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Mathematicians Eliminate Long-Standing Threat to Knot Conjecture

Over 60 years ago, Ralph Fox posed a problem about knots that haunts mathematicians to this day. His question is now often formulated as the “slice-ribbon conjecture,” which posits that two seemingly distinct groups of knots are actually the same. With its suggestion of elegant simplicity within the world of knots, it’s become one of the most high-profile...

Machines Learn Better if We Teach Them the Basics

Imagine that your neighbor calls to ask a favor: Could you please feed their pet rabbit some carrot slices? Easy enough, you’d think. You can imagine their kitchen, even if you’ve never been there — carrots in a fridge, a drawer holding various knives. It’s abstract knowledge: You don’t know what your neighbor’s carrots and knives look like exactly,...

When Does the Brain Operate at Peak Performance?

Over the last few decades, an idea called the critical brain hypothesis has been helping neuroscientists understand how the human brain operates as an information-processing powerhouse. It posits that the brain is always teetering between two phases, or modes, of activity: a random phase, where it is mostly inactive, and an ordered phase, where it is...

Astronomers Say They Have Spotted the Universe’s First Stars

A group of astronomers poring over data from the James Webb Space Telescope (JWST) has glimpsed light from ionized helium in a distant galaxy, which could indicate the presence of the universe’s very first generation of stars. These long-sought, inaptly named “Population III” stars would have been ginormous balls of hydrogen and helium sculpted from...

How Quantum Physicists ‘Flipped Time’ (and How They Didn’t)

Physicists have coaxed particles of light into undergoing opposite transformations simultaneously, like a human turning into a werewolf as the werewolf turns into a human. In carefully engineered circuits, the photons act as if time were flowing in a quantum combination of forward and backward. “For the first time ever, we kind of have a time-traveling...

The Cause of Depression Is Probably Not What You Think

People often think they know what causes chronic depression. Surveys indicate that more than 80% of the public blames a “chemical imbalance” in the brain. That idea is widespread in pop psychology and cited in research papers and medical textbooks. Listening to Prozac, a book that describes the life-changing value of treating depression with medications...

The Computer Scientist Who Finds Life Lessons in Games

For Shang-Hua Teng, theoretical computer science has never been purely theoretical. Now 58, Teng is a professor of computer science at the University of Southern California and a two-time winner of the Gödel Prize, an annual award recognizing groundbreaking theoretical work. But he often strives to connect that abstract theory to everyday life in ways...

Mathematicians Find an Infinity of Possible Black Hole Shapes

The cosmos seems to have a preference for things that are round. Planets and stars tend to be spheres because gravity pulls clouds of gas and dust toward the center of mass. The same holds for black holes — or, to be more precise, the event horizons of black holes — which must, according to theory, be spherically shaped in a universe with three dimensions...

The Basic Algebra Behind Secret Codes and Space Communication

Space exploration requires tremendous precision. When you’re landing a rover on Mars 70 million miles away from the nearest service station, you need to maximize efficiency and prepare for the unexpected. This applies to everything from spacecraft design to data transmission: Those messages returning to Earth as a steady stream of 0s and 1s are bound...

Standard Model of Cosmology Survives a Telescope’s Surprising Finds

The cracks in cosmology were supposed to take a while to appear. But when the James Webb Space Telescope (JWST) opened its lens last spring, extremely distant yet very bright galaxies immediately shone into the telescope’s field of view. “They were just so stupidly bright, and they just stood out,” said Rohan Naidu, an astronomer at the Massachusetts...

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