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
2. Computer Proof
3. Issues of Trust
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 C. Hales" examines how modern mathematics is evolving under the influence of "computation" and "algorithms". The book reflects on a major shift in mathematical practice: from proofs checked entirely by humans to results that rely on computers for verification. Hales places this transformation in the broader context of 20th- and 21st-century mathematics, inspired by the conceptual framework of the "Turing machine".
A central theme of the book is "computer-assisted proof", illustrated through landmark examples such as the proof of the Kepler Conjecture and the Flyspeck Project. Hales explains how formal proof systems and software tools can increase reliability while also raising new questions about understanding, transparency, and trust. The work carefully balances technical insight with philosophical reflection, making it accessible to mathematicians beyond a narrow specialty.
Overall, the book offers a thoughtful perspective on the future of "mathematical proof" and practice. It explores how "logic", rigor, and creativity interact with machines, and what this means for the identity of mathematics itself. Rather than presenting computers as replacements for mathematicians, Hales argues that they are becoming essential collaborators in mathematical discovery.
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 C. Hales
The author
Thomas C. 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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