Alan Turing was an inspirational figure who is now recognised as a genius of modern mathematics. In addition to leading the Allied forces' code-breaking effort at Bletchley Park in World War II, he proposed the theoretical foundations of modern computing and anticipated developments in areas from information theory to computer chess. His ideas have been extraordinarily influential in modern mathematics and this book traces such developments by bringing together essays by leading experts in logic, artificial intelligence, computability theory and related areas. Together, they give insight into this fascinating man, the development of modern logic, and the history of ideas. The articles within cover a diverse selection of topics, such as the development of formal proof, differing views on the Church–Turing thesis, the development of combinatorial group theory, and Turing's work on randomness which foresaw the ideas of algorithmic randomness that would emerge many years later.

- Cover Page
- Series Page
- Title Page
- Copyright Page
- Contents
- Turing’s legacy: developments from Turing’s ideas in logic
- Computability and analysis: the legacy of Alan Turing
- Alan Turing and the other theory of computation (expanded)
- Turing in Quantumland
- Computability theory, algorithmic randomness and Turing’s anticipation
- Computable model theory
- Towards common-sense reasoning via conditional simulation: legacies of Turing in Artificial Intelligence
- Mathematics in the age of the Turing machine
- Turing and the development of computational complexity
- Turing machines to word problems
- Musings on Turing’s Thesis
- Higher generalizations of the Turing Model
- Step by recursive step: Church’s analysis of effective calculability
- Turing and the discovery of computability
- Transfinite machine models