Ernst Zermelo

Ernst Friedrich Ferdinand Zermelo was born in Berlin in 1871. He studied mathematics, physics, and philosophy at Berlin, Halle, and Freiburg, completing a dissertation on the calculus of variations in 1894. Early in his career he worked as an assistant to Max Planck and was deeply engaged with the foundations of statistical mechanics and thermodynamics before turning to the work for which he is best remembered.

In 1896, as a young thermodynamicist, Zermelo published the recurrence objection to Boltzmann's statistical mechanics: invoking Poincaré's recurrence theorem, he argued that a bounded mechanical system must eventually return near its initial state, so entropy could not increase monotonically forever. Boltzmann replied that the recurrence time is so astronomically long as to be physically irrelevant. The exchange helped clarify that the second law is statistical and time-scale dependent rather than absolute.

Zermelo's greatest fame came in the foundations of mathematics. In 1904 he proved the well-ordering theorem using what he made explicit as the axiom of choice, igniting a major controversy. To secure the result he formulated, in 1908, the first axiomatisation of set theory; refined by Abraham Fraenkel and others, it became Zermelo–Fraenkel set theory (ZF, or ZFC with choice), the standard foundation of modern mathematics.

He held a professorship at Zürich and later an honorary post at Freiburg, which he resigned in 1935 in protest against the Nazi regime; it was restored to him after the war. He died in Freiburg in 1953.