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The p-adics form an infinite collection of number systems based on prime numbers. They’re at the heart of modern number theory.

Have fun exploring a numerical puzzle, a geometric puzzle and a game of random patterns, all inspired by the playful genius of the legendary mathematician.

A small community of mathematicians is using a software program called Lean to build a new digital repository. They hope it represents the future of their field.

Despite recent progress on the notorious Collatz conjecture, we still don’t know whether a number can escape its infinite loop.

Computer scientists are trying to build an AI system that can win a gold medal at the world’s premier math competition.

Two computer scientists found — in the unlikeliest of places — just the idea they needed to make a big leap in graph theory.

Mathematicians have long grappled with the reality that some problems just don’t have solutions.

For millennia, mathematicians have wondered whether odd perfect numbers exist, establishing an extraordinary list of restrictions for the hypothetical objects in the process. Insight on this question could come from studying the next best things.

Emily Riehl is rewriting the foundations of higher category theory while also working to make mathematics more inclusive.

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