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Mathematics
topology
Unimaginable Surfaces Discovered After Decades-Long Search
Using ideas borrowed from graph theory, two mathematicians have shown that extremely complex surfaces are easy to traverse.
Quantized Columns
What Is the Langlands Program?
The Langlands program provides a beautifully intricate set of connections between various areas of mathematics, pointing the way toward novel solutions for old problems.
Insights puzzle
The Secret Math Behind Mind-Reading Magic Tricks
Four puzzle solutions reveal different ways to divine someone’s hidden number with impossibly little information.
Quantized Academy
Why Claude Shannon Would Have Been Great at Wordle
A bit of information theory can help you analyze — and improve — your Wordle game.
topology
How Complex Is a Knot? New Proof Reveals Ranking System That Works.
“Ribbon concordance” will let mathematicians compare knots by linking them across four-dimensional space.
Insights puzzle
Think of a Number. How Do Math Magicians Know What It Is?
Mathematical magic can seem like mind reading. Your job is to reveal the secret behind these four tricks.
fluid dynamics
Mathematicians Coax Fluid Equations Into Nonphysical Solutions
The famed Navier-Stokes equations can lead to cases where more than one result is possible, but only in an extremely narrow set of situations.
graph theory
Elegant Six-Page Proof Reveals the Emergence of Random Structure
Two young mathematicians have astonished their colleagues with a full proof of the Kahn-Kalai conjecture — a sweeping statement about how structure emerges in random sets and graphs.
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.