Kevin Hartnett

Senior Writer

Illustration of a complex shape casting a shadow

Tinkertoy Models Produce New Geometric Insights

An upstart field that simplifies complex shapes is letting mathematicians understand how those shapes depend on the space in which you visualize them.


Universal Method to Sort Complex Information Found

The nearest neighbor problem asks where a new point fits into an existing data set. A few researchers set out to prove that there was no universal way to solve it. Instead, they found such a way.

Photo illustration of Caucher Birkar
2018 Fields Medal and Nevanlinna Prize Winners

An Innovator Who Brings Order to an Infinitude of Equations

The mathematician Caucher Birkar was born on a subsistence farm and raised in the middle of the brutal war between Iran and Iraq. After fleeing to England, he has gone on to impose order on a wild landscape of mathematical equations.

Photo illustration of Alessio Figalli
2018 Fields Medal and Nevanlinna Prize Winners

A Traveler Who Finds Stability in the Natural World

The mathematician Alessio Figalli is rarely in one place for very long. But his work has established the stability of everything from crystals to weather fronts by using concepts derived from Napoleonic fortifications.

Art for "Major Quantum Computing Advance Made Obsolete by Teenager"
quantum computing

Major Quantum Computing Advance Made Obsolete by Teenager

18-year-old Ewin Tang has proven that classical computers can solve the “recommendation problem” nearly as fast as quantum computers. The result eliminates one of the best examples of quantum speedup.

Diagram showing show the hierarchy of different classes.
Abstractions blog

A Short Guide to Hard Problems

What’s easy for a computer to do, and what’s almost impossible? Those questions form the core of computational complexity. We present a map of the landscape.

Illustration for "Finally, A Problem That Only Quantum Computers Will Ever Be Able to Solve"
computational complexity

Finally, a Problem That Only Quantum Computers Will Ever Be Able to Solve

Computer scientists have been searching for years for a type of problem that a quantum computer can solve but that any possible future classical computer cannot. Now they’ve found one.

Art for "A Classical Math Problem Gets Pulled Into the Modern World"

A Classical Math Problem Gets Pulled Into the Modern World

A century ago, the great mathematician David Hilbert posed a probing question in pure mathematics. A recent advance in optimization theory is bringing Hilbert’s work into a world of self-driving cars.

Illustration of a black hole with a Cauchy horizon
general relativity

Mathematicians Disprove Conjecture Made to Save Black Holes

Mathematicians have disproved the strong cosmic censorship conjecture. Their work answers one of the most important questions in the study of general relativity and changes the way we think about space-time.