Mathematics

Playing with arithmetic can lead us to unexpected and profound discoveries that point toward deeper mathematics and sometimes even deeper science.

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster.

Quantitative models built by the mathematical biologist Trachette Jackson can make cancer therapies safer and more effective.

Inside the symmetries of a crystal shape, a postdoctoral researcher has unearthed a counterexample to a basic conjecture about multiplicative inverses.

The computer scientist Rediet Abebe’s passion for applied mathematics closely aligns with her passion to solve problems with poverty and social inequality.

Fifty years ago, Paul Erdős and two other mathematicians came up with a graph theory problem that they thought they might solve on the spot. A team of mathematicians has finally settled it.

Rediet Abebe uses the tools of theoretical computer science to understand pressing social problems — and try to fix them.

Despite finding no specific examples, researchers have proved the existence of a pervasive kind of prime number so delicate that changing any of its infinite digits renders it composite.

The mathematician Federico Ardila takes a creative approach to the search for useful answers hiding among inconceivably huge numbers of possible ones.