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Combinatorics
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Why the Key to a Mathematical Life is Collaboration
Fan Chung, who has an Erdős number of 1, discusses the importance of connection — both human and mathematical.
Graduate Student Solves Classic Problem About the Limits of Addition
A new proof illuminates the hidden patterns that emerge when addition becomes impossible.
How a Problem About Pigeons Powers Complexity Theory
When pigeons outnumber pigeonholes, some birds must double up. This obvious statement — and its inverse — have deep connections to many areas of math and computer science.
New Proofs Probe the Limits of Mathematical Truth
By proving a broader version of Hilbert’s famous 10th problem, two groups of mathematicians have expanded the realm of mathematical unknowability.
The Year in Math
Landmark results in geometry and number theory marked an exciting year for mathematics, at a time when advances in artificial intelligence are starting to transform the subject’s future.
Math’s ‘Bunkbed Conjecture’ Has Been Debunked
It was intuitive, even obvious. It was also wrong.
Math Is Still Catching Up to the Mysterious Genius of Srinivasa Ramanujan
Born poor in colonial India and dead at 32, Ramanujan had fantastical, out-of-nowhere visions that continue to shape the field today.
Grad Students Find Inevitable Patterns in Big Sets of Numbers
A new proof marks the first progress in decades on a problem about how order emerges from disorder.
Merging Fields, Mathematicians Go the Distance on Old Problem
Mathematicians have illuminated what sets of points can look like if the distances between them are all whole numbers.