Abstractions blog

The Markov numbers reveal the secrets of irrational numbers and the patterns of the Fibonacci sequence. But there’s one question about them that has resisted proof for over a century.

A century ago, the Stern-Gerlach experiment established the truth of quantum mechanics. Now it’s being used to probe the clash of quantum theory and gravity.

Paradoxically, natural selection can sometimes seem to block organisms from evolving useful adaptations. But a new study of “fitness landscapes” and antibiotic resistance in bacteria shows that life still finds a way.

Three computer scientists have disproved a long-standing conjecture about a fundamental problem involving imperfect information.

Some strange mathematical sequences are always whole numbers — until they’re not. The puzzling patterns have revealed ties to graph theory and prime numbers, awing mathematicians.

Cells in the placenta have an unusual trick for activating gentle immune defenses and keeping them turned on when no infection is present. It involves crafting and deploying a fake virus.

Three researchers have found a long-sought way to pull information from large databases secretly, moving us closer to fully private internet searches.

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

After identifying interlocking symmetries in mammalian cells, scientists can describe some tissues as liquid crystals — an observation that lays the groundwork for a fluid-dynamic theory of how tissues move.