For the third time this year, a major problem in combinatorics has been solved. The new proof provides a way for mathematicians to answer questions about Ramsey numbers, quantities that measure when structure must emerge in graphs. https://www.quantamagazine.org/mathematicians-discover-new-way-to-predict-structure-in-graphs-20230622/

The mathematicians Kathryn Mann, Thomas Barthelmé and Steven Frankel have found a new way to distinguish Anosov flows, dynamical systems that can help reveal structure in chaos. https://www.quantamagazine.org/flow-proof-helps-mathematicians-find-stability-in-chaos-20230615/

“Embryo models” derived entirely from stem cells could transform developmental biology. Recent experiments with these embryolike constructs raise complex questions about what they are — and what their limits ought to be. https://www.quantamagazine.org/embryo-models-challenge-legal-ethical-and-biological-concepts-20230613/

A new measurement of the strong nuclear force, which binds protons and neutrons together, challenges our understanding of the nucleus. Theorists hope they can bring balance to the force. https://www.quantamagazine.org/a-new-experiment-casts-doubt-on-the-leading-theory-of-the-nucleus-20230612/

Chris German, a marine geochemist at Woods Hole and the leader of NASA’s Exploring Ocean Worlds project, has perhaps done more than anyone to explore hydrothermal vents. His work is helping inform the search for life on other worlds. “It never gets boring.” https://www.quantamagazine.org/ocean-vent-explorer-guides-nasas-look-at-icy-alien-worlds-20230607/

Gerrymandering is more sophisticated than it once was. Mathematicians are pioneering new ways to determine electoral fairness — and their work is ending up in court. https://www.quantamagazine.org/how-math-has-changed-the-shape-of-gerrymandering-20230601/

Skates are flat like a pancake but evolved from ancient sharklike creatures. Biologists have shown that the rays got their shape not from a simple gene mutation, but from a change to the 3D architecture of its genome. https://www.quantamagazine.org/how-3d-changes-in-the-genome-turned-sharks-into-skates-20230530/

A recent neuroscience study hints at how our brains distinguish between what we imagine and what we observe. https://www.quantamagazine.org/is-it-real-or-imagined-how-your-brain-tells-the-difference-20230524/

The recent discovery of the aperiodic hat tile inspired mathematicians around the world. In this month’s Quantized Academy column, Patrick Honner breaks down the basic concepts behind this beautiful pattern: https://www.quantamagazine.org/math-that-goes-on-forever-but-never-repeats-20230523/

A study led by researchers at UC Berkeley, the University of Washington and Johns Hopkins University suggests that natural and artificial networks learn in similar ways, at least when it comes to language. Steve Nadis reports: https://www.quantamagazine.org/some-neural-networks-learn-language-like-humans-20230522/