https://jaalonso.github.io/vestigium/esContents © 2026 <a href="mailto:">José A. Alonso</a> <a rel="license" href="https://creativecommons.org/licenses/by-nc-sa/4.0/"> <img alt="Creative Commons License BY-NC-SA" style="border-width:0; margin-bottom:12px;" src="https://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png"></a>Thu, 01 Oct 2026 13:00:03 GMTNikola (getnikola.com)http://blogs.law.harvard.edu/tech/rsshttps://jaalonso.github.io/vestigium/posts/2025/11/08-readings_shared_11-07-25/José A. Alonso<p>The readings shared in <a href="https://bsky.app/profile/jalonso.bsky.social">Bluesky</a> on 7 November 2025 are:</p> <ul> <li><a href="https://youtu.be/omfZbs2v_dQ">An introduction to formal real analysis (Lecture 16: Completeness of the real numbers)</a>. ~ Alex Kontorovich. #ITP #LeanProver #Math</li> <li><a href="https://cacm.acm.org/news/the-path-to-a-superhuman-ai-mathematician/">The path to a superhuman AI mathematician</a>. ~ Lawrence Fisher. #AI #Math #ITP #LeanProver</li> <li><a href="https://home.zcu.cz/~danek/DATA/WWW_STRANKY/soubory/materialy/poster-lean-2025-09-22-EUPeace-Plzen.pdf">Math reasoning in times of AI: Lean way of theorem proving</a>. ~ Jan Cepika et als. #ITP #LeanProver #Math #AI #LLM</li> <li><a href="https://hal.science/hal-05342510/document">Babel-formal: Translation of proofs between Lean and Rocq</a>. ~ Théo Stoskopf, Cyril Cohen, Nicolas Tabarea. #ITP #LeanProver #Rocq</li> <li><a href="https://arxiv.org/abs/2511.02164v1">ScenicProver: A framework for compositional probabilistic verification of learning-enabled systems</a>. ~ Eric Vin et als. #ITP #LeanProver</li> <li><a href="https://arxiv.org/abs/2409.19176">Polynomial universes in Homotopy Type Theory</a>. ~ C.B. Aberlé, David I. Spivak. #ITP #Agda #HoTT</li> <li><a href="https://arxiv.org/abs/2511.02864v1">Mathematical exploration and discovery at scale</a>. ~ Bogdan Georgiev, Javier Gómez-Serrano, Terence Tao, Adam Zsolt Wagner. #AI #Math #AlphaEvolve #ITP #LeanProver</li> <li><a href="https://dl.acm.org/doi/full/10.1145/3736710">It’s the specification, stupid! (Seeking a significant shift in the traditional software development and verification paradigm)</a>. ~ Manfred Broy, Harald Ruess, Natarajan Shankar. #FormalVerification</li> <li><a href="https://www.gaussianos.com/cual-es-el-siguiente-termino/">¿Cuál es el siguiente término?</a> ~ Miguel Ángel Morales. #Matemáticas</li> <li><a href="https://jaalonso.github.io/exercitium/posts/2014/11/17-mayores_elementos_de_una_matriz/">#Exercitium: Mayores elementos de una matriz</a>. #Haskell #ProgramaciónFuncional #Matemáticas</li> </ul>AgdaAIAlphaEvolveFormalVerificationFunctionalProgrammingHaskellHoTTITPLeanProverLLMMathRocqhttps://jaalonso.github.io/vestigium/posts/2025/11/08-readings_shared_11-07-25/Sat, 08 Nov 2025 04:00:00 GMThttps://jaalonso.github.io/vestigium/posts/2025/11/03-readings_shared_11-02-25/José A. Alonso<p>The readings shared in <a href="https://bsky.app/profile/jalonso.bsky.social">Bluesky</a> on 2 November 2025 are:</p> <ul> <li><a href="https://lawrencecpaulson.github.io//2025/11/02/Why-not-dependent.html">"Why don't you use dependent types?"