**Johann Friedrich Pfaff** was an influential German mathematician who worked on systems of partial differential equations.

- Johann Friedrich was the second of his parents seven sons and, although perhaps the one to attain the greatest fame, he was certainly not the only one to excel in science.
- The second youngest, Christoph Heinrich Pfaff was born in 1773 and, with interests in chemistry, medicine and pharmacy, he worked with Volta on electricity in animals.
- There was a school in Stuttgart, the Hohe Karlsschule, which was run to train sons of government officials of Württemberg and Johann Friedrich attended this school from the age of nine.
- Pfaff did not learn much in the way of mathematics there despite attending the school until he was nearly twenty.
- Despite a lack of training in mathematics at his school, Pfaff had studied mathematics on his own and began to study the works of Euler.
- From Göttingen, Pfaff moved to Berlin in the summer of 1787.
- There he studied astronomy under J E Bode, and Pfaff wrote his first paper which was on a problem in astronomy.
- In the spring of 1788 Pfaff set off on a journey to Vienna but he visited many universities on the way, in particular Halle, Jena, Helmstedt, Dresden, and Prague.
- Pfaff's physics professor at Göttingen recommended him for the chair, and Pfaff submitted a dissertation on the occasion of his election as professor of mathematics at the University of Helmstedt.
- Pfaff's inaugural dissertation was titled Programma inaugurale in quo peculiarem differentialia investigandi rationem ex theoria functionum deducit Ⓣ(Inaugural programme in which special differential investigation leads to the theory of functions).
- From his appointment in 1788 until 1810 Pfaff held the chair at Helmstedt.
- He attended Pfaff's lectures and even lived in his house.
- By the time Gauss studied with Pfaff at Helmstedt, the university was under threat of closure.
- Pfaff fought hard to prevent this and for a few years he was successful.
- By 1810 Pfaff's attempts to preserve the University of Helmstedt finally failed with the closure of the university.
- The staff were given a number of different choices as to which university they might move to, and Pfaff chose to move to Halle.
- Pfaff did important work in analysis working on partial differential equations, special functions and the theory of series.
- His most important work on Pfaffian forms was published in 1815 when Pfaff was nearly fifty years old but its importance was not recognised until 1827 when Jacobi published a paper on Pfaff's method.
- In the 1815 paper, which Pfaff submitted to the Berlin Academy on 11 May, he presented a transformation of a first-order partial differential equation into a differential system.
- This theory of equations in total differentials is undoubtedly Pfaff's most significant contribution.

Born 22 December 1765, Stuttgart, Württemberg (now Germany). Died 21 April 1825, Halle, Saxony (now Germany).

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Astronomy, Origin Germany

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive