The paper discusses new constructions of Nikodym sets over finite fields, building on previous work involving optimization tools like AlphaEvolve and DeepThink. It explores the relationship between Nikodym sets and Kakeya sets, pr...
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The blog post discusses the concept of -smooth numbers, which are natural numbers whose prime factors are all less than or equal to a given threshold. It explores the asymptotic behavior of the count of -smooth numbers, referencin...
This paper establishes new bounds for the maximal length of polynomial lemniscates, resolving a longstanding question in mathematics related to the Erdős–Herzog–Piranian conjecture.
This paper establishes a qualitative inverse theorem for bounded-exponent finite abelian groups, linking polynomial structures to Gowers norms through an ergodic-theoretic approach.
Rogers' theorem reveals that the density of a sieved set of integers is maximized when all congruence classes are removed, despite its obscurity in mathematical literature.
The post discusses the abrupt suspension of NSF funding to UCLA's Institute of Pure and Applied Mathematics (IPAM) and the ongoing fundraising efforts to raise $500,000 for continuity. It highlights a new research paper titled 'Ro...
The paper discusses the application of modern analytic number theory, particularly the Maynard sieve and correlation estimates for bounded multiplicative functions, to address longstanding problems related to prime factors of cons...
The paper discusses growth rates of sequences of natural numbers constrained by their interactions with squarefree numbers, addressing Erdős's problems regarding the properties of such sequences. It reveals that sequences can grow...
The paper discusses the computation of sum-difference constants using the AlphaEvolve tool, revealing new asymptotic behaviors and providing rigorous demonstrations. It connects the sum-difference problem to Kakeya sets and explor...
The Mathematics Distillation Challenge seeks to improve AI performance on universal algebra problems through the creation of concise cheat sheets by participants.
A new network aims to formalize explicit analytic number theory results using AI tools, addressing numerical errors and enhancing collaboration among researchers.
Erdős problem #1026 was solved through collaboration, literature review, and AI tools, showcasing the importance of diverse approaches in mathematical problem-solving.
The paper discusses the use of the AlphaEvolve tool developed by Google DeepMind for mathematical exploration and optimization. It contrasts AlphaEvolve's approach of evolving computer code to generate inputs for optimization prob...
The Equational Theories Project successfully explored and resolved implications among 4684 equational laws of magmas through collaborative research and innovative mathematical techniques.
The blog post discusses a crowdsourced project initiated by Thomas Bloom to systematically compute and cross-check integer sequences associated with Paul Erdős's problems on the erdosproblems.com site against the On-line Encyclope...
The post proposes a crowdsourced repository for optimization constants to enhance collaboration and progress in solving mathematical problems, inspired by the success of the Erdös problem site.
The author announces the completion of a second draft chapter of a popular science book on the cosmic distance ladder, focusing on the 'seventh rung' of measuring distances across the Milky Way. The project faced delays due to une...
SLMath has restructured its program formats and announced three new research initiatives: AxIOM, a month-long program starting in Spring 2027 aimed at accelerating innovation in mathematics; PROOF, a two-week summer program for U....
A new book titled 'Six Math Essentials' will cover fundamental mathematical concepts and their real-world applications, available for preorder with a release date of October 27.
The Salem Prize, established in 1968 in honor of mathematician Raphaël Salem, recognizes significant contributions in mathematics, particularly in Fourier series and number theory. After a hiatus from 2019-2022 due to the COVID pa...
The blog post announces a call for industry sponsors for the RIPS program at UCLA, which runs for nine weeks. It highlights various projects from the previous year, showcasing collaborations with notable companies like Microsoft, ...
The authors have uploaded a second version of their paper 'Decomposing a factorial into large factors' to arXiv. They have rewritten and expanded the paper, settling previous conjectures about the main quantity studied. They have ...
The paper discusses the relationship between zero density theorems and prime number theorems in short intervals. It makes explicit some relationships between zero density theorems and prime number theorems in short intervals which...
The author discusses the creation of a Lean companion to his real analysis textbook 'Analysis I', focusing on foundational issues and formal verification using Lean. The companion translates the definitions, theorems, and exercise...