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Mathematics
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.
Insights puzzle
Where Transcendental Numbers Hide in Everyday Math
The transcendental number π is as familiar as it is ubiquitous, but how does Euler’s number e transcend the ordinary?
topology
How Tadayuki Watanabe Disproved a Major Conjecture About Spheres
Watanabe invented a new way of distinguishing shapes on his way to solving the last open case of the Smale conjecture, a central question in topology about symmetries of the sphere.