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polynomials
2022 Fields and Abacus Medals
He Dropped Out to Become a Poet. Now He’s Won a Fields Medal.
June Huh wasn’t interested in mathematics until a chance encounter during his sixth year of college. Now his profound insights connecting combinatorics and geometry have led to math’s highest honor.
Quantized Columns
The Sordid Past of the Cubic Formula
The quest to solve cubic equations led to duels, betrayals — and modern mathematics.
number theory
New Proof Illuminates the Hidden Structure of Common Equations
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
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
A team of mathematicians has solved an important question about how solutions to polynomial equations relate to sophisticated geometric objects called Shimura varieties.
polynomials
Mathematicians Find Structure in Biased Polynomials
New work establishes a tighter connection between the rank of a polynomial and the extent to which it favors particular outputs.
polynomials
Surprising Limits Discovered in Quest for Optimal Solutions
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
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
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.