#theorem-proving — Public Fediverse posts

I'm trying out Aristotle and Lean Copilot for formalizing and proving theorems, and, so far, Aristotle feels way more powerful. Lean Copilot's suggestions aren't always right. Aristotle, on the other hand, can bring in previous lemmas, figure out missing hypotheses, and so on –besides, of course, finishing the proofs themselves.

Disclaimer: this is probably mostly down to the underlying model: Aristotle uses a specialized in-house model (within an agentic architecture), while Lean Copilot is using a more general-purpose one (and not a particularly strong one, at least in my setup... DeepSeek-R1, I think).

#lean #theoremproving #aristotle

I'm trying out Aristotle and Lean Copilot for formalizing and proving theorems, and, so far, Aristotle feels way more powerful. Lean Copilot's suggestions aren't always right. Aristotle, on the other hand, can bring in previous lemmas, figure out missing hypotheses, and so on –besides, of course, finishing the proofs themselves.

Disclaimer: this is probably mostly down to the underlying model: Aristotle uses a specialized in-house model (within an agentic architecture), while Lean Copilot is using a more general-purpose one (and not a particularly strong one, at least in my setup... DeepSeek-R1, I think).

#lean #theoremproving #aristotle

Want to learn more about the latest developments on using AI and (interactive) theorem proving in Mathematics? Wait no longer!

We have a great line-up of speakers at our online Workshop on AI and Theorem Provers in Mathematics. The workshop will be held online from 8th to 10th of April and attendance is free (registration required). For more details, visit the workshop website: https://aitpm.github.io/

#math #itp #theoremProving #isabelleHOL #lean #llm #ai #formal_mehods #agda #hol #mathematics

Want to learn more about the latest developments on using AI and (interactive) theorem proving in Mathematics? Wait no longer!

We have a great line-up of speakers at our online Workshop on AI and Theorem Provers in Mathematics. The workshop will be held online from 8th to 10th of April and attendance is free (registration required). For more details, visit the workshop website: https://aitpm.github.io/

#math #itp #theoremProving #isabelleHOL #lean #llm #ai #formal_mehods #agda #hol #mathematics

[New Blog Post] State of Knuckledragger III: Kernel Changes, Symbolic Union, AI, and more https://www.philipzucker.com/state_o_knuck_3/ #python #logic #theoremproving

[New Blog Post] State of Knuckledragger III: Kernel Changes, Symbolic Union, AI, and more https://www.philipzucker.com/state_o_knuck_3/ #python #logic #theoremproving

Terminal now can help you with formal proofs and theorem provers 🤯

📐 **lean-tui** — A TUI for visualizing Lean programs and proofs

💯 Live proof trees, data/effect flow views & real-time updates from your editor

🦀 Written in Rust & built with @ratatui_rs

⭐ Source: https://codeberg.org/wvhulle/lean-tui

#rustlang #ratatui #tui #lean #theoremproving #cli #devtools #terminal

Terminal now can help you with formal proofs and theorem provers 🤯

📐 **lean-tui** — A TUI for visualizing Lean programs and proofs

💯 Live proof trees, data/effect flow views & real-time updates from your editor

🦀 Written in Rust & built with @ratatui_rs

⭐ Source: https://codeberg.org/wvhulle/lean-tui

#rustlang #ratatui #tui #lean #theoremproving #cli #devtools #terminal

Lean 4 is apparently the new secret sauce of #AI dominance, because who knew that theorem proving could be so *riveting*? 🤔✨ But don't worry, before you can learn how to take over the world with math, you'll need to pass the Vercel Security Checkpoint IQ test, where only the chosen ones with #JavaScript enabled may proceed. 🛂🔒
https://venturebeat.com/ai/lean4-how-the-theorem-prover-works-and-why-its-the-new-competitive-edge-in #Lean4 #TheoremProving #VercelSecurity #HackerNews #ngated

Lean 4 is apparently the new secret sauce of #AI dominance, because who knew that theorem proving could be so *riveting*? 🤔✨ But don't worry, before you can learn how to take over the world with math, you'll need to pass the Vercel Security Checkpoint IQ test, where only the chosen ones with #JavaScript enabled may proceed. 🛂🔒
https://venturebeat.com/ai/lean4-how-the-theorem-prover-works-and-why-its-the-new-competitive-edge-in #Lean4 #TheoremProving #VercelSecurity #HackerNews #ngated

Agentic system design paper:
https://althofer.de/agentic_strategy_design_for_math_proofs.pdf
#1stProof #TheoremProving

Agentic system design paper:
https://althofer.de/agentic_strategy_design_for_math_proofs.pdf
#1stProof #TheoremProving

First Proof (#1stProof): We ran an AI-only workflow (no human mathematical input) and published a writeup + outputs.
Report: https://althofer.de/first-proof-competition/first-proof-report.html
Official: https://1stproof.org/
I’d appreciate critique—especially rigor/correctness checks and suggestions for better verification.
#1stProof #Mathematics #TheoremProving #AI

First Proof (#1stProof): We ran an AI-only workflow (no human mathematical input) and published a writeup + outputs.
Report: https://althofer.de/first-proof-competition/first-proof-report.html
Official: https://1stproof.org/
I’d appreciate critique—especially rigor/correctness checks and suggestions for better verification.
#1stProof #Mathematics #TheoremProving #AI

Lean Theorem Prover Mathlib

https://github.com/leanprover-community/mathlib4

#HackerNews #Lean #Theorem #Prover #Mathlib #mathlib4 #LeanProver #theoremProving #functionalProgramming

Lean Theorem Prover Mathlib

https://github.com/leanprover-community/mathlib4

#HackerNews #Lean #Theorem #Prover #Mathlib #mathlib4 #LeanProver #theoremProving #functionalProgramming

Does anyone know if an inductive Nat datatype defined as a place-value system could replace the need to rewrite the PA definition to bigints in the compiler?

#theoremProving #types #functional_programming

Does anyone know if an inductive Nat datatype defined as a place-value system could replace the need to rewrite the PA definition to bigints in the compiler?

#theoremProving #types #functional_programming

Emily Riehl: How I became seduced by Univalent Foundations

[tbh I think shes only disclosing her theoretical motivations her; I recall she was posting questions about Linux distros a few years ago, and if we're honest being a nerd is the actual reason 99% of people get into HoTT]
https://www.youtube.com/watch?v=XIYoI5j5Flo&t=486s

#hott #mathematics #categorytheory #theoremproving

Emily Riehl: How I became seduced by Univalent Foundations

[tbh I think shes only disclosing her theoretical motivations her; I recall she was posting questions about Linux distros a few years ago, and if we're honest being a nerd is the actual reason 99% of people get into HoTT]
https://www.youtube.com/watch?v=XIYoI5j5Flo&t=486s

#hott #mathematics #categorytheory #theoremproving

DeepSeekMath‑V2 è un AI che dimostra teoremi matematici passo dopo passo.
Genera prove, le verifica con un LLM dedicato e corregge gli errori per migliorarsi continuamente. 🤖📐

#AIperLaMatematica #TheoremProving #VerificaAutomatica

DeepSeekMath‑V2 è un AI che dimostra teoremi matematici passo dopo passo.
Genera prove, le verifica con un LLM dedicato e corregge gli errori per migliorarsi continuamente. 🤖📐

#AIperLaMatematica #TheoremProving #VerificaAutomatica

New research shows how Lean4 can turn large‑language models into AI advisers that pair hypotheses with physics‑consistent proofs. This blend of theorem proving and formal verification promises safer AI and more reliable software. Dive into the details of how AI meets the laws of physics. #Lean4 #TheoremProving #PhysicsConsistent #FormalVerification

🔗 https://aidailypost.com/news/lean4-powers-ai-advisers-pair-hypotheses-physicsconsistent-proofs

#CondensedDetachment example

Axiom 1: ⊢ (𝜑 → (𝜓 → 𝜑))
Axiom 2: ⊢ ((𝜑 → (𝜓 → 𝜒)) → ((𝜑 → 𝜓) → (𝜑 → 𝜒)))
Rule of Modus Ponens:
• Major hypothesis: ⊢ (𝜓 → 𝜑)
• Minor hypothesis: ⊢ 𝜓
• Resulting Assertion: ⊢ 𝜑
——
D<major><minor> applies the Rule of Modus Ponens treating the two given tautologies as having metavariables living in different namespaces and returning the normalized result. We extend by using underscore as a placeholder, so D__ recovers the rule of modus ponens.
——
"D2_" is proof of the rule:
• Hypothesis: ⊢ (𝜑 → (𝜓 → 𝜒))
• Resulting assertion: ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜒))
——
"D21" is a proof which unifies "1" ⊢ (𝜑′ → (𝜓′ → 𝜑′)) with the hypothesis of "D2_" giving the substitution map 𝜎: {𝜑′ ↦ 𝜑, 𝜓′ ↦ 𝜓, 𝜒 ↦ 𝜑} resulting in the tautology: ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜑))

(Note that unification can map variables from either side, but when faced with a variable matching a term has to match the variable to that term.)
——
"DD21_" is proof of the rule:
• Hypothesis: ⊢ (𝜑 → 𝜓)
• Resulting assertion: ⊢ ((𝜑 → 𝜑)
——
"DD211" is a proof which unifies "1" ⊢ (𝜑″ → (𝜓″ → 𝜑″)) with the hypothesis of "DD21_" giving the substitution map 𝜎: {𝜑″ ↦ 𝜑, 𝜓 ↦ (𝜓″ → 𝜑)} resulting in the tautology: ⊢ (𝜑 → 𝜑)

This has been adapted and expanded from a run of my symbolic-mgu pre-release crate. https://crates.io/crates/symbolic-mgu

cargo run -r --bin compact -- --wide D__ 1 2 D2_ D21 DD21_ DD211

#math #logic #theoremProving #rust #mostGeneralUnifier #mgu

#CondensedDetachment example

Axiom 1: ⊢ (𝜑 → (𝜓 → 𝜑))
Axiom 2: ⊢ ((𝜑 → (𝜓 → 𝜒)) → ((𝜑 → 𝜓) → (𝜑 → 𝜒)))
Rule of Modus Ponens:
• Major hypothesis: ⊢ (𝜓 → 𝜑)
• Minor hypothesis: ⊢ 𝜓
• Resulting Assertion: ⊢ 𝜑
——
D<major><minor> applies the Rule of Modus Ponens treating the two given tautologies as having metavariables living in different namespaces and returning the normalized result. We extend by using underscore as a placeholder, so D__ recovers the rule of modus ponens.
——
"D2_" is proof of the rule:
• Hypothesis: ⊢ (𝜑 → (𝜓 → 𝜒))
• Resulting assertion: ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜒))
——
"D21" is a proof which unifies "1" ⊢ (𝜑′ → (𝜓′ → 𝜑′)) with the hypothesis of "D2_" giving the substitution map 𝜎: {𝜑′ ↦ 𝜑, 𝜓′ ↦ 𝜓, 𝜒 ↦ 𝜑} resulting in the tautology: ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜑))

(Note that unification can map variables from either side, but when faced with a variable matching a term has to match the variable to that term.)
——
"DD21_" is proof of the rule:
• Hypothesis: ⊢ (𝜑 → 𝜓)
• Resulting assertion: ⊢ ((𝜑 → 𝜑)
——
"DD211" is a proof which unifies "1" ⊢ (𝜑″ → (𝜓″ → 𝜑″)) with the hypothesis of "DD21_" giving the substitution map 𝜎: {𝜑″ ↦ 𝜑, 𝜓 ↦ (𝜓″ → 𝜑)} resulting in the tautology: ⊢ (𝜑 → 𝜑)

This has been adapted and expanded from a run of my symbolic-mgu pre-release crate. https://crates.io/crates/symbolic-mgu

cargo run -r --bin compact -- --wide D__ 1 2 D2_ D21 DD21_ DD211

#math #logic #theoremProving #rust #mostGeneralUnifier #mgu

An abbreviated run for examining sub-proofs of propositional logic from Russell and Whitehead, and proving that they are all tautologies:

```
% cargo test --features serde,bigint -r --test pmproofs_validation -- --include-ignored --no-capture

running 1 test
Validating PM subproofs...
Variable limit: unlimited (bigint feature enabled)
Total subproofs in database: 2997
Processed 100/2997 subproofs...
Processed 200/2997 subproofs...

...

Processed 2800/2997 subproofs...
Processed 2900/2997 subproofs...

========================================
PM SUBPROOF VALIDATION RESULTS
========================================
Total subproofs: 2997
Parse failures: 0
Skipped (too many variables): 0
Validation errors: 0
Not tautologies: 0
Successfully validated: 2997

✓ Successfully validated 2997 subproofs!
test all_pm_subproofs_are_tautologies ... ok

test result: ok. 1 passed; 0 failed; 0 ignored; 0 measured; 0 filtered out; finished in 2.60s

```

#Rust #logic #math #theoremProving #condensedDetachment #mostGeneralUnifier #mgu

I'm writing an open source math library in #Rust to do symbolic unification. (following Meredith, Robinson, Megill) It's in pre-release (v0.1.0-alpha.13) now but I'm nearly feature-complete and I'm beginning to write interesting demonstrations with it.

I thought now would be a time to solicit feedback before the API stabilizes as per semantic versioning best practices.

Like many compilers built on top of the LLVM architecture, un-optimized Rust is about 10 times slower than the optimized code produced with the --release flag. You can really notice this with the test that sets out to exhaustively produce all expressions on sets of limited operators until all 16 Boolean functions are produced. https://docs.rs/crate/symbolic-mgu/latest/source/tests/functional_completeness.rs

Also I run through Norm Megill's archive of shortest known proofs of propositional logic statements from Whitehead and Russell's Prinicipia Mathematica and test that they and all subproofs produce tautologies. https://docs.rs/crate/symbolic-mgu/latest/source/tests/pmproofs_validation.rs

Documentation: https://docs.rs/symbolic-mgu/latest/symbolic_mgu/
Distribution: https://crates.io/crates/symbolic-mgu
Repository: https://github.com/arpie-steele/symbolic-mgu

#logic #theoremProving #condensedDetachment #mostGeneralUnifier #mgu #math

We're thrilled to welcome Alexander Bentkamp to the Cryspen family!

Alex joins our Tools and Proofs team with a deep background in automated and interactive theorem proving, especially with the Lean proof assistant. We're excited to have his expertise as we continue our work on formally verifying security-critical software.

Welcome aboard, Alex!

https://cryspen.com/post/welcome_alex/

#Cryspen #Welcome #FormalVerification #TheoremProving

🤔 Oh joy, another "Python for Dummies" guide that promises to solve world peace with 20 lines of code. 🎉 Who knew #Sudoku and N-Queens could be fixed with a side of theorem proving—thanks Microsoft! 🥳 But don't worry, you don't actually need to know Python, because why bother learning a "fun" language, right? 🙄
https://ericpony.github.io/z3py-tutorial/guide-examples.htm #PythonForDummies #Microsoft #NQueens #TheoremProving #CodingHumor #HackerNews #ngated

🤔 Oh joy, another "Python for Dummies" guide that promises to solve world peace with 20 lines of code. 🎉 Who knew #Sudoku and N-Queens could be fixed with a side of theorem proving—thanks Microsoft! 🥳 But don't worry, you don't actually need to know Python, because why bother learning a "fun" language, right? 🙄
https://ericpony.github.io/z3py-tutorial/guide-examples.htm #PythonForDummies #Microsoft #NQueens #TheoremProving #CodingHumor #HackerNews #ngated

Automated Lean Proofs for Every Type

https://www.galois.com/articles/automated-lean-proofs-for-every-type

#HackerNews #AutomatedLeanProofs #Lean #TheoremProving #Automation #Technology #Galois

Automated Lean Proofs for Every Type

https://www.galois.com/articles/automated-lean-proofs-for-every-type

#HackerNews #AutomatedLeanProofs #Lean #TheoremProving #Automation #Technology #Galois

Claude Can (Sometimes) Prove It
https://www.galois.com/articles/claude-can-sometimes-prove-it

"Claude Code can complete many complex proof steps independently, but it still needs a ‘project manager’ (me) to guide it through the whole formalization. But I think Claude Code points to a world where experts aren’t necessary, and theorem provers can be used by many more people.

The rest of this post digs into what Claude Code can actually do...."

#theoremProving #LLM #Lean

Claude Can (Sometimes) Prove It
https://www.galois.com/articles/claude-can-sometimes-prove-it

"Claude Code can complete many complex proof steps independently, but it still needs a ‘project manager’ (me) to guide it through the whole formalization. But I think Claude Code points to a world where experts aren’t necessary, and theorem provers can be used by many more people.

The rest of this post digs into what Claude Code can actually do...."

#theoremProving #LLM #Lean

Faithful logic embeddings in HOL (Deep and shallow). ~ Christoph Benzmüller. https://arxiv.org/abs/2502.19311 #ITP #TheoremProving #IsabelleHOL #Logic #Math

Faithful logic embeddings in HOL (Deep and shallow). ~ Christoph Benzmüller. https://arxiv.org/abs/2502.19311 #ITP #TheoremProving #IsabelleHOL #Logic #Math

REAL-Prover: Retrieval augmented Lean prover for mathematical reasoning. ~ Ziju Shen et als. https://arxiv.org/abs/2505.20613 #AI #TheoremProving #LeanProver #Math

