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modular forms

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A modular form is shown as a distorted, rainbow-hued dome atop concentric circles.
number theory

New Proof Distinguishes Mysterious and Powerful ‘Modular Forms’

By Jordana Cepelewicz
March 9, 2023
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Using “refreshingly old” tools, mathematicians resolved a 50-year-old conjecture about how to categorize important functions called modular forms, with consequences for number theory and theoretical physics.

Maryna Viazovska seated on the wooden steps of an amphitheater at the Swiss Federal Institute of Technology Lausanne.
2022 Fields and Abacus Medals

In Times of Scarcity, War and Peace, a Ukrainian Finds the Magic in Math

By Thomas Lin +1 authors
Erica Klarreich
July 5, 2022
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With her homeland mired in war, the sphere-packing number theorist Maryna Viazovska has become the second woman to win a Fields Medal in the award’s 86-year history.

Black and white photo of John Conway against a black background
Abstractions blog

John Conway Solved Mathematical Problems With His Bare Hands

By Kevin Hartnett
April 20, 2020
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The legendary mathematician, who died on April 11, was curious, colorful and one of the greatest problem-solvers of his generation.

Art for "How Feynman Diagrams Revolutionized Physics"
sphere packing

Out of a Magic Math Function, One Solution to Rule Them All

By Erica Klarreich
May 13, 2019
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Mathematicians used “magic functions” to prove that two highly symmetric lattices solve a myriad of problems in eight- and 24-dimensional space.

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.

geometry

Sphere Packing Solved in Higher Dimensions

By Erica Klarreich
March 30, 2016
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The Ukrainian mathematician Maryna Viazovska has solved the centuries-old sphere-packing problem in dimensions eight and 24.

number theory

Mathematicians Chase Moonshine’s Shadow

By Erica Klarreich
March 12, 2015
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Researchers are on the trail of a mysterious connection between number theory, algebra and string theory.

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