Johann Friedrich Pfaff (sometimes spelled Friederich; 22 December 1765 – 21 April 1825) was a German mathematician.

[1] 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.

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).

[1] His brother Johann Wilhelm Andreas Pfaff was a professor of pure and applied mathematics.