Appendix C: Biographies
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- 1.1: C.1- Georg Cantor
- Georg Cantor is known for his work in set theory, and is credited with founding set theory as a distinctive research discipline.
- 1.2: C.2- Alonzo Church
- Alonzo Church developed a theory of effective calculability, the lambda calculus, independently of Alan Turing’s development of the Turing machine. He also proved what is now known as Church’s Theorem: The decision problem for the validity of first-order formulas is unsolvable.
- 1.3: C.3- Gerhard Gentzen
- Gerhard Gentzen is known primarily as the creator of structural proof theory, and specifically the creation of the natural deduction and sequent calculus proof systems.
- 1.4: C.4- Kurt Gödel
- Kurt Gödel's dissertation proved the completeness theorem of first-order predicate logic with identity. Only a year later, he obtained his most famous results—the first and second incompleteness theorems.
- 1.5: C.5- Emmy Noether
- Hailed as the “mother of modern algebra,” Noether made groundbreaking contributions to both mathematics and physics, despite significant barriers to women’s education.
- 1.6: C.6- Bertrand Russell
- Bertrand Russell is hailed as one of the founders of modern analytic philosophy.
- 1.7: C.7- Alfred Tarski
- Tarski completed some of his most important work while working as a secondary school teacher in Warsaw. His work on logical consequence and logical truth were written during this time.
- 1.8: C.8- Alan Turing
- Alan Turing is considered the father of theoretical computer science. He developed (what is now called) the Turing machine as an attempt to precisely define the notion of a computable function and to prove the undecidability of the decision problem.
- 1.9: C.9- Ernst Zermelo
- Ernst Zermelo's most celebrated mathematical achievements include the introduction of the axiom of choice, and his axiomatization of set theory.