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elliptic curves

An illustration of a doughnut-shaped elliptic curve intertwined with the Julia set.
number theory

Mathematicians Set Numbers in Motion to Unlock Their Secrets

February 22, 2021

A new proof demonstrates the power of arithmetic dynamics, an emerging discipline that combines insights from number theory and dynamical systems.

Langlands program

‘Amazing’ Math Bridge Extended Beyond Fermat’s Last Theorem

April 6, 2020

Mathematicians have figured out how to expand the reach of a mysterious bridge connecting two distant continents in the mathematical world.

Multimedia

The Map of Mathematics

February 13, 2020

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

Art for "Where Proof, Evidence and Imagination Intersect"
Quantized Academy

Where Proof, Evidence and Imagination Intersect

March 14, 2019

In mathematics, where proofs are everything, evidence is important too. But evidence is only as good as the model, and modeling can be dangerous business. So how much evidence is enough?

Abstractions blog

New Proof Shows Infinite Curves Come in Two Types

November 7, 2018

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

October 31, 2018

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

August 1, 2018

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

September 22, 2017

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

June 28, 2016

At 28, Peter Scholze is uncovering deep connections between number theory and geometry.