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.
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.
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.
machine learning
In New Math Proofs, Artificial Intelligence Plays to Win
A new computer program fashioned after artificial intelligence systems like AlphaGo has solved several open problems in combinatorics and graph theory.
number theory
Mathematicians Prove 30-Year-Old André-Oort Conjecture
A team of mathematicians has solved an important question about how solutions to polynomial equations relate to sophisticated geometric objects called Shimura varieties.
combinatorics
Mathematician Answers Chess Problem About Attacking Queens
The n-queens problem is about finding how many different ways queens can be placed on a chessboard so that none attack each other. A mathematician has now all but solved it.