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polynomials

A mathematical graph with plant roots.
number theory

New Proof Illuminates the Hidden Structure of Common Equations

By Leila Sloman
April 21, 2022
Read Later

Van der Waerden’s conjecture mystified mathematicians for 85 years. Its solution shows how polynomial roots relate to one another.

machine learning

Machine Learning Becomes a Mathematical Collaborator

By Kelsey Houston-Edwards
February 15, 2022
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Two recent collaborations between mathematicians and DeepMind demonstrate the potential of machine learning to help researchers generate new mathematical conjectures.

number theory

Mathematicians Prove 30-Year-Old André-Oort Conjecture

By Leila Sloman
February 3, 2022
Read Later

A team of mathematicians has solved an important question about how solutions to polynomial equations relate to sophisticated geometric objects called Shimura varieties.

An image with Lego blocks representing polynomials and their factors.
polynomials

Mathematicians Find Structure in Biased Polynomials

By Tamar Lichter Blanks
November 9, 2021
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New work establishes a tighter connection between the rank of a polynomial and the extent to which it favors particular outputs.

A graphic of global air travel.
polynomials

Surprising Limits Discovered in Quest for Optimal Solutions

By Max G. Levy
November 1, 2021
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Algorithms that zero in on solutions to optimization problems are the beating heart of machine reasoning. New results reveal surprising limits.

Quantized Academy

The Simple Math Behind the Mighty Roots of Unity

By Patrick Honner
September 23, 2021
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Solutions to the simplest polynomial equations — called “roots of unity” — have an elegant structure that mathematicians still use to study some of math’s greatest open questions.

number theory

How Ancient War Trickery Is Alive in Math Today

By Lakshmi Chandrasekaran
September 14, 2021
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Legend says the Chinese military once used a mathematical ruse to conceal its troop numbers. The technique relates to many deep areas of modern math research.

Animated illustration showing multiple permutations of colorful letters
group theory

Galois Groups and the Symmetries of Polynomials

By Allison Whitten
August 3, 2021
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By focusing on relationships between solutions to polynomial equations, rather than the exact solutions themselves, Évariste Galois changed the course of modern mathematics.

Illustration of figures building a large structure, with a new material being used for the latest additions
polynomials

Mathematicians Find Long-Sought Building Blocks for Special Polynomials

By Kelsey Houston-Edwards
May 25, 2021
Read Later

Hilbert’s 12th problem asked for novel analogues of the roots of unity, the building blocks for certain number systems. Now, over 100 years later, two mathematicians have produced them.


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