Ernst Friedrich Ferdinand Zermelo Biography

Ernst Friedrich Ferdinand Zermelo made major contributions to mathematics in the area of set theory, especially by extending David Hilbert's work in solving the continuum hypothesis. The Zermelo-Fraenkel set theory is still in wide use.

Zermelo was born in Berlin, Germany on July 27, 1871. His father was a college professor, which helped set the academic tone of Zermelo's childhood. He attended a gymnasium (a classical college-preparatory school) in Berlin, graduating in 1889. Then, as was customary at the time, Zermelo took classes in mathematics, physics, and philosophy at a variety of universities--namely those at Berlin, Freiburg, and Halle.

Earning his doctorate in 1894 from the University of Berlin, Zermelo began working as an assistant to physicist Max Planck. Soon he began studying for a teaching certificate, which he obtained in 1899 at the University of Gôttingen with a dissertation on hydrodynamics. The school, which then was the world's leading center for mathematical research, appointed him as a lecturer based on the quality of his work.

At this point, Zermelo's research changed direction. In 1900, Hilbert suggested that mathematicians could solve Georg Ferdinand Ludwig Philipp Cantor's 1878 continuum hypothesis by first proving that any set can be well ordered. Zermelo accepted this challenge, and in 1902 published his first work on set theory, which centered on the addition of transfinite cardinals. Two years later, he met Hilbert's challenge by using the axiom of choice to prove that all sets can be well ordered. His achievement brought the mathematician immediate renown in the academic world and even led to a promotion to full professor at Gôttingen in 1905.

However, Zermelo also endured much criticism for his work on set theory, since many mathematicians of the period did not accept the type of proofs that he had discovered. Thus, in 1908 he used another, more traditional proof to accomplish the same goal. Later that year, Zermelo published the results of his efforts to axiomize set theory despite his failure to prove that the seven axioms were consistent. Nevertheless, his system would turn out to be tremendously important to the development of mathematics. (It would eventually be improved by two other mathematicians in 1922, resulting in a 10-axiom system that is now commonly used for axiomatic set theory.)

Zermelo, who was beginning to suffer from poor health, left the University of Gôttingen in 1910 to take up the chair of mathematics at the University of Zurich in Switzerland. Despite efforts to rest and recover, by 1916 his health had not improved, so he resigned his post and moved to the Black Forest. He lived there until 1926, when he accepted an honorary chair at the University of Freiburg. By 1935 Zermelo had resigned the position to protest the regime of Adolf Hitler, but after the war, he accepted reinstatement.

Zermelo died in Breisgau, Germany on May 21, 1953.