Archivo: Quanta

Modular forms are one of the most beautiful and mysterious objects in mathematics. What are they?

Number theorist Andrew Granville on what mathematics really is — and why objectivity is never quite within reach.


By treating Earth as a topological insulator — a state of quantum matter — physicists found a powerful explanation for the movements of the planet’s air and seas.


Mathematicians can often figure out what happens as quantities grow infinitely large. What about when they are just a little big?

Mathematicians probe the limits of randomness in new work estimating quantities called Ramsey numbers.

The puzzling behavior of black hole interiors has led researchers to propose a new physical law: the second law of quantum complexity.

Renate Loll has helped pioneer a radically new approach to quantum gravity. She assumes that the fabric of space-time is a blend of all possible fabrics, and she has developed the computational tools needed to calculate the far-reaching implications of that assumption.

In two landmark experiments, researchers used quantum processors to engineer exotic particles that have captivated physicists for decades. The work is a step toward crash-proof quantum computers.

If we want to understand complex constructions, such as ourselves, assembly theory says we must account for the entire history of how such entities came to be.

It’s been known for thousands of years that the primes go on forever, but new proofs give fresh insights into how theorems depend on one another.