</a> ~ Lawrence Paulson. #ITP #Automath #LCF #IsabelleHOL #LeanProver #TypeTheory</li> <li><a href="https://arxiv.org/abs/2510.26094v1">Lean4Physics: Comprehensive reasoning framework for college-level Physics in Lean4</a>. ~ Yuxin Li et als. #ITP #LeanProver #Physics #AI #LLM</li> <li><a href="https://granule-project.github.io/papers/security-coeffects-mycroftfest.pdf">On graded coeffect types for information-flow control</a>. ~ Vilem-Benjamin Liepelt et als. #ITP #Agda</li> <li><a href="https://bahr.io/pubs/files/propratt-paper.pdf">Property-based testing for asynchronous functional reactive programming using linear temporal logic</a>. ~ Christian Emil Nielsen, Mathias Faber Kristiansen, Patrick Bahr. #Haskell #FunctionalProgramming</li> </ul>AgdaAIAutomathFunctionalProgrammingHaskellIsabelleHOLITPLCFLeanProverLLMPhysicsTypeTheoryhttps://jaalonso.github.io/vestigium/posts/2025/11/03-readings_shared_11-02-25/Mon, 03 Nov 2025 04:00:00 GMThttps://jaalonso.github.io/vestigium/posts/2025/10/28-readings_shared_10-27-25/José A. Alonso<p>The readings shared in <a href="https://bsky.app/profile/jalonso.bsky.social">Bluesky</a> on 27 October 2025 are:</p> <ul> <li><a href="https://mmhaskell.com/blog/2025/10/27/stock-market-shark-more-multidimensional-dp">Stock market shark: More multidimensional DP</a>. ~ James Bowen. #Haskell #FunctionalProgramming #RustLang</li> <li><a href="https://arxiv.org/abs/2505.05758">APOLLO: Automated LLM and Lean collaboration for advanced formal reasoning</a>. ~ Azim Ospanov, Farzan Farnia, Roozbeh Yousefzadeh. #ITP #LeanProver #LLM</li> <li><a href="https://jaalonso.github.io/exercitium/posts/2014/11/03-mayusculas_inicial/">#Exercitium: Poner en mayúscula la primera letra y las restantes en minúsculas</a>. #Haskell #ProgramaciónFuncional</li> </ul>FunctionalProgrammingHaskellITPLeanProverLLMRustLanghttps://jaalonso.github.io/vestigium/posts/2025/10/28-readings_shared_10-27-25/Tue, 28 Oct 2025 04:00:00 GMThttps://jaalonso.github.io/vestigium/posts/2025/10/26-readings_shared_10-25-25/José A. Alonso<p>The readings shared in <a href="https://bsky.app/profile/jalonso.bsky.social">Bluesky</a> on 25 October 2025 are:</p> <ul> <li><a href="https://youtu.be/Ko-PzGlzYrc">Gauss: towards autoformalization for the working mathematician</a>. ~ Jared Duker Lichtman, Jesse Han. #AI #Math #Autoformalization #LLM #ITP #LeanProver</li> <li><a href="https://cs.brynmawr.edu/Courses/cs373/Fall2025/Slides/01-Introduction.pdf">Course "Artificial Intelligence": 1. Introduction to AI</a>. ~ Deepak Kumar. #AI #History</li> <li><a href="https://cs.brynmawr.edu/Courses/cs373/Fall2025/Slides/02-Introduction.pdf">Course "Artificial Intelligence": 2. Introduction to AI</a>. ~ Deepak Kumar. #AI #History</li> <li><a href="https://cs.brynmawr.edu/Courses/cs373/Fall2025/Slides/03-SHRDLU-SHAKEY.pdf">Course "Artificial Intelligence": 3. Two early examples of AI systems: SHRDLU and SHAKEY</a>. ~ Deepak Kumar. #AI #History</li> <li><a href="https://cs.brynmawr.edu/Courses/cs373/Fall2025/Slides/04-ProblemSolvingSearch.pdf">Course "Artificial Intelligence": 4. Problem solving as search</a>. ~ Deepak Kumar. #AI #History</li> <li><a href="https://cs.brynmawr.edu/Courses/cs373/Fall2025/Slides/05-GamePlaying.pdf">Course "Artificial Intelligence": 5. Game playing</a>. ~ Deepak Kumar. #AI</li> <li><a href="https://cs.brynmawr.edu/Courses/cs373/Fall2025/Slides/06-ExpertSystems.pdf">Course "Artificial Intelligence": 6. Expert systems</a>. ~ Deepak Kumar. #AI</li> <li><a href="https://cs.brynmawr.edu/Courses/cs373/Fall2025/Slides/07-Logic.pdf">Course "Artificial Intelligence": 7. Representing knowledge using logic</a>. ~ Deepak Kumar. #AI #Logic #KRR</li> <li><a href="https://cs.brynmawr.edu/Courses/cs373/Fall2025/Slides/08-LogicInPROLOG.pdf">Course "Artificial Intelligence": 8. Logic in Prolog</a>. ~ Deepak Kumar. #AI #Logic #KRR</li> <li><a href="https://cs.brynmawr.edu/Courses/cs373/Fall2025/Slides/09-KowledgeRepresentations.pdf">Course "Artificial Intelligence": 9. Other knowledge