Tag

Mathematics

All articles tagged with #mathematics

physics-and-chemistry9 days ago•16 min saved

AI-Fueled Breakthrough Clears Decades-Old Jamming Mystery

Physicists Parisi and Zamponi credit Claude, an AI model, with sparking a simple idea that, despite initial errors, guided a clean proof that two parameters in the jamming (granular) model sum to one. The researchers refined Claude’s premise and published their result in the Journal of Statistical Mechanics: Theory and Experiment, illustrating AI’s potential to surface patterns and literature while underscoring that human verification remains essential.

via Gizmodo|

#artificial-intelligence #claude #jamming

mathematics14 days ago•11 min saved

Geometry Boosts Erdős’s Probabilistic Method to Crack Ramsey Numbers

Eight decades after Erdős introduced the probabilistic method, researchers Ma, Shen, and Xie used the geometry of high-dimensional spheres to improve lower bounds on near-diagonal Ramsey numbers, reviving progress on a stubborn problem and signaling a new geometric twist on Erdős’s randomness-based approach.

via Quanta Magazine|

#erdos #graph-theory #high-dimensional-spheres

science23 days ago•116 min saved

Crows Reveal an Ancient Foundation for Math: Zero, Probability, and the Neural Roots of Numbers

New findings from crow research by Andreas Nieder show that carrion crows understand zero as a numerical quantity and can perform probabilistic reasoning to pick the more rewarding option, suggesting that the cognitive building blocks of mathematics—quantity sense and probabilistic inference—are ancient and shared with primates and preverbal human infants, implying human math evolved by building on these prehuman foundations.

via Live Science|

#animal-cognition #crows #mathematics

science1 month ago•11 min saved

AI Partners with Humans to Redefine Math and Physics Discovery

AI augments, not replaces, human creativity in math and physics by helping formalize informal arguments, check proofs, generate conjectures, and surface overlooked connections. With fast, digital mathematics data and cheap experiments, researchers outline a multi-stage pipeline (setting the agenda, formalizing ideas, proposing conjectures, solving) and point to examples like Aristotle and Axiom Math as progress, while stressing that human insight remains essential.

via Nature|

#artificial-intelligence #formalization #mathematics

technology1 month ago•8 min saved

Math under pressure: Leiden Declaration warns AI risks to mathematical research

Mathematicians, led by a Leiden University group and endorsed by the International Mathematical Union, warn that AI’s growing role risks undermining math research through unreliable proofs, poor citation practices, and corporate influence. The Leiden Declaration urges transparency, proper credit, ethical partnerships, and policy actions to protect scholarly integrity as AI disrupts hiring, funding, and dissemination of results—highlighting OpenAI’s recent claim as a case study in rushed, market-driven announcements.

via Ars Technica|

#artificial-intelligence #international-mathematical-union #leiden-declaration

technology1 month ago•9 min saved

Leiden Declaration Signals Caution as AI Probes Theorems in Math

A group of 16 mathematicians released the Leiden Declaration on Artificial Intelligence and Mathematics to frame future directions and push back against unchecked AI use in math. It follows OpenAI’s recent AI-generated proof of a Erdos problem and warns of accuracy, transparency, and access issues when commercial AI research drives questions and methodologies. The declaration, endorsed by the International Mathematical Union and tied to discussions at the International Congress of Mathematicians, urges preserving core mathematical values—openness, credit, verification—and calls for responsible collaboration with industry to ensure human insight remains central.

via The New York Times|

#artificial-intelligence #ethics #mathematics

science1 month ago•4 min saved

Mathematicians Call for Guardrails as AI Enters Mathematical Proofs

Sixteen mathematicians, with more than 130 signatories, issued the Leiden Declaration on Artificial Intelligence and Mathematics to warn that unchecked AI could undermine the autonomy and rigor of mathematics while urging transparency, disclosure of AI use, stricter peer review, and investment in public computational infrastructure to balance power between researchers and tech firms; the declaration emphasizes human judgment and cautions that AI-generated proofs are hard to validate and cite, setting up ongoing discussions ahead of the International Congress of Mathematicians.

via Gizmodo|

#artificial-intelligence #ethics #mathematics

technology1 month ago•58 min saved

AI cracks long-standing Erdős puzzle with human-backed validation

OpenAI says its internal AI model autonomously solved the planar unit distance problem—an Erdős puzzle from 1946—finding arrangements that exceed the previous human upper bound; mathematicians reviewed the AI’s proof and published a companion paper detailing the approach and refinements, underscoring AI as a tool to assist mathematicians rather than replace them.

via Live Science|

#artificial-intelligence #erdos #mathematics

technology1 month ago•47 min saved

Consciousness Isn’t a Bug in the Code: AI Won’t Be Truly Conscious, Mathematically

In a math-grounded argument, the Slate piece contends that modern AI simply performs massive calculations and creates the illusion of consciousness, just as Muybridge’s rapid-fire photos suggested movement without life. By viewing AI as a sequence of mathematical operations, the author argues there is no mechanism by which current neural networks can achieve true self-awareness or continuous, sentient experience, regardless of how impressive their outputs may seem.

via Slate|

#artificial-intelligence #consciousness #mathematics

science2 months ago•2 min saved

AI-Driven Erdős Breakthrough or Mirage? Math World Watches Closely

A 23-year-old Liam Price reportedly used GPT-5.4 to solve a longstanding Erdős problem, prompting cautious excitement; Terence Tao says the AI found a novel approach, but the raw proof required human interpretation and the long-term significance remains uncertain after earlier AI claims were debunked.

via Futurism|

#ai #breakthrough #chatgpt

mathematics2 months ago•14 min saved

Colorful QR Codes Put Knot Theory on a Faster Track

A new knot invariant designed to be both strong and fast to compute outputs hexagonal QR-code images for each knot, enabling reliable distinction even for knots with hundreds of crossings and offering potential insights into genus and other topological features, with the work tying to the Kontsevich integral's two-loop approximation.

via Quanta Magazine|

#invariants #knot-theory #mathematics

science2 months ago•11 min saved

Breakthroughs Extend the Lonely Runner Problem to 10 Runners

The lonely runner problem asks whether, on a circular track with N runners at unique speeds, every runner will eventually be far from all others; it has been proven for up to seven runners, with recent computer-assisted work extending the result to eight (Rosenfeld) and then nine and ten (Trakulthongchai and Rosenfeld). These advances hint at a new, cross-disciplinary approach and have researchers planning a workshop to bridge number theory, geometry, and graph theory in pursuit of a general proof—though solving the full conjecture for all N may still take decades.

via WIRED|

#computer-assisted-proofs #graph-theory #lonely-runner-problem

science2 months ago•30 min saved

AI Tools Spark a New Era of Mathematical Discovery

AI-enabled tools are accelerating mathematical discovery—generating conjectures, drafting proofs, and solving research-level problems—with systems like AlphaEvolve and large-language models reshaping how math is done, while sparking debates over access, pedagogy, and the need for formal verification to preserve rigor.

via Quanta Magazine|

#alphaevolve #artificial-intelligence #large-language-models

science3 months ago•15 min saved

Pi Day spotlights how pi powers rockets, research, and real-world science

Pi Day honors the constant pi and its pervasive role in science and engineering, from calculating trajectories for spaceflight to modeling cancer research, illustrating how a single number underpins complex work across disciplines.

via AP News|

#cancer-research #mathematics #note-extra-tag-would-be-removed

science4 months ago•2 min saved

Unveiled Letters Cast Cantor’s Infinity Breakthrough in a New Light

Quanta previews a special series on the evolving foundations of mathematics, highlighting newly unearthed letters that suggest Cantor’s 1874 proof of different-sized infinities may have involved plagiarism, underscoring ongoing efforts to rethink math’s core ideas.

via Quanta Magazine|

#cantor #foundations #history