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[2610.30176] When Stable and Preferred Semantics Agree: A Path-Based Approach

The paper develops path-based criteria to determine when preferred and stable semantics agree in abstract argumentation, generalizing known conditions and introducing two infinite path-set sequences that yield distinct agreement criteria applicable to finite and infinite frameworks, including conditions for stable extensions.

[1208.5205] Monoidal computer I: Basic computability by string diagrams

This paper introduces a monoidal-category-based model of computation that aligns with the Church-Turing Thesis and standard computable functions, using string diagrams as a graphical formalism to provide a high-level interface while hiding low-level details. It aims to enable a programming approach for computational resources and outlines a path pursued in three follow-up papers.

Will mathematics survive? What is its future in the era of smart machines - Echo24.cz

Translated title. Original: Přežije matematika? Jaká je její budoucnost v éře chytrých strojů - Echo24.cz

A panel explores whether mathematics will survive in the AI era, arguing that while traditional methods may change, mathematics itself remains about understanding abstract concepts; AI will automate routine tasks and augment human reasoning, effectively acting as a cognitive prosthesis.

OpenAI releases AI claims in maths, computer science

OpenAI released AI-generated results in mathematics, computer science, and a collaborative physics assessment, with different release approaches per field. Mathematics claims include a proof of the local smoothing conjecture and a disproof of ETH in CS; external researchers will verify, explain, and formalise findings, while keeping artifacts confidential until formalisation is complete.

[2610.25501] Formal Raising: Embedding Verifiable Ethical Properties into the Development of AI

The paper proposes Formal Raising, embedding machine-checkable moral properties into AI development to guide actions and evaluation from the outset, using a C-based reasoning framework and a PSL-inspired property layer to handle ethical conflicts and exceptions.

Georgia Institute Of Technology Finds Limits To Ground State Preparation

The document presents a spectral criterion, via space analyticity, that governs when locally implemented dissipation can prepare the ground state of geometrically local free-fermion Hamiltonians. It proves a no-go result for 1D systems with sign-changing Fermi-level crossings, notes higher-dimensional obstructions, and uses quadratic-band-touching models to illustrate locality constraints. It links spectral properties, translation invariance, and momentum-space analysis to the feasibility of local jump operators for ground-state preparation, showing that analytic jump coefficients lead to meromorphic energy relations and potential local dissipation within a dark subspace.

MathePhysics on X: "MathePhysics is making public our LLM-driven efforts to resolve the four-dimensional Yang-Mills (YM) existence problem, by continuing the programme Balaban began in the 1980s. Our manuscript, progress, and updates can be tracked here: https://t.co/y2bpG6fyRf" / X

MathePhysics announces publicly their use of large language models to advance the four-dimensional Yang-Mills existence problem, continuing Balaban's 1980s program; progress and updates are trackable via a link.

When AI Finds Mistakes the Experts Missed: Inside Science's New Co-Author | MindStudio

AI can outperform when human error exists in test keys or papers; correcting keys reveals higher AI capability and raises questions about how we measure intelligence, with similar patterns seen in math benchmarks.

Scott Armstrong says OpenAI's Navier-Stokes result may exceed human invention

OpenAI's Navier-Stokes work draws praise from PDE expert Scott Armstrong, who suggests the construction may exceed human invention yet remain understandable; the piece debates whether OpenAI's Lean formalization aligns with the written proof, framing Armstrong's view as an assessment of ambition rather than a proof verdict.

Math's 'Romantic Era' Is Over, UCLA Prodigy Says - Business Insider

AI is changing math by solving many problems with prompts, leading a shift from heroic, solitary proofs to large-scale, industrial-style work; this raises concerns about lost artistry and threats to early-career researchers, and includes notable events around OpenAI's problem-solving milestones and a canceled AI-driven mathathon.