Abstractions blog

A new model of learning centers on bursts of neural activity that act as teaching signals — approximating backpropagation, the algorithm behind learning in AI.

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.

The unexpected discovery of the double-charm tetraquark has given physicists a new tool with which to hone their understanding of the strongest of nature’s fundamental forces.

The n-queens problem is about finding how many different ways queens can be placed on a chessboard so that none attack each other. A mathematician has now all but solved it.

A painstaking study of wing morphology shows both the striking uniformity of individuals in a species and a subtle pattern of linked variations that evolution can exploit.

Legend says the Chinese military once used a mathematical ruse to conceal its troop numbers. The technique relates to many deep areas of modern math research.

Computational neuroscientists taught an artificial neural network to imitate a biological neuron. The result offers a new way to think about the complexity of single brain cells.

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