Tag
This article provides detailed notes on discrete-time Fourier series (DTFS) and discrete-time Fourier transform (DTFT), covering their theoretical foundations and examples for signal processing applications.
Mathematicians like Tristan Buckmaster and Andreas Thom continue using AI tools from OpenAI and Anthropic despite grievances over intellectual property and ethical concerns, highlighting the tension between AI utility and academic integrity.
The article proposes that 'motivated explanations' in mathematics should be academically credited alongside proofs, particularly as AI-generated proofs challenge traditional measures of contribution.
The article discusses the verification of OpenAI's Lean proof for the Navier-Stokes problem, highlighting the importance of ensuring formal proofs align with intended mathematical problems and the need for further scrutiny by mathematicians.
FrontierMath has successfully solved its first 'Major Advance' problem, marking a significant milestone in mathematical research and AI collaboration.
The author describes using AI to assist in proving Conway's refinement conjecture on omnific integers, claiming to have obtained a Lean proof after extensive token use. The proof has passed mechanical checks but awaits independent verification.
A researcher reports significant but incomplete progress on the Hodge conjecture, a famous unsolved problem in algebraic geometry.
OpenAI is reportedly nearing a breakthrough in solving the Hodge Conjecture, one of the Millennium Prize Problems, using artificial intelligence.
Ben Goertzel comments on the anti-AI declaration by Fields Medalists, discussing the relevance of big prizes and the true aims of AI in mathematics.
Timothy Gowers explains why he did not sign a letter from 25 Fields medallists about AI's impact on mathematics, sharing a personal story and offering an alternative perspective on the crisis.
Sam Altman stated in a conversation with Mark Benioff that an internal post-Astra AI model can solve problems beyond the capabilities of the world's best mathematicians, following advancements from GPT 5.5 to 5.6 to Astra.
The article discusses preventing mathematics from becoming secretive, referencing the Medieval Era as a cautionary example.
The article discusses how AI solving major mathematical problems is prompting mathematicians to question the impact on expertise, emphasizing the difference between puzzle-solving and idea-generating in mathematics.
A preprint paper presents a geometric framework for addressing the Yang-Mills mass-gap problem, offering partial results that reduce the continuum problem to specific uniform estimates without requiring extra dimensions.
This blog post explains the inverse-square law, deriving the surface area of a sphere to show why intensity decreases with the square of distance.
This article shares Paul Halmos' perspectives on the connection between mathematics and computers, likely from a historical or philosophical angle.
The article discusses how artificial intelligence is revolutionizing the production of deep theorems in mathematics, challenging traditional measures of success, with a focus on the Nivat conjecture.
Paul Dirac explores the deep connection between mathematics and physics, emphasizing their interdependence in scientific frameworks.
Richard Feynman discusses the difference between physics and mathematics, emphasizing that physics requires symbols to connect to reality, whereas mathematics focuses on abstract structures and logic.
The article critiques the misalignment between AI companies and the mathematics community, arguing that both fail to nurture students and ideas, using historical examples to highlight ongoing issues.