Heinrich August Rothe

Heinrich August Rothe was a German mathematician, born in Dresden in 1773, who died in 1842. A student of Carl Hindenburg and a member of Hindenburg's school of combinatorics, he became a docent at the University of Leipzig in 1793 and an extraordinary professor there in 1796, then in 1804 moved to Erlangen as a full professor, taking over the chair formerly held by Karl Christian von Langsdorf. His 1793 thesis contained the summation formula for binomial coefficients now called the Rothe-Hagen identity and a formula for the Taylor series of an inverse function. In 1800 he was the first to define the inverse of a permutation, introduced the square table now called a Rothe diagram to count inversions, and was the first to consider permutations that are their own inverse, finding the recurrence that counts them. In 1811 he was the first to state the q-binomial theorem. His Erlangen chair passed on his death to Johann Wilhelm Pfaff.