Explainers

Useful mathematical concepts, like the number line, can linger for millennia before they are rigorously defined.

Making ice requires more than subzero temperatures. The unpredictable process takes microscopic scaffolding, random jiggling and often a little bit of bacteria.

Particle physicists in search of the next theory of reality are consulting a mathematical structure that they know will never fail: a table of possibilities known as the S-matrix.

By making use of randomness, a team has created a simple algorithm for estimating large numbers of distinct objects in a stream of data.

By apparently overtraining them, researchers have seen neural networks discover novel solutions to problems.

When your mind is wandering, your brain’s “default mode” network is active. Its discovery 20 years ago inspired a raft of research into networks of brain regions and how they interact with each other.

Quadratic reciprocity lurks around many corners in mathematics. By proving it, number theorists reimagined their whole field.

Mathematical logic and the code of computer programs are, in an exact way, mirror images of each other.

Exposure to a virus isn’t an all-or-nothing proposition. The concept of “infectious dose” suggests ways to keep ourselves safer from harm.