Abstractions blog

A new paper establishes a long-conjectured bound about the size of the overlap between sets of lines and points.

Some modern image generators rely on the principles of diffusion to create images. Alternatives based on the process behind the distribution of charged particles may yield even better results.

Because tree seedlings don’t grow as well when close to their parents, more tree species can be packed into tropical forests.

On its surface, the Kakeya conjecture is a simple statement about rotating needles. But it underlies a wealth of mathematics.

Scientists have struggled to accurately forecast the strength of the sun’s 11-year cycle — even after centuries of solar observations.

Mathematical proofs based on a technique called diagonalization can be relentlessly contrarian, but they help reveal the limits of algorithms.

New research finds that the memories useful for future generalizations are held in the brain separately from those recording unusual events.

Quantum computing is still really, really hard. But the rise of a powerful class of error-correcting codes suggests that the task might be slightly more feasible than many feared.

Researchers have discovered ways around a fundamental trade-off between accuracy and beauty in digital images.