**Carl Friedrich Hindenburg** was the son of a merchant. He did not attend school but his father arranged that he be taught privately in his home by a tutor. Hindenburg entered the University of Leipzig in 1757 but at this stage his interests were not focused on mathematics, rather he was interested in a wide range of subjects. he took courses in medicine, philosophy, Latin, Greek, physics, mathematics, and aesthetics.

Christian Fürchtegott Gellert, whose whole career was spent at the University of Leipzig, had been promoted to professor there six years before Hindenburg entered the university. Gellert's lectures on poetry, rhetoric, and ethics were exceptionally popular. Gellert, who tutored Hindenburg, arranged with him that he should take on the task of accompanying a student named Schönborn through his education.

This was an important event for Hindenburg for Schönborn's increasing interest in mathematics took Hindenburg in that direction too. As well as at Leipzig, Schönborn studied at Göttingen and while he was there Hindenburg became a friend of Kästner, who had himself taught at Leipzig earlier in his career. Through this Hindenburg did not neglect his own studies and he was awarded a Master's degree from the University of Leipzig in 1771 and appointed as a Privatdozent there in that year.

Even before his appointment as a Privatdozent, Hindenburg had published articles but these were not in mathematics. In 1763 and 1769 he published on philology which is the study of language. His first papers on mathematics were published in 1776 when he studied series. Two years later he published his first papers on combinatorics, the topic for which he became famous.

Hindenburg published a series of works on combinatorial mathematics, in particular probability, series and formulae for higher differentials. Hindenburg hoped for combinatorial operations to have the same importance as those of arithmetic, algebra and analysis but his expectations were not realised. He is recognised, however, as starting [2]:-

... the first scientific school of combinatorial mathematics.

Although essentially forgotten now, Hindenburg's combinatorics was very fashionable 1800 although it is now clear that its importance being much overestimated. His ideas centred around the so-called polynomial theorem which was a generalisation of the binomial theorem. It would be too easy to dismiss Hindenburg's combinatorics, however, for they had some important consequences. Gudermann, best known as the teacher of Weierstrass, worked on the expansion of functions into power series and, as shown by Manning in [4], it was Hindenburg's combinatorial analysis which was the main influence on this work.

In 1781 Hindenburg was appointed as professor of philosophy in the University of Leipzig. After presenting a dissertation on water pumps, he was appointed as professor of physics in 1786. This later post was one which he continued to hold until his death over twenty years later.

It was not only for his school of combinatorial analysis that Hindenburg is famous. He also made important contributions to publishing mathematics in Germany. Between 1780 and 1800 he was involved at different times with the publishing of four different journals all relating to mathematics and its applications.

**Article by:** *J J O'Connor* and *E F Robertson*

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