Ernst Zermelo: An Approach to His Life and Work

ISBN-13: 9783662500972 / Angielski / Miękka / 2016 / 384 str.

Heinz Dieter Ebbinghaus; Volker Peckhaus

Recenzje

"This is the second edition of the well-received scientific biography of Ernst Zermelo. ... The second edition has retained the readability of the first edition and is a great read for all interested in the history of axiomatic set theory. The author succeeded in writing a very valuable scientific biography of one of the greatest abstract thinkers in the foundations of mathematics whose private and scientific life is almost unknown otherwise." (Thomas Sonar, zbMATH 1328.01002, 2016)

Spis treści

1 Berlin 1871–1897: 1.1 Family and Youth.- 1.2 School and University Studies.- 1.3 Ph.D. Thesis and the Calculus of Variations.- 1.4 The Boltzmann Controversy.- 2 Göttingen 1897–1910: 2.1 Introduction.- 2.2 Working in Applied Mathematics.- 2.3 First Years as a Privatdozent in Göttingen.- 2.4 The Context: Hilbert’s Research on Foundations.- 2.5 Starting Set Theory.-  2.6 Zermelo’s First Well-Ordering Proof.- 2.7 Finite Sets.- 2.8 The New Proof Paper.- 2.9 The Axiomatization of Set Theory.- 2.10 The Institutionalization of Mathematical Logic.- 2.11 Waiting for a Professorship.- 3 Zurich 1910–1921: 3.1 A Full Professorship.- 3.2 Colleagues and a Friend.- 3.3 Teaching in Zurich.- 3.4 Scientific Work in Zurich.- 3.5 The Fraenkel Correspondence of 1921 and the Axiom of Replacement.- 4 Freiburg 1921–1953: 4.1 A New Start.-  4.2 Research in Applied Mathematics.- 4.3 The Return to the Foundations of Mathematics.- 4.4 Warsaw 1929.- 4.5 Foundational Controversies: An Introduction.- 4.6 Definiteness Revisited.- 4.7 The Cumulative Hierarchy.- 4.8 The Skolem Controversy.- 4.9 Infinitary Languages and Infinitary Logic.- 4.10 The Gödel Controversy.- 4.11 The Loss of the Honorary Professorship.- 4.12 Retreat.- 5 A Final Word.- 6 Zermelo’s Curriculum Vitae.- 7 Appendix: Selected Original Versions: 7.1 Berlin.- 7.2 Göttingen.- 7.3 Zurich.- 7.4 Freiburg.- References.- Index.

Blurb

This biography sheds light on all facets of the life and the achievements of Ernst Zermelo (1871-1953). Zermelo is best-known for the statement of the axiom of choice and his axiomatization of set theory. However, he also worked in applied mathematics and mathematical physics. His dissertation, for example, promoted the calculus of variations, and he created the pivotal method in the theory of rating systems.

The presentation of Zermelo's work explores motivations, aims, acceptance, and influence. Selected proofs and information gleaned from letters add to the analysis. The description of his personality owes much to conversations with his late wife Gertrud.

This second edition provides additional information. The system of citations has been adapted to that of Zermelo's Collected Works in order to facilitate side-by-side reading and thus profit from the thorough commentaries written for the Collected Works by experts in the respective fields.

All facts presented are documented by appropriate sources. The biography contains nearly 50 photos and facsimiles.