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# Infinity

## Latest Articles

### How the Square Root of 2 Became a Number

Useful mathematical concepts, like the number line, can linger for millennia before they are rigorously defined.

### How Math Achieved Transcendence

Transcendental numbers include famous examples like e and π, but it took mathematicians centuries to understand them.

### How Can Some Infinities Be Bigger Than Others?

All infinities go on forever, so how is it possible for some infinities to be larger than others? The mathematician Justin Moore discusses the mysteries of infinity with Steven Strogatz.

### How Big Is Infinity?

Of all the endless questions children and mathematicians have asked about infinity, one of the biggest has to do with its size.

### The Year in Math and Computer Science

Mathematicians and computer scientists answered major questions in topology, set theory and even physics, even as computers continued to grow more capable.

### 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.

### In Quantum Games, There’s No Way to Play the Odds

These games combine quantum entanglement, infinity and impossible-to-calculate winning probabilities. But if researchers can crack them, they’ll reveal deep mathematical secrets.