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algebraic geometry

Art for "Titans of Mathematics Clash Over Epic Proof of ABC Conjecture"
number theory

Titans of Mathematics Clash Over Epic Proof of ABC Conjecture

Two mathematicians have found what they say is a hole at the heart of a proof that has convulsed the mathematics community for nearly six years.

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

Why Mathematicians Can’t Find the Hay in a Haystack

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

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

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.

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.

June Huh at the Institute for Advanced Study in Princeton, N.J.
algebraic geometry

A Path Less Taken to the Peak of the Math World

June Huh thought he had no talent for math until a chance meeting with a legendary mind. A decade later, his unorthodox approach to mathematical thinking has led to major breakthroughs.

mathematical physics

Strange Numbers Found in Particle Collisions

An unexpected connection has emerged between the results of physics experiments and an important, seemingly unrelated set of numbers in pure mathematics.

Mathematics

Hope Rekindled for Perplexing Proof

Three years ago, a solitary mathematician released an impenetrable proof of the famous abc conjecture. At a recent conference dedicated to the work, optimism mixed with bafflement.

Mathematics

Math Quartet Joins Forces on Unified Theory

A new breakthrough that bridges number theory and geometry is just the latest triumph for a close-knit group of mathematicians.