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Mathematics
combinatorics
Mathematician Hurls Structure and Disorder Into Century-Old Problem
A new paper shows how to create longer disordered strings than mathematicians had thought possible, proving that a well-known recent conjecture is “spectacularly wrong.”
geometry
Mathematicians Transcend Geometric Theory of Motion
More than 30 years ago, Andreas Floer changed geometry. Now, two mathematicians have finally figured out how to extend his revolutionary perspective.
Insights puzzle
Why e, the Transcendental Math Constant, Is Just the Best
The solution to our puzzle about Euler’s number explains why e pops up in situations that involve optimality.
information theory
Researchers Defeat Randomness to Create Ideal Code
By carefully constructing a multidimensional and well-connected graph, a team of researchers has finally created a long-sought locally testable code that can immediately betray whether it’s been corrupted.
Quantized Academy
What Hot Dogs Can Teach Us About Number Theory
The Chinese remainder theorem is an ancient and powerful extension of the simple math of least common multiples.
Q&A
The Mathematician Who Delights in Building Bridges
Ana Caraiani seeks to unify mathematics through her work on the ambitious Langlands program.
mathematical physics
A New Theory for Systems That Defy Newton’s Third Law
In nonreciprocal systems, where Newton’s third law falls apart, “exceptional points” are helping researchers understand phase transitions and possibly other phenomena.
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.