Mathematics in the Age of the Turing Machine (Thomas C. Hales)

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Mathematics in the Age of the Turing Machine (Thomas C. Hales)

Future generations might consider this day to be a pivotal one in the development of computers in mathematics because of how quickly it has happened. The article provides an overview of formal and computer-assisted mathematical proofs.

Where is the mathematical project now?

Numerous mathematical utilities are consolidating in 2012. The arXiv, Math Reviews, and euDML, which claim to aggregate the numerous European archives like Zentralblatt Math and Numdam, are examples of the enormous aggregates and large reservoirs of mathematics that characterize this era. Sage unifies a number of computer applications with a mathematical focus under a single Python-scripted front end.

Over the past few years, book sales in the US have decreased. Instead, kids are increasingly favoring internet resources for arithmetic, such as Wikipedia and Math Overflow. Huge mathematical partnerships are arranged by the Polymath blog. Other blogs integrate previously disparate researchers into brand-new study disciplines. In place of the old-school referees' deliberate, methodical pace, Tao now blogs, receives feedback and publishes all at once.

The field of machine learning is growing. Watson responds to our Jeopardy questions, while Wolfram Alpha and LogAnswer provide answers to our basic quantitative queries. By determining the biggest eigenvalue of the largest matrix ever created, Google Page ranks our searches. Playing our chess matches is Deep Blue. Our Netflix searches are improved by the Pragmatic Chaos algorithm, the winner of the $1 million prize. Tens of thousands of formal proofs are currently being mined from the major proof assistants for information on how to establish the upcoming generation of theorems.

Ebook Details

About the Authors
American mathematician Thomas C. Hales specializes in formal verification, discrete geometry, and representation theory.
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