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

Three mathematicians show, for the first time, how to form a square with the same area as a circle by cutting them into interchangeable pieces that can be visualized.

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

Scientists have never been able to adequately explain where lightning comes from. Now the first detailed observations of its emergence inside a cloud have exposed how electric fields grow strong enough to let bolts fly.

The “gravitational memory effect” predicts that a passing gravitational wave should forever alter the structure of space-time. Physicists have linked the phenomenon to a potential solution to the black hole information paradox.

Tiny amounts of artificial noise can fool neural networks, but not humans. Some researchers are looking to neuroscience for a fix.

One of the first goals of quantum computing has been to recreate bizarre quantum systems that can’t be studied in an ordinary computer. A dark-horse quantum simulator has now done just that.

New work establishes a tighter connection between the rank of a polynomial and the extent to which it favors particular outputs.

Time was found to flow differently between the top and bottom of a single cloud of atoms. Physicists hope that such a system will one day help them combine quantum mechanics and Einstein’s theory of gravity.

Built upon the ubiquitous Fourier transform, the mathematical tools known as wavelets allow unprecedented analysis and understanding of continuous signals.

As topologists seek to classify shapes, the effort hinges on how to define a manifold and what it means for two of them to be equivalent.

Genomes hold immense quantities of noncoding DNA. Some of it is essential for life, some seems useless, and some has its own agenda.

The most widely used technique for finding the largest or smallest values of a math function turns out to be a fundamentally difficult computational problem.

The mechanism behind leopard spots and zebra stripes also appears to explain the patterned growth of a bismuth crystal, extending Alan Turing’s 1952 idea to the atomic scale.

The DNA of some viruses doesn’t use the same four nucleotide bases found in all other life. New work shows how this exception is possible and hints that it could be more common than we think.