Kevin Hartnett

Senior Writer

Photo of smoke
Abstractions blog

What Makes the Hardest Equations in Physics So Difficult?

The Navier-Stokes equations describe simple, everyday phenomena, like water flowing from a garden hose, yet they provide a million-dollar mathematical challenge.

520px photo of Richard Schwartz
Q&A

In Praise of Simple Problems

The mathematician Richard Schwartz finds the hidden depth lurking in simple mathematical puzzles.

Simulation of Kelvin-Helmholz Instability
fluid dynamics

Mathematicians Find Wrinkle in Famed Fluid Equations

Two mathematicians prove that under certain extreme conditions, the Navier-Stokes equations output nonsense.

Jennifer Balakrishnan and Sachi Hashimoto, plotted using SageMath
Abstractions blog

Mathematicians Crack the Cursed Curve

A famously difficult mathematical problem resisted solution for over 40 years. Mathematicians have finally resolved it by following an intuition that links number theory to physics.

Minhyong Kim in front of a whiteboard
number theory

Secret Link Uncovered Between Pure Math and Physics

An eminent mathematician reveals that his advances in the study of millennia-old mathematical questions owe to concepts derived from physics.

A blue person made of code walks down a pink road patterned with hexagons
algorithms

Best-Ever Algorithm Found for Huge Streams of Data

To efficiently analyze a firehose of data, scientists first have to break big numbers into bits.

Photo of AlphaGo board by dreamdream | Quanta Magazine
Abstractions blog

Artificial Intelligence Learns to Learn Entirely on Its Own

A new version of AlphaGo needed no human instruction to figure out how to clobber the best Go player in the world — itself.

Vladimir Voevodsky
Abstractions blog

Visionary Mathematician Vladimir Voevodsky Dies at 51

Voevodsky’s friends remember him as constitutionally unable to compromise on the truth — a quality that led him to produce some of the most important mathematics of the 20th century.

Measuring tapes
infinity

Mathematicians Measure Infinities and Find They’re Equal

Two mathematicians have proved that two different infinities are equal in size, settling a long-standing question. Their proof rests on a surprising link between the sizes of infinities and the complexity of mathematical theories.