representation formalisms: frames, conceptual dependency, semantic networks</a>. ~ Deepak Kumar. #AI #KRR</li> <li><a href="https://cs.brynmawr.edu/Courses/cs373/Fall2025/Slides/10-RobotsAndRationality.pdf">Course "Artificial Intelligence": 10. Robots and rationality. Subsumption architectures. Agent-based AI. IBM's Watson. Second AI winter</a>. ~ Deepak Kumar. #AI</li> <li><a href="https://cs.brynmawr.edu/Courses/cs373/Fall2025/Slides/11-SubsymbolicAI.pdf">Course "Artificial Intelligence": 11. Subsymbolic AI. McCulloch-Pitts neuron. The Perceptron. Example implementation</a>. ~ Deepak Kumar. #AI</li> </ul>AIAutoformalizationHistoryITPKRRLeanProverLLMLogicMathhttps://jaalonso.github.io/vestigium/posts/2025/10/26-readings_shared_10-25-25/Sun, 26 Oct 2025 04:00:00 GMThttps://jaalonso.github.io/vestigium/posts/2025/10/24-readings_shared_10-23-25/José A. Alonso<p>The readings shared in <a href="https://bsky.app/profile/jalonso.bsky.social">Bluesky</a> on 23 October 2025 are:</p> <ul> <li><a href="https://arxiv.org/abs/2501.14542">Constructive ordinal exponentiation</a>. ~ Tom de Jong, Nicolai Kraus, Fredrik Nordvall Forsberg, Chuangjie Xu. #ITP #Agda #SetTheory</li> <li><a href="https://arxiv.org/abs/2510.12829">Mathematics with large language models as provers and verifiers</a>. ~ Hieu Le Duc, Leo Liberti. #AI #Math #LLM #ITP #LeanProver</li> <li><a href="https://www.jotdown.es/2025/10/las-mejores-peliculas-sobre-matematicas/">Las mejores películas sobre matemáticas</a>. ~ Eduardo Sastre. #Matemáticas</li> </ul>AgdaAIITPLeanProverLLMMathSetTheoryhttps://jaalonso.github.io/vestigium/posts/2025/10/24-readings_shared_10-23-25/Fri, 24 Oct 2025 04:00:00 GMThttps://jaalonso.github.io/vestigium/posts/2025/10/23-readings_shared_10-22-25/José A. Alonso<p>The readings shared in <a href="https://bsky.app/profile/jalonso.bsky.social">Bluesky</a> on 22 October 2025 are:</p> <ul> <li><a href="https://xenaproject.wordpress.com/2025/10/22/formal-or-not-formal-that-is-the-question-in-ai-for-theorem-proving/">Formal or not formal? That is the question in AI for theorem proving</a>. ~ Kevin Buzzard. #AI #Math #LLM #ITP #LeanProver</li> <li><a href="https://florisvandoorn.com/theses/FelixPernegger.pdf">Formalisation of the Calderón transference principle in ergodic theory</a>. ~ Felix Pernegger. #ITP #LeanProver #Math</li> <li><a href="https://futurism.com/artificial-intelligence/openai-researcher-deletes-tweet">OpenAI researcher forced to delete “embarrassing” tweet claiming huge breakthrough</a>. ~ Frank Landymore. #AI #Math</li> <li><a href="https://the-decoder.com/leading-openai-researcher-announced-a-gpt-5-math-breakthrough-that-never-happened/">Leading OpenAI researcher announced a GPT-5 math breakthrough that never happened</a>. ~ Matthias Bastian. #AI #Math</li> <li><a href="https://youtu.be/qcTfXvkBUPA">PhysLean: A talk for physics undergraduates</a>. ~ Joseph Tooby-Smith. #ITP #LeanProver #Math #Physics</li> <li><a href="https://borisalexeev.com/pdf/erdos707.pdf">Forbidden Sidon subsets of perfect difference sets, featuring a human-assisted proof</a>. ~ Boris Alexeev, ChatGPT, Lean, Dustin G. Mixon. #AI #Math #LLM #ChatGPT #ITP #LeanProver</li> <li><a href="https://jaalonso.github.io/vestigium/posts/2025/10/22-una-refutacion-inusual-del-problema-de-erdos-707-colaboracion-humano-ia-y-el-papel-de-lean/">Una refutación inusual del problema de Erdős #707: Colaboración humano-IA y el papel de Lean</a>. #AI #Math #LLM #ITP #LeanProver</li> <li><a href="https://jaalonso.github.io/exercitium/posts/2014/11/01-elementos_no_repetidos/">#Exercitium: