Mathematician:Ernst Friedrich Ferdinand Zermelo

Mathematician

German mathematician best known for his work on the foundations of mathematics.

Laid the groundwork (later to be enhanced by Abraham Fraenkel) for what are now known as the Zermelo-Fraenkel axioms of axiomatic set theory.

Nationality

Germany

History

• Born: July 27, 1871, Berlin, German Empire
• Died: May 21, 1953, Freiburg im Breisgau, West Germany

Theorems and Definitions

• Zermelo Universe
• Zermelo Construction of Natural Numbers

• Zermelo-Fraenkel axioms:
  • Zermelo-Fraenkel Set Theory and ZFC (with Abraham Halevi Fraenkel)
  • Zermelo-Fraenkel Universe (with Abraham Halevi Fraenkel)

• Zermelo-Fraenkel-Skolem Set Theory (with Abraham Halevi Fraenkel and Thoralf Albert Skolem)

• Zermelo's Theorem (Game Theory)
• Zermelo's Theorem (Set Theory)
• Zermelo's Well-Ordering Theorem

Results named for Ernst Friedrich Ferdinand Zermelo can be found here.

Definitions of concepts named for Ernst Friedrich Ferdinand Zermelo can be found here.

Axioms named for Ernst Friedrich Ferdinand Zermelo can be found here.

Publications

• 1904: Beweis dass jede Menge wohlgeordnet werden kann ("Proof that every set can be well-ordered") (Math. Ann. Vol. 59: pp. 514 – 516)
• 1908: Neuer Beweis füe die Möglichkeit einer Wohlordnung ("A new proof of the possibility of well-ordering") (Math. Ann. Vol. 65: pp. 107 – 128)
• 1908: Untersuchungen über die Grundlagen der Mengenlehre. $\text I$ ("Investigations in the Foundations of Set Theory $\text I$") (Math. Ann. Vol. 65: pp. 261 – 281)
• 1913: Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels ("On an Application of Set Theory to the Theory of the Game of Chess") (Proceedings of the Fifth International Congress of Mathematicians Vol. 2: pp. 501 – 504) (edited by E.W. Hobson)
• 1930: On boundary numbers and domains of sets: new investigations in the foundations of set theory

Critical view

On Zermelo's noble battle against choice-deniers:

Zermelo has found a new proof of the well-ordering theorem. I held its proof sheets in my own hands yesterday. The proof is marvellous and very simple. I myself had failed to go that way. He also has $8$ pages of polemics with Poincaré, Bernstein, Jourdain, Peano, Hardy, Schoenflies etc., which are very funny and hit the logicists hard. He stresses the synthetic character of mathematics everywhere and accuses Poincaré of confusing set theory and logicism.

-- Gerhard Hessenberg

[A] treatise which has in respect to its sarcasm nothing like it in mathematical literature.

-- Abraham Fraenkel

Sources

• John J. O'Connor and Edmund F. Robertson: "Ernst Friedrich Ferdinand Zermelo": MacTutor History of Mathematics archive

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Zermelo's theorem
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Zermelo, Ernst (1871-1953)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Zermelo, Ernst (1871-1953)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Zermelo, Ernst (Friedrich Ferdinand) (1871-1953)
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): Zermelo, Ernst (Friedrich Ferdinand) (1871-1953)