Decades ago, a mathematician posed a warmup problem for some of the most difficult questions about prime numbers. It turned out to be just as difficult to solve, until now.

In the 1960s, drillers noticed that certain fluids would firm up if they flowed too fast. Researchers have finally explained why.

New studies reveal the ancient, shared genetic “grammar” underpinning the diverse evolution of fish fins and tetrapod limbs.

A new result shows that quantum information can theoretically be protected from errors just as well as classical information can.

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

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

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…

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

The electrical chatter of our working memories reflects our uncertainty about their contents.

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.

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.

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.

By using hypernetworks, researchers can now preemptively fine-tune artificial neural networks, saving some of the time and expense of training.

The same phenomenon by which an opera singer can shatter a wineglass also underlies the very existence of subatomic particles.

Back when the sun was 30% dimmer, Earth should have frozen solid. Yet water flowed and life blossomed. The solution to the paradox shows that we might have that faint sun to owe for life’s existence —…

The triangle angle sum theorem makes working with triangles easy. What happens when you can’t rely on it?

Large blocks of genes conserved through hundreds of millions of years of evolution hint at how the first animal chromosomes came to be.

A team of mathematicians has solved an important question about how solutions to polynomial equations relate to sophisticated geometric objects called Shimura varieties.

Two teams have shown how quantum approaches can solve problems faster than classical computers, bringing physics and computer science closer together.

If only scientists understood exactly how electrons act in molecules, they’d be able to predict the behavior of everything from experimental drugs to high-temperature superconductors.