Elementos no repetidos</a>. #Haskell #ProgramaciónFuncional #Matemáticas</li> </ul>AIChatGPTFunctionalProgrammingHaskellITPLeanProverLLMMathPhysicshttps://jaalonso.github.io/vestigium/posts/2025/10/23-readings_shared_10-22-25/Thu, 23 Oct 2025 04:00:00 GMThttps://jaalonso.github.io/vestigium/posts/2025/10/22-una-refutacion-inusual-del-problema-de-erdos-707-colaboracion-humano-ia-y-el-papel-de-lean/José A. Alonso<p>Terence Tao ha <a href="https://mathstodon.xyz/@tao/115416208975810074">comentado en Mastodon</a> otro ejemplo interesante de la asistencia informática en matemáticas, que involucra nuevamente a los <a href="https://www.erdosproblems.com/">problemas de Erdös</a>: el <a href="https://www.erdosproblems.com/707">Problema #707</a>, anteriormente marcado como "abierto", ahora está "refutado" - con la <a href="https://borisalexeev.com/papers/erdos707.html">refutación formalizada en Lean</a>. Pero el camino hacia esa refutación fue bastante inusual, y no encajaba perfectamente en ninguna de las narrativas estándar sobre la IA en las matemáticas.</p> <p>La refutación inicial fue obra de humanos usando argumentos convencionales, sin ayuda inicial de LLMs. Sin embargo, descubrieron después que el problema ya había sido resuelto tres décadas antes por Hall, un hallazgo que las búsquedas bibliográficas humanas y asistidas por IA no detectaron. Para formalizar su prueba en Lean, los autores, sin experiencia previa, usaron ChatGPT en un proceso de "codificación por vibraciones", logrando generar unas 3000 líneas de código verificadas. Este proceso incluso permitió corregir un error en la formalización original del problema.</p> <p>Este caso ilustra un uso muy específico y responsable de la IA: no para generar ideas matemáticas, sino para asistir en la creación de código formal verificable. La formalización complementa, pero no reemplaza, la prueba humana central. Debido a su contribución crucial en esta etapa, tanto ChatGPT como Lean aparecen como coautores del <a href="https://borisalexeev.com/pdf/erdos707.pdf">artículo</a>, destacando un modelo inusual de colaboración humano-IA.</p>AIITPLeanProverLLMMathhttps://jaalonso.github.io/vestigium/posts/2025/10/22-una-refutacion-inusual-del-problema-de-erdos-707-colaboracion-humano-ia-y-el-papel-de-lean/Wed, 22 Oct 2025 09:00:00 GMThttps://jaalonso.github.io/vestigium/posts/2025/10/08-readings_shared_10-07-25/José A. Alonso<p>The readings shared in <a href="https://bsky.app/profile/jalonso.bsky.social">Bluesky</a> on 7 October 2025 are:</p> <ul> <li><a href="https://arxiv.org/abs/2501.10127">A formally verified IEEE 754 floating-point implementation of interval iteration for MDPs</a>. ~ Bram Kohlen, Maximilian Schäffeler, Mohammad Abdulaziz, Arnd Hartmanns, Peter Lammich. #ITP #IsabelleHOL</li> <li><a href="https://marcosh.github.io/post/2025/10/07/the-mondrian-introduction-to-functional-optics.html">The Mondrian introduction to functional optics</a>. ~ Marco Perone. #Haskell #FunctionalProgramming</li> <li><a href="https://funcall.blogspot.com/2025/09/using-llm-on-advent-of-code.html">Using an LLM on the Advent of Code</a>. ~ Joe Marshall. #Advent_of_Code #AI_coding #CommonLisp #Gemini #LLM</li> <li><a href="https://jaalonso.github.io/exercitium/posts/2014/07/21-numeros_con_digitos_primos/">#Exercitium: Números con todos sus dígitos primos</a>. #Haskell #ProgramaciónFuncional #Matemáticas</li> </ul>Advent_of_CodeAI_codingCommonLispFunctionalProgrammingGeminiHaskellIsabelleHOLITPLLMMathhttps://jaalonso.github.io/vestigium/posts/2025/10/08-readings_shared_10-07-25/Wed, 08 Oct 2025 04:00:00 GMT