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# Mathematics

## Latest Articles

### Surfaces So Different Even a Fourth Dimension Can’t Make Them the Same

For decades mathematicians have searched for a specific pair of surfaces that can’t be transformed into each other in four-dimensional space. Now they’ve found them.

### Graduate Student’s Side Project Proves Prime Number Conjecture

Jared Duker Lichtman, 26, has proved a longstanding conjecture relating prime numbers to a broad class of “primitive” sets. To his adviser, it came as a “complete shock.”

### Surfaces Beyond Imagination Are Discovered After Decades-Long Search

Using ideas borrowed from graph theory, two mathematicians have shown that extremely complex surfaces are easy to traverse.

### 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.

### The Secret Math Behind Mind-Reading Magic Tricks

Four puzzle solutions reveal different ways to divine someone’s hidden number with impossibly little information.

### Why Claude Shannon Would Have Been Great at Wordle

A bit of information theory can help you analyze — and improve — your Wordle game.

### 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.

### 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.

### 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.