Reinhold Hoppe

Ernst Reinhold Eduard Hoppe (November 18, 1816 – May 7, 1900) was a German mathematician who worked as a professor at the University of Berlin.

Education and career Hoppe was a student of Johann August Grunert at the University of Greifswald, In 1890, Hoppe was one of the 31 founding members of the German Mathematical Society.

Contributions Hoppe wrote over 250 scientific publications, including one of the first textbooks on differential geometry. and coining the term "polytope". In 1880 he published a closed-form expression for all triangles with consecutive integer sides and rational area, also known as almost-equilateral Heronian triangles. He is sometimes credited with having proven Isaac Newton's conjecture on the kissing number problem, that at most twelve congruent balls can touch a central ball of the same radius, but his proof was incorrect, and a valid proof was not found until 1953.

Hoppe published several works on a formula for the m-fold derivative of a composition of functions. The formula, now known as "Hoppe's formula", is a variation of Faà di Bruno's formula. Hoppe's publication of his formula in 1845 predates Faà di Bruno's in 1852, but is later than some other independent discoveries of equivalent formulas.

In his work on special functions, Hoppe belonged to the Königsberg school of thought, led by Carl Jacobi. He also published research in fluid mechanics.

Awards and honors He was elected to the Academy of Sciences Leopoldina in 1890.

Books Theorie Der Independenten Darstellung Der Höhern Differentialquotienten (Leipzig: Joh. Ambr. Barth, 1845) Zulänglichkeit Des Empirismus In Der Philosophie (Berlin: Wilhelm Thome, 1852) Lehrbuch Der Differentialrechnung Und Reihentheorie Mit Strenger Begründung (Berlin: G. F. Otto Müller, 1865) Principien Der Flächentheorie (Leipzig: C. A. Koch, 1876) Tafeln Zur Dreissigstelligen Logarithmischen Rechnung (Leipzig: C. A. Koch, 1876) Lehrbuch Der Analytischen Geometrie (Leipzig: C. A. Koch, 1880)