Tootfinder

Banach modules, almost mathematics and condensed mathematics
Dimitri Dine
https://arxiv.org/abs/2508.11268 https://arxiv.org/pdf/2508.11268

Banach modules, almost mathematics and condensed mathematics
We study the relationship between almost mathematics, condensed mathematics and the categories of seminormed and Banach modules over a Banach ring $A$, with submetric (norm-decreasing) $A$-module homomorphisms for morphisms. If $A$ is a Banach ring with a norm-multiplicative topologically nilpotent unit $\varpi$ contained in the closed unit ball $A_{\leq1}$ such that $\varpi$ admits a compatible system of $p$-power roots $\varpi^{1/p^{n}}$ with \begin{equation*}\lVert\varpi^{1/p^{n}}\rVert=\lVe…

THOR: Tool-Integrated Hierarchical Optimization via RL for Mathematical Reasoning
Qikai Chang, Zhenrong Zhang, Pengfei Hu, Jiefeng Ma, Yicheng Pan, Jianshu Zhang, Jun Du, Quan Liu, Jianqing Gao
https://arxiv.org/abs/2509.13761

THOR: Tool-Integrated Hierarchical Optimization via RL for Mathematical Reasoning
Large Language Models (LLMs) have made remarkable progress in mathematical reasoning, but still continue to struggle with high-precision tasks like numerical computation and formal symbolic manipulation. Integrating external tools has emerged as a promising approach to bridge this gap. Despite recent advances, existing methods struggle with three key challenges: constructing tool-integrated reasoning data, performing fine-grained optimization, and enhancing inference. To overcome these limitati…

The EPR Paradox of Quantum Mechanics in the Light of Four Unpublished Letters between A. Einstein and the Mathematician J. L. B. Cooper
P. L. Butzer (Lehrstuhl A f\"ur Mathematik, RWTH Aachen, Aachen, Germany), D. E. Edmunds (Department of Mathematics, University of Sussex, Brighton, U. K), G. Roepstorff (Department of Mathematics, University of Erlangen-Nuremberg, Erlangen, Germany), G. Schmeisser (Department of Mathematics, University of Erlangen-Nuremberg, Erlangen, Germany), R…

The EPR Paradox of Quantum Mechanics in the Light of Four Unpublished Letters between A. Einstein and the Mathematician J. L. B. Cooper
This paper presents correspondence between Albert Einstein and the mathematical analyst J. L. B. Cooper on the Einstein-Podolsky-Rosen (EPR) paradox of quantum theory published in 1935. Two letters written by Cooper, and the replies from Einstein, all written between October and December 1949, are retyped from the original ones. Furthermore, Einstein's second letter, which he wrote in German, is translated into English. The lack of agreement, arising from very different points of view, is analy…

Scale Up Analysis of Inductively Heated Metamaterial Reactors
Chenghao Wan, Conner Cremers, Ariana B. H\"ofelmann, Zhennan Ru, Calvin H. Lin, Kesha N. Tamakuwala, Dolly Mantle, Pinak Mohapatra, Juan Rivas-Davila, Matthew W. Kanan, Jonathan A. Fan
https://arxiv.org/abs/2509.13719

Scale Up Analysis of Inductively Heated Metamaterial Reactors
Inductively heated metamaterial reactors, which utilize an open cell lattice baffle structure as a heating susceptor for magnetic induction, are promising candidates for scaled electrified thermochemical reactor operation due to their ability to support volumetric heating profiles and enhanced heat transfer properties. In this work, we present a systematic scale up analysis of inductive metamaterial reactors where we utilize a combination of analytic modeling, numerical simulations, and experim…

research quality is often no longer measured directly by the content of publications, but increasingly by commercial indicators?
#thisplanetisdoomed
https://phys.org/news/2025-09-systematic-fraud-uncovered-mathematics.html

Evaluating undergraduate mathematics examinations in the era of generative AI: a curriculum-level case study
Benjamin J. Walker, Beatriz Navarro Lameda, Ruth A. Reynolds
https://arxiv.org/abs/2509.13359

Evaluating undergraduate mathematics examinations in the era of generative AI: a curriculum-level case study
Generative artificial intelligence (GenAI) tools such as OpenAI's ChatGPT are transforming the educational landscape, prompting reconsideration of traditional assessment practices. In parallel, universities are exploring alternatives to in-person, closed-book examinations, raising concerns about academic integrity and pedagogical alignment in uninvigilated settings. This study investigates whether traditional closed-book mathematics examinations retain their pedagogical relevance when hypotheti…

Bundesdigitalministerium will über IT-Ausgaben des Bundes mitentscheiden
Sollen künftig wesentliche IT-Ausgaben aller Ressorts vom Digitalminister Karsten Wildberger freigegeben werden? Er hält daran weiter fest.

🔍 Inverse Probleme - mit Mathematik das Unsichtbare sichtbar machen
Wir erklären interaktiv, wie inverse Probleme in Wissenschaft & Technik gelöst werden – am Beispiel der Computertomographie.
⏲ Uhrzeit: 17:00-24:00 Uhr
🗓️ Datum: 21.06.2025
🧑‍🔬 Veranstalter: Institut für Numerische und Angewandte Mathematik
📍 Veranstaltungsort: Foyer ZHG, Platz der Göttinger Sieben 5

FMC: Formalization of Natural Language Mathematical Competition Problems
Jiaxuan Xie, Chengwu Liu, Ye Yuan, Siqi Li, Zhiping Xiao, Ming Zhang
https://arxiv.org/abs/2507.11275

FMC: Formalization of Natural Language Mathematical Competition Problems
Efficient and accurate autoformalization methods, which leverage large-scale datasets of extensive natural language mathematical problems to construct formal language datasets, are key to advancing formal mathematical reasoning. In this paper, we propose an autoformalization pipeline based on large language models with error feedback, achieving a fully automatic and training-free formalization approach. Using this pipeline, we curate an Olympiad-level dataset aligning natural language problems …