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After 44 years, there’s finally a better way to find approximate solutions to the notoriously difficult traveling salesperson problem.
Vesselin Dimitrov’s proof of the Schinzel-Zassenhaus conjecture quantifies the way special values of polynomials push each other apart.
Sizing up patternless sets is hard, so mathematicians rely on simple bounds to help answer their questions.
We finally know how big a set of numbers can get before it has to contain a pattern known as a “polynomial progression.”
Digital security depends on the difficulty of factoring large numbers. A new proof shows why one method for breaking digital encryption won’t work.