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elliptic curves

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Abstractions blog

New Proof Shows Infinite Curves Come in Two Types

By Kevin Hartnett
November 7, 2018
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Alexander Smith’s work on the Goldfeld conjecture reveals fundamental characteristics of elliptic curves.

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?

Photo of Dr. Peter Scholze
2018 Fields Medal and Nevanlinna Prize

A Master of Numbers and Shapes Who Is Rewriting Arithmetic

By Erica Klarreich
August 1, 2018
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The 30-year-old math sensation Peter Scholze is now one of the youngest Fields medalists for “the revolution that he launched in arithmetic geometry.”

Pariah moonshine
number theory

Mathematicians Find Moonshine Link for Pariah Symmetries

By Erica Klarreich
September 22, 2017
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A type of symmetry so unusual that it was called a “pariah” turns out to have deep connections to number theory.

profiles

The Oracle of Arithmetic

By Erica Klarreich
June 28, 2016
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At 28, Peter Scholze is uncovering deep connections between number theory and geometry.

Manjul Bhargava video
2014 Fields Medal and Nevanlinna Prize

The Musical, Magical Number Theorist

By Erica Klarreich
August 12, 2014
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The search for artistic truth and beauty has led Manjul Bhargava to some of the most profound recent discoveries in number theory, which have helped earn him the Fields Medal.

number theory

Mathematicians Shed Light on Elliptic Curves

By Erica Klarreich
July 9, 2013
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Two young mathematicians are illuminating a frontier in the study of rational solutions to polynomial equations: the cubics.


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