Kevin Hartnett

Senior Writer

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"
algorithms

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.

Photo of Judea Pearl
Q&A

To Build Truly Intelligent Machines, Teach Them Cause and Effect

Judea Pearl, a pioneering figure in artificial intelligence, argues that AI has been stuck in a decades-long rut. His prescription for progress? Teach machines to understand the question why.

Art for "Three Decades Later, Mystery Numbers Explained"
Abstractions blog

Three Decades Later, Mystery Numbers Explained

Zeta values seem to connect distant geometric worlds. In a new proof, mathematicians finally explain why.

Illustration for "Mathematicians Explore Mirror Link Between Two Geometric Worlds"
geometry

Mathematicians Explore Mirror Link Between Two Geometric Worlds

Decades after physicists happened upon a stunning mathematical coincidence, researchers are getting close to understanding the link between two seemingly unrelated geometric universes.

520px photo of Robert Langlands
Abstractions blog

Robert Langlands, Mathematical Visionary, Wins the Abel Prize

Generations of researchers have pursued his “Langlands program,” which seeks to create a grand unified theory of mathematics.

Photograph of Albert Einstein in his office at the University of Berlin, published in the USA in 1920.
Abstractions blog

How Einstein Lost His Bearings, and With Them, General Relativity

By 1913, Albert Einstein had nearly completed general relativity. But a simple mistake set him on a tortured, two-year reconsideration of his theory. Today, mathematicians still grapple with the issues he confronted.

About the author

Kevin Hartnett is a senior writer at Quanta Magazine covering mathematics and computer science. His work has been collected in the “Best Writing on Mathematics” series in 2013 and 2016. From 2013-2016 he wrote “Brainiac,” a weekly column for the Boston Globe‘s Ideas section.