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Mathematics

Animation showing multiple particles of light flowing together and leaving blue trails
Abstractions blog

Graced With Knowledge, Mathematicians Seek to Understand

April 8, 2020

A landmark proof in computer science has also solved an important problem called the Connes embedding conjecture. Mathematicians are working to understand it.

Langlands program

‘Amazing’ Math Bridge Extended Beyond Fermat’s Last Theorem

April 6, 2020

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

Photo of two mathematicians drawing on a chalkboard
topology

Mathematics as a Team Sport

March 31, 2020

When 50 mathematicians spend a week in the woods, there’s no telling what will happen. And that’s the point.

An animation showing a 3-by-3 Latin square, with numbers color coded, and the equivalent graph.
Abstractions blog

‘Rainbows’ Are a Mathematician’s Best Friend

March 18, 2020

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

Multimedia

What Is the Geometry of the Universe?

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.

Photo of Ronald Rivest sitting in his office
Q&A

Cryptography Pioneer Seeks Secure Elections the Low-Tech Way

March 12, 2020

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

Quantized Academy

How Rational Math Catches Slippery Irrational Numbers

March 10, 2020

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

Animation showing toy-like depictions of computer science, quantum mechanics and pure math affecting each other.
computational complexity

Landmark Computer Science Proof Cascades Through Physics and Math

March 4, 2020

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

Animated demonstration of a colorful complete graph being tiled by a smaller tree
combinatorics

Rainbow Proof Shows Graphs Have Uniform Parts

February 19, 2020

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