What's up in
infinity
explainers
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.
set theory
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.
foundations of mathematics
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.
Abstractions blog
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.
quantum information theory
The Universe’s Ultimate Complexity Revealed by Simple Quantum Games
A two-player game can reveal whether the universe has an infinite amount of complexity.
infinity
Mathematicians Measure Infinities and Find They’re Equal
Two mathematicians have proved that two different infinities are equal in size, settling a long-standing question. Their proof rests on a surprising link between the sizes of infinities and the complexity of mathematical theories.
Insights puzzle
Solution: ‘Puzzles Inspired by Ramanujan’
What can the mathematical genius Srinivasa Ramanujan teach us about number theory through mathematical structures involving infinity?
Insights puzzle
Three Puzzles Inspired by Ramanujan
Insights from the mathematical genius Srinivasa Ramanujan give us a number of ways to explore the infinite.
Insights puzzle
Solution: ‘Is Infinity Real?’
Hilbert’s Hotel, an incredibly thin triangle and an elliptical pool table help us test the concept of infinity in the physical world.