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# Set theory

## Latest Articles

### ‘A-Team’ of Math Proves a Critical Link Between Addition and Sets

A team of four prominent mathematicians, including two Fields medalists, proved a conjecture described as a “holy grail of additive combinatorics.”

### Ninth Dedekind Number Found by Two Independent Groups

The numbers count a variety of seemingly unrelated mathematical structures.

### Is There Math Beyond the Equal Sign?

Can mathematics handle things that are essentially the same without being exactly equal? Category theorist Eugenia Cheng and host Steven Strogatz discuss the power and pleasures of abstraction.

### Google Researcher, Long Out of Math, Cracks Devilish Problem About Sets

On nights and weekends, Justin Gilmer attacked an old question in pure math using the tools of information 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.

### Banach-Tarski and the Paradox of Infinite Cloning

One of the strangest results in mathematics explains how it’s possible to turn one sphere into two identical copies, simply by rearranging its pieces.

### Mathematicians Solve Decades-Old Classification Problem

A pair of researchers has shown that trying to classify groups of numbers called “torsion-free abelian groups” is as hard as it can possibly be.

### How Many Numbers Exist? Infinity Proof Moves Math Closer to an Answer.

For 50 years, mathematicians have believed that the total number of real numbers is unknowable. A new proof suggests otherwise.

### How Gödel’s Proof Works

His incompleteness theorems destroyed the search for a mathematical theory of everything. Nearly a century later, we’re still coming to grips with the consequences.