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“Rainbow colorings” recently led to a new proof. It’s not the first time they’ve come in handy.

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.

Ronald Rivest helped come up with the RSA algorithm, which safeguards online commerce. Now he’s hoping to make democratic elections more trustworthy.

Finding the best way to approximate the ever-elusive irrational numbers pits the infinitely large against the infinitely small.

Computer scientists established a new boundary on computationally verifiable knowledge. In doing so, they solved major open problems in quantum mechanics and pure mathematics.

Mathematicians have proved that copies of smaller graphs can always be used to perfectly cover larger ones.

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

Mathematicians have studied knots for centuries, but a new material is showing why some knots are better than others.

By exploiting randomness, three mathematicians have proved an elegant law that underlies the chaotic motion of turbulent systems.