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algebraic geometry

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number theory

Without a Proof, Mathematicians Wonder How Much Evidence Is Enough

By Kevin Hartnett
October 31, 2018
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A new statistical model appears to undermine long-held assumptions in number theory. How much should it be trusted when all that really matters is proof?

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

Titans of Mathematics Clash Over Epic Proof of ABC Conjecture

By Erica Klarreich
September 20, 2018
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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

By Kevin Hartnett
September 17, 2018
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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

By Kevin Hartnett
September 5, 2018
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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

An Innovator Who Brings Order to an Infinitude of Equations

By Kevin Hartnett
August 1, 2018
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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

By Kevin Hartnett
October 11, 2017
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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

By Kevin Hartnett
June 27, 2017
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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

By Kevin Hartnett
November 15, 2016
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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

By Kevin Hartnett
December 21, 2015
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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.


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