New Proofs Probe Soap-Film Singularities Mathematicians have broken through a long-standing barrier in the study of “minimizing surfaces,” which play an important role in both math and physics. The post [New Proofs Probe Soap-Film Singularities][1] first appeared on [Quanta Magazine][2] [1]: https://www.quantamagazine.org/new-proofs-probe-soap-film-singularities-20251112/ [2]: https://www.quantamagazine.org https://www.quantamagazine.org/new-proofs-probe-soap-film-singularities-20251112/

To Have Machines Make Math Proofs, Turn Them Into a Puzzle Marijn Heule uses turns mathematical statements into something like Sudoku puzzles, then has computers go to work on them. His proofs have been called “disgusting,” but they go beyond what any human can do. The post [To Have Machines Make Math Proofs, Turn Them Into a Puzzle][1] first appeared on [Quanta Magazine][2] [1]: https://www.quantamagazine.org/to-have-machines-make-math-proofs-turn-them-into-a-puzzle-20251110/ [2]: https://www.quantamagazine.org https://www.quantamagazine.org/to-have-machines-make-math-proofs-turn-them-into-a-puzzle-20251110/

Physicists Take the Imaginary Numbers Out of Quantum Mechanics Quantum mechanics has at last been formulated exclusively with real numbers, bringing a mathematical puzzle at the heart of the theory into a new era of inquiry. The post [Physicists Take the Imaginary Numbers Out of Quantum Mechanics][1] first appeared on [Quanta Magazine][2] [1]: https://www.quantamagazine.org/physicists-take-the-imaginary-numbers-out-of-quantum-mechanics-20251107/ [2]: https://www.quantamagazine.org https://www.quantamagazine.org/physicists-take-the-imaginary-numbers-out-of-quantum-mechanics-20251107/

How Your Brain Creates ‘Aha’ Moments and Why They Stick A sudden flash of insight is a product of your brain. Neuroscientists track the neural activity underlying an “aha” and how it might boost memory. The post [How Your Brain Creates ‘Aha’ Moments and Why They Stick][1] first appeared on [Quanta Magazine][2] [1]: https://www.quantamagazine.org/how-your-brain-creates-aha-moments-and-why-they-stick-20251105/ [2]: https://www.quantamagazine.org https://www.quantamagazine.org/how-your-brain-creates-aha-moments-and-why-they-stick-20251105/

What Is a Manifold? In the mid-19th century, Bernhard Riemann conceived of a new way to think about mathematical spaces, providing the foundation for modern geometry and physics. The post [What Is a Manifold?][1] first appeared on [Quanta Magazine][2] [1]: https://www.quantamagazine.org/what-is-a-manifold-20251103/ [2]: https://www.quantamagazine.org https://www.quantamagazine.org/what-is-a-manifold-20251103/

In a First, AI Models Analyze Language As Well As a Human Expert If language is what makes us human, what does it mean now that large language models have gained “metalinguistic” abilities? The post [In a First, AI Models Analyze Language As Well As a Human Expert][1] first appeared on [Quanta Magazine][2] [1]: https://www.quantamagazine.org/in-a-first-ai-models-analyze-language-as-well-as-a-human-expert-20251031/ [2]: https://www.quantamagazine.org https://www.quantamagazine.org/in-a-first-ai-models-analyze-language-as-well-as-a-human-expert-20251031/

Carlo Rovelli’s Radical Perspective on Reality The theoretical physicist and best-selling author finds inspiration in politics and philosophy for rethinking space and time. The post [Carlo Rovelli’s Radical Perspective on Reality][1] first appeared on [Quanta Magazine][2] [1]: https://www.quantamagazine.org/carlo-rovellis-radical-perspective-on-reality-20251029/ [2]: https://www.quantamagazine.org https://www.quantamagazine.org/carlo-rovellis-radical-perspective-on-reality-20251029/

Shark Data Suggests Animals Scale Like Geometric Objects Despite their wide variety of sizes, niches and shapes, sharks scale geometrically, pointing to possible fundamental constraints on evolution. The post [Shark Data Suggests Animals Scale Like Geometric Objects][1] first appeared on [Quanta Magazine][2] [1]: https://www.quantamagazine.org/shark-data-suggests-animals-scale-like-geometric-objects-20251027/ [2]: https://www.quantamagazine.org https://www.quantamagazine.org/shark-data-suggests-animals-scale-like-geometric-objects-20251027/

First Shape Found That Can’t Pass Through Itself After more than three centuries, a geometry problem that originated with a royal bet has been solved. The post [First Shape Found That Can’t Pass Through Itself][1] first appeared on [Quanta Magazine][2] [1]: https://www.quantamagazine.org/first-shape-found-that-cant-pass-through-itself-20251024/ [2]: https://www.quantamagazine.org https://www.quantamagazine.org/first-shape-found-that-cant-pass-through-itself-20251024/

The Game Theory of How Algorithms Can Drive Up Prices Recent findings reveal that even simple pricing algorithms can make things more expensive. The post [The Game Theory of How Algorithms Can Drive Up Prices][1] first appeared on [Quanta Magazine][2] [1]: https://www.quantamagazine.org/the-game-theory-of-how-algorithms-can-drive-up-prices-20251022/ [2]: https://www.quantamagazine.org https://www.quantamagazine.org/the-game-theory-of-how-algorithms-can-drive-up-prices-20251022/