Kevin Hartnett

Senior Writer

Art for "Why Mathematicians Can’t Find the Hay in a Haystack"
Abstractions blog

Why Mathematicians Can’t Find the Hay in a Haystack

September 17, 2018

In math, sometimes the most common things are the hardest to find.

Illustration of a complex shape casting a shadow
geometry

Tinkertoy Models Produce New Geometric Insights

September 5, 2018

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

algorithms

Universal Method to Sort Complex Information Found

August 13, 2018

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

An Innovator Who Brings Order to an Infinitude of Equations

August 1, 2018

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

A Traveler Who Finds Stability in the Natural World

August 1, 2018

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

July 31, 2018

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

July 16, 2018

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

June 21, 2018

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"
algorithms

A Classical Math Problem Gets Pulled Into the Modern World

May 23, 2018

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.