Mathematics in the Age of the Turing Machine by Thomas C. Hales
Mathematics in the Age of the Turing Machine - Table of Contents
- 1. Computer Calculation and computer calculation in modern mathematics
- 2. Computer Proof and formal verification systems in mathematics
- 3. Issues of Trust and trustworthiness of computer assisted proofs
- 4. Concluding Remarks
What You Will Learn in Mathematics in the Age of the Turing Machine
Mathematics in the Age of the Turing Machine by Thomas Hales is a groundbreaking contemporary treatise examining the profound shift in mathematical practice brought about by computer-assisted proofs and formal verification systems. Written by the mathematician who famously solved the Kepler Conjecture and led the Flyspeck project, this text investigates interactive theorem provers, proof assistants like Lean and Coq, automated deduction, type theory, and the computational verification of complex proofs.
Tailored for graduate students, theoretical computer scientists, logicians, and research mathematicians, Prof. Hales bridges traditional human-written proofs with machine-checkable formal logic. The volume explores how computation is transforming foundational mathematics, addressing formalization challenges, structural type theory, constructive logic, and the future of mathematical discovery in an era dominated by automated tools.
Celebrated for its visionary scope, intellectual clarity, and cutting-edge analytical insights, it stands as one of the best modern formalized mathematics textbooks pdf available for advanced study. It systematically equips scholars with modern theoretical frameworks for mastering computer-verified mathematics with confidence.
Book Details & Specifications
Title:
Mathematics in the Age of the Turing Machine by Thomas C. Hales
Publisher:
University of Pittsburgh
Year:
2013
Pages:
45
Type:
PDF
Language:
English
ISBN-10 #:
1107043484
ISBN-13 #:
978-1107043480
License:
Arxiv License
Amazon:
Amazon
About the Author: Thomas Callister Hales
The author Thomas Callister Hales
is an American "mathematician" known for his groundbreaking work in "geometry", "number theory", and the use of "computer-assisted proofs". He is best known for proving the "Kepler Conjecture", a centuries-old problem on sphere packing, combining traditional mathematics with large-scale computation. In "Mathematics in the Age of the Turing Machine", Hales explores how "algorithms", computers, and formal verification are transforming modern mathematics.
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