Tag

Mathematics

All articles tagged with #mathematics

technology1 day 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

science24 days 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

mathematics1 month 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

science1 month 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

science1 month 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

science2 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

science2 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

technology3 months ago•1 min saved

Mathematicians Put AI to the Test on Complex Problems

Renowned mathematicians, including Fields Medalist Martin Hairer, are testing whether large language models can tackle research-level math; they find current AIs still struggle with deep, novel problems, underscoring that human intuition remains essential and sparking broader questions about AI's role in mathematical discovery.

via The New York Times|

#artificial-intelligence #education #large-language-models

science4 months ago•1 min saved

Infinite Pancake Scrutiny: Extending the Lazy Caterer’s Puzzle with an Endless Knife

Mathematicians explore maximizing the number of pieces from slicing an infinitely large pancake with a straight knife, reworking the classic Lazy Caterer’s puzzle in an infinite-plane setting.

via The New York Times|

#combinatorics #geometry #infinity

science4 months ago•15 min saved

New Bridge Connects Infinity Math to Computer Science

Descriptive set theorists have established a surprising connection between the abstract mathematics of infinity and practical computer science, showing that problems involving infinite sets can be translated into algorithms and network communication issues, thereby bridging a gap between theoretical and applied mathematics.

via WIRED|

#computer-science #graph-coloring #infinity

science4 months ago•8 min saved

The Manifold: Revolutionizing Mathematical Space Concepts

The article explains how the concept of manifolds, introduced by Bernhard Riemann, revolutionized the understanding of space in mathematics and physics, enabling the study of complex, higher-dimensional spaces and playing a crucial role in fields like general relativity, data analysis, and dynamical systems.

via WIRED|

#geometry #manifolds #mathematics

science5 months ago•9 min saved

Donald Knuth's 2025 Christmas Lecture on Knight's Tours

Donald Knuth's 2025 Christmas Lecture at Stanford focused on the Knight's Tour problem, exploring its mathematical beauty, solutions, and recent computational breakthroughs, highlighting the intersection of math, art, and computer science.

via The New Stack|

#art #computer-science #donald-knuth

mathematics5 months ago•10 min saved

The 9th Dedekind Number: A 32-Year Quest and the Elusive 10th

Dedekind numbers are a sequence of mathematical values with complex growth, first studied by Richard Dedekind, and are extremely difficult to compute beyond the eighth term due to their exponential complexity. The ninth Dedekind number was only recently discovered through advanced computational methods, but finding the tenth may be impossible for the foreseeable future due to the astronomical computational power required.

via IFLScience|

#boolean-functions #computational-complexity #dedekind-numbers

science5 months ago•4 min saved

Study Finds Best Strategies for Optimization

Research reveals that the simplex method, a widely used optimization algorithm developed during WWII, is faster and more reliable in practice than its worst-case exponential runtime predictions suggest, thanks to recent theoretical advancements.

via WIRED|

#algorithm #mathematics #optimization

science5 months ago•10 min saved

AI Tackles 'Impossible' Math Challenges, Outperforming Top Mathematicians

AI has made significant progress in solving complex mathematical problems, such as stability equations and Olympiad questions, but still requires human oversight and hasn't yet surpassed top mathematicians in generating groundbreaking discoveries. Experts believe AI will increasingly assist in research, potentially transforming the field and the role of mathematicians in the future.

via Live Science|

#ai #future #mathematics