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“Ribbon concordance” will let mathematicians compare knots by linking them across four-dimensional space.

Mathematical magic can seem like mind reading. Your job is to reveal the secret behind these four tricks.

The famed Navier-Stokes equations can lead to cases where more than one result is possible, but only in an extremely narrow set of situations.

Two young mathematicians have astonished their colleagues with a full proof of the Kahn-Kalai conjecture — a sweeping statement about how structure emerges in random sets and graphs.

Van der Waerden’s conjecture mystified mathematicians for 85 years. Its solution shows how polynomial roots relate to one another.

For centuries, mathematicians have tried to prove that Euler’s fluid equations can produce nonsensical answers. A new approach to machine learning has researchers betting that “blowup” is near.

Learn the magic and math of how to win games when your opponent goes first.

The existence of secure cryptography depends on one of the oldest questions in computational complexity.

The result could help researchers answer a larger question about flattening objects from the fourth dimension to the third dimension.

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