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An OpenAI model has disproved a central conjecture in discrete geometry

Today, we share a breakthrough on the unit distance problem. Since Erdős’s original work, the prevailing belief has been that the “square grid” constructions depicted further below were essentially optimal for maximizing the number of unit-distance pairs. An internal OpenAI model has disproved this longstanding conjecture, providing an infinite family of examples that yield a polynomial improvement. The proof has been checked by a group of external mathematicians. They have also written a companion paper explaining the argument and providing further background and context for the significance of the result.

The result is also notable for how it was found. The proof came from a new general-purpose reasoning model, rather than from a system trained specifically for mathematics, scaffolded to search through proof strategies, or targeted at the unit distance problem in particular. As part of a broader effort to test whether advanced models can contribute to frontier research, we evaluated it on a collection of Erdős problems. In this case, it produced a proof resolving the open problem.

This proof is an important milestone for the math and AI communities. It marks the first time that a prominent open problem, central to a subfield of mathematics, has been solved autonomously by AI. It also demonstrates the depth of reasoning these systems now support. Mathematics provides a particularly clear testbed for reasoning: the problems are precise, potential proofs can be checked, and a long argument only works if the reasoning holds together from beginning to end. The method by which the problem was solved is also notable. The proof brings unexpected, sophisticated ideas from algebraic number theory to bear on an elementary geometric question.

AI atlas reveals hidden whole-body-damage caused by obesity

Obesity affects far more than metabolism and fat storage. It alters immune activity, nerve structure, and tissue organization across multiple organ systems, increasing the risk of diseases including type 2 diabetes, cardiovascular disease, stroke, neuropathy and cancer. Yet despite these systemic effects, researchers have lacked tools capable of studying disease-associated changes across the entire body in intact organisms and at high resolution.

A team led by Prof. Ali Ertürk, Director of the Institute for Biological Intelligence (iBIO) at Helmholtz Munich and Professor at the LMU, has now developed MouseMapper, a suite of foundation-model-based deep-learning algorithms designed to analyze whole-body biological imaging data. The framework automatically segments 31 organs and tissue types while quantitatively mapping nerves and immune cells throughout the body, enabling comprehensive multi-system analysis in intact mice.

“MouseMapper is built on a foundation model, which means it generalizes far beyond the data it was originally trained on,” says Ying Chen, co-first author of the study published in Nature.

To study how chips really work, MIT researchers built their own operating system

When security researchers want to understand what a modern processor is really doing with the kind of detail that determines whether attacks like Spectre and Meltdown are possible, they usually run their experiments on top of an operating system that was never built for the job. They open up macOS or Linux, patch the kernel by hand, and hope the modifications hold. The approach is unstable, hard to reproduce, and on Apple’s platforms, slated for deprecation.

A team at MIT’s Computer Science and Artificial Intelligence Laboratory (CSAIL) decided to build something different. Fractal, a new operating system kernel written from the ground up, treats the hardware itself as the object of study. Its first major use, a deep look at the branch predictors (CPU’s way of guessing what code to run next before it knows for certain), so it doesn’t have to waste time waiting to find out) inside Apple’s M1 processor, has already turned up findings that prior work missed, including the first evidence that a class of speculative attack known as “Phantom” affects Apple Silicon.

“We’re using hardware in ways it wasn’t designed for,” says Joseph Ravichandran, the MIT PhD student who led the project. “It’s not even obvious that this is a possible thing you could do with the hardware. But we found a way to pull all these different primitives off. It’s like a microscope. If you’ve got a hand magnifying glass, you can see a little bit. But if you had an electron microscope, now we’re really talking. That’s what Fractal is. The electron microscope of operating systems.”

Is materialism holding science back? | Adam Frank, Lisa Feldman Barrett, Michael Levin

Lisa Feldman Barrett, Michael Levin and Adam Frank discuss whether science should abandon its materialist framework.

Could a different metaphysics help science to progress further?

With a free trial, you can watch the full debate NOW at https://iai.tv/video/science-beyond-t… centuries, we’ve assumed that science has banished the transcendent and established that reality is entirely physical. But critics argue there are signs that a rigorous materialism might be holding science back. Increasingly, “emergence” is used to account for everything from consciousness to spacetime – a convenient placeholder for what materialist science may be unable to explain. Physicists like Heisenberg and Hawking concluded that science gives us models of reality, rather than final descriptions of its true nature, while there are scientists working in everything from biology to computer science who suggest that dualism is a productive metaphysical framework for their research. Materialism may have enabled science to reach beyond the dogmas of religion, but there are now those who are restlessly probing the limits of materialism itself. Does science need to assume a materialist account of the world or might this have fundamental limitations? Could a different metaphysics help science make progress on key questions, from the origin of life to the mysteries of quantum gravity? Or would abandoning materialism risk returning us to the myths of superstition and religion? #science #materialism #metaphysics Lisa Feldman Barrett is among the most cited scientists in the world for her research on the psychology and neuroscience of emotions. Adam Frank is an astrophysicist who explores the origins of stars, civilizations and consciousness, and is a leading figure in astrobiology and the search for alien life. Michael Levin is a synthetic biologist whose pioneering work in regenerative biology involves building biological robots to probe the nature of life, intelligence and evolution. Güneş Taylor hosts. The Institute of Art and Ideas features videos and articles from cutting edge thinkers discussing the ideas that are shaping the world, from metaphysics to string theory, technology to democracy, aesthetics to genetics. Subscribe today! https://iai.tv/subscribe?utm_source=Y… 0:00 Intro 1:34 Science cannot reveal objective reality 5:28 — History shows that materialism is one of many philosophies of science 8:59 There are some mathematical facts which are discovered, not chosen 12:14 Does materialism prevent mythical and superstitious views of reality? 14:56 There is no 3rd person view of the universe 18:05 Is science truly reproducible? For debates and talks: https://iai.tv For articles: https://iai.tv/articles For courses: https://iai.tv/iai-academy/courses.

For centuries, we’ve assumed that science has banished the transcendent and established that reality is entirely physical. But critics argue there are signs that a rigorous materialism might be holding science back. Increasingly, “emergence” is used to account for everything from consciousness to spacetime – a convenient placeholder for what materialist science may be unable to explain. Physicists like Heisenberg and Hawking concluded that science gives us models of reality, rather than final descriptions of its true nature, while there are scientists working in everything from biology to computer science who suggest that dualism is a productive metaphysical framework for their research. Materialism may have enabled science to reach beyond the dogmas of religion, but there are now those who are restlessly probing the limits of materialism itself.

Does science need to assume a materialist account of the world or might this have fundamental limitations? Could a different metaphysics help science make progress on key questions, from the origin of life to the mysteries of quantum gravity? Or would abandoning materialism risk returning us to the myths of superstition and religion?

#science #materialism #metaphysics.

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