Maggie Chiang for Quanta Magazine

Infinite sums are among the most underrated yet powerful concepts in mathematics, capable of linking concepts across math’s vast web.

In a quest to map out a quantum theory of gravity, researchers have used logical rules to calculate how much Einstein’s theory must change. The result matches string theory perfectly.

In computer simulations of possible universes, researchers have discovered that a neural network can infer the amount of matter in a whole universe by studying just one of its galaxies.

For years, intermediate measurements made it hard to quantify the complexity of quantum algorithms. New work establishes that those measurements aren’t necessary after all.

Paul Nelson has solved the subconvexity problem, bringing mathematicians one step closer to understanding the Riemann hypothesis and the distribution of prime numbers.

Physicists have been busy exploring how our universe might emerge like a hologram out of a two-dimensional sheet. New clues have come from the symmetries found on an infinitely distant “celestial sphere.”

Studies that map the adaptive value of viral mutations hint at how the COVID-19 pandemic might progress next.

A surprising new solution to Leonhard Euler’s famous “36 officers puzzle” offers a novel way of encoding quantum information.

By carefully constructing a multidimensional and well-connected graph, a team of researchers has finally created a long-sought locally testable code that can immediately betray whether it’s been corrupted.

The solution to our puzzle about Euler’s number explains why e pops up in situations that involve optimality.

In our mind’s eye, the universe seems to go on forever. But using geometry we can explore a variety of three-dimensional shapes that offer alternatives to “ordinary” infinite space.

*Quanta Magazine* is committed to in-depth, accurate journalism that serves the public interest. Each article braids the complexities of science with the malleable art of storytelling and is meticulously reported, edited and fact-checked. Launched and funded by the Simons Foundation, *Quanta* is editorially independent — our articles do not reflect or represent the views of the foundation.