In his rapid ascent to the top of his field, James Maynard has cut a path through simple-sounding questions about prime numbers that have stumped mathematicians for centuries.

To distinguish between fundamentally different objects, mathematicians turn to invariants that encode the objects’ essential features.

It took Lisa Piccirillo less than a week to answer a long-standing question about a strange knot discovered over half a century ago by the legendary John Conway.

Mathematicians have figured out how to expand the reach of a mysterious bridge connecting two distant continents in the mathematical world.

In our mind’s eye, the universe seems to go on forever. But using geometry we can explore a variety of three-dimensional shapes that offer alternatives to “ordinary” infinite space.

The “sensitivity” conjecture stumped many top computer scientists, yet the new proof is so simple that one researcher summed it up in a single tweet.

In just three pages, a Russian mathematician has presented a better way to color certain types of networks than many experts thought possible.

Mathematicians used “magic functions” to prove that two highly symmetric lattices solve a myriad of problems in eight- and 24-dimensional space.

A founder of modern geometric analysis who produced “some of the most dramatic advances in mathematics in the last 40 years,” Uhlenbeck is the first woman to be awarded this top honor.

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