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mathematics
topology
How Complex Is a Knot? New Proof Reveals Ranking System That Works
“Ribbon concordance” will let mathematicians compare knots by linking them across four-dimensional space.
Insights puzzle
Think of a Number. How Do Math Magicians Know What It Is?
Mathematical magic can seem like mind reading. Your job is to reveal the secret behind these four tricks.
fluid dynamics
Mathematicians Coax Fluid Equations Into Nonphysical Solutions
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.
graph theory
Elegant Six-Page Proof Reveals the Emergence of Random Structure
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.
number theory
New Proof Illuminates the Hidden Structure of Common Equations
Van der Waerden’s conjecture mystified mathematicians for 85 years. Its solution shows how polynomial roots relate to one another.
mathematical physics
Deep Learning Poised to ‘Blow Up’ Famed Fluid Equations
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.
Insights puzzle
The Secrets of Zugzwang in Chess, Math and Pizzas
Learn the magic and math of how to win games when your opponent goes first.
computational complexity
Researchers Identify ‘Master Problem’ Underlying All Cryptography
The existence of secure cryptography depends on one of the oldest questions in computational complexity.
geometry
Father-Son Team Solves Geometry Problem With Infinite Folds
The result could help researchers answer a larger question about flattening objects from the fourth dimension to the third dimension.