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elliptic curves

number theory

Mathematicians Prove 30-Year-Old André-Oort Conjecture

By Leila Sloman
February 3, 2022
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A team of mathematicians has solved an important question about how solutions to polynomial equations relate to sophisticated geometric objects called Shimura varieties.

Quantized Academy

How to Find Rational Points Like Your Job Depends on It

By Patrick Honner
July 22, 2021
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Using high school algebra and geometry, and knowing just one rational point on a circle or elliptic curve, we can locate infinitely many others.

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

Mathematicians Set Numbers in Motion to Unlock Their Secrets

By Kelsey Houston-Edwards
February 22, 2021
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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

By Erica Klarreich
April 6, 2020
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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

By Kevin Hartnett
February 13, 2020
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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

By Patrick Honner
March 14, 2019
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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

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.”


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