Ernst Zermelo (person)

Ernst Friedrich Ferdinand Zermelo

Born: 1871-07-27 in Berlin
Died: 1953-05-21 in Freiburg im Breisgau

Mathematician who did research in:

• Calculus of variations
• Hydrodynamics
• Statistical mechanics
• Axiomatic set theory

Significant work:

• Proved that every set can be well-ordered.
• Discovered (but did not publish) a varient of Russell's Paradox.
• Created first axiomatic system of mathematics.
• Created a reduction of natural numbers to sets.

An modification of his axiomatic system, called Zermelo-Fraenkel, is still the most widely used such system today. Zermelo's original axioms:

1. Axiom of Extensionality
2. Axiom of Elementary Sets
3. Axiom of Separation
4. Power Set Axiom
5. Union Axiom
6. Axiom of Choice
7. Axiom of Infinity

ZF's axioms:

1. Axiom of Extensionality
2. Power Set Axiom
3. Union Axiom
4. Axiom of Infinity
5. Foundation Axiom
6. Selection Axiom

Sources:

1. Omega Help Index: http://www.ags.uni-sb.de/~omega/omegaindex/theories/zermelo-fraenkel.html
2. MacTutor History of Mathematics: http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Zermelo.html