribed in a quadrilateral, a problem posed by Gauss.
Pfaff was the official doctoral advisor to Carl Friedrich Gauss, who lived with him in Helmstedt in 1798, the one year of Gauss's residence at the university. Another notable acquaintance was Alexander von Humboldt, whom Pfaff recommended to Göttingen.
While at Helmstedt, Pfaff was active outside of mathematics too, collaborating with Gottfried Gabriel Bredow on historical works. When the university's finances were in trouble, he wrote an essay defending it, preventing its closure. Pfaff served Helmstedt loyally, administering the university's pension fund for widows and refusing appointments at both Göttingen, for which he proposed Gauss, and Dorpat, for which he proposed his brother; for his loyalty he was appointed Hofrat by the Duke of Brunswick.
At Halle, Pfaff completed his most significant 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. Despite a favorable review from Gauss on publication, it was not until a later assessment by Jacobi in 1827 that his work was widely recognized.