Mathematics

A graduate student has helped illuminate a long-suspected connection between addition and multiplication.

Neural networks can be as unpredictable as they are powerful. Now mathematicians are beginning to reveal how a neural network’s form will influence its function.

Turbulence is everywhere, yet it is one of the most difficult concepts for physicists to understand.

The Brazilian mathematician Carolina Araujo, who calls herself “a bit of an anarchist,” is organizing meetings and building a support network to study and solve the problems women face in mathematics.

A science fiction novelist and an internet commenter made breakthroughs on a longstanding problem about the number of ways you can arrange a set of items. What did they discover?

Several mathematicians under the age of 30 left their marks all over the field, and amateur problem-solvers of all ages made significant contributions to long-dormant puzzles.

In a Paris lab, researchers have shown for the first time that quantum methods of transmitting information are superior to classical ones.

Digital security depends on the difficulty of factoring large numbers. A new proof shows why one method for breaking digital encryption won’t work.

Equations, like numbers, cannot always be split into simpler elements.