Mathwar/Personlist/Zermelo Ernst
Ernst Zermelo
(* July 27th 1871 in Berlin, † May 21st Freiburg im Breisgau)
German mathematician, whose work has major implications for the foundations of mathematics and hence on philosophy.
Life
In 1900, in the Paris conference of the International Congress of Mathematicians, David Hilbert challenged the mathematical community with his famous Hilbert's problems, a list of 23 unsolved fundamental questions which mathematicians should attack during the coming century. The first of these, a problem of set theory, was the continuum hypothesis introduced by Cantor in 1878.
Zermelo began to work on the problems of set theory and in 1902 published his first work concerning the addition of transfinite cardinals. In 1904, he succeeded in taking the first step suggested by Hilbert towards the continuum hypothesis when he proved the well-ordering theorem (every set can be well ordered). This result brought fame to Zermelo, who was appointed Professor in Göttingen, in 1905. His proof of the well-ordering theorem, based on the axiom of choice, was not accepted by all mathematicians, partly because set theory was not axiomatized at this time. In 1908, Zermelo succeeded in producing a much more widely-accepted proof.
In 1905, Zermelo began to axiomatize set theory; in 1908, he published his results despite his failure to prove the consistency of his axiomatic system. See the article on Zermelo set theory for an outline of this paper, together with the original axioms, with the original numbering.
In 1922, Adolf Fraenkel and Thoralf Skolem independently improved Zermelo's axiom system. The resulting 10 axiom system, now called Zermelo-Fraenkel axioms (ZF), is now the most commonly used system for axiomatic set theory.
Proposed in 1931, the Zermelo's Navigation Problem is a classic optimal control problem. The problems deals with a boat navigating on a body of water, originating from a point O to a destination point D. The boat is capable of a certain maximum speed, and we want to derive the best possible control to reach D in the least possible time.
Without considering external forces such as current and wind, the optimal control is to follow a straight line segment from O to D. WIth consideration of current and wind, the shortest path from O to D is in fact, not the optimal solution.