Mathematics

Mathematics News & Discoveries

Pure and applied mathematics: proofs, conjectures, new theorems, and the ideas reshaping our understanding of numbers and structure.

New Proof of Four-Color Theorem Offers Fresh Insight into Graph Theory
Mathematics
New Proof of Four-Color Theorem Offers Fresh Insight into Graph Theory
Mathematicians have found a new proof of the four-color theorem, offering fresh perspectives on graph theory and the rol
The Langlands Program: Hidden Bridges Across the Mathematical Universe
Mathematics
The Langlands Program: Hidden Bridges Across the Mathematical Universe
The Langlands program proposes hidden correspondences between distant mathematical realms. Here's what it is, why it mat
First Improvement in 30 Years for the Komlós Problem
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First Improvement in 30 Years for the Komlós Problem
After 30 years, researchers have improved the bound for the Komlós problem, a fundamental question in discrepancy theory
The Hidden Math of River Networks: How a Simple Law Governs Flow
Mathematics
The Hidden Math of River Networks: How a Simple Law Governs Flow
A simple scaling law, Hack's law, reveals that river lengths scale with drainage area to the 0.6 power, offering a unive
How AI Is Rewriting the Rules of Erdős's Legendary Math Problems
Mathematics
How AI Is Rewriting the Rules of Erdős's Legendary Math Problems
Large language models are cracking problems posed by the legendary mathematician Paul Erdős, offering a glimpse into how
Fields Medal 2026: Jacob Tsimerman's Proof of André-Oort Conjecture
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Fields Medal 2026: Jacob Tsimerman's Proof of André-Oort Conjecture
Jacob Tsimerman has been awarded the 2026 Fields Medal for his proof of the André-Oort conjecture, solving a decades-old
From Manga to Fields Medal: Yu Deng's Path to Taming Randomness in PDEs
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From Manga to Fields Medal: Yu Deng's Path to Taming Randomness in PDEs
Yu Deng has won the 2026 Fields Medal for his groundbreaking work on the random data problem in partial differential equ
Sloppy Shuffles Need More Mixes: New Math Pinpoints the Magic Number
Mathematics
Sloppy Shuffles Need More Mixes: New Math Pinpoints the Magic Number
Seven perfect shuffles randomize a deck of cards, but sloppy cuts need more. A new proof finally calculates the number f
How Terry Tao Became a Champion for AI in Mathematical Discovery
Mathematics
How Terry Tao Became a Champion for AI in Mathematical Discovery
Terry Tao champions AI in mathematics, using Lean to verify theorems and inspire new insights. Automated proof-checkers
Gödel's Incompleteness Theorems: Why Mathematics Can Never Be Complete
Mathematics
Gödel's Incompleteness Theorems: Why Mathematics Can Never Be Complete
At 25, Kurt Gödel proved that mathematics can never be fully captured by a finite set of axioms. His incompleteness theo
What Mathematics Gains by Rejecting Infinity: Ultrafinitism's Surprising Insights
Mathematics
What Mathematics Gains by Rejecting Infinity: Ultrafinitism's Surprising Insights
Ultrafinitism, long dismissed as mathematical heresy, rejects infinity entirely. This radical philosophy is now yielding
AI Unlocks Hidden Mathematical Patterns Through Self-Directed Code Generation
Mathematics
AI Unlocks Hidden Mathematical Patterns Through Self-Directed Code Generation
Researchers using DeepMind's AlphaEvolve AI discovered surprising mathematical patterns in permutation groups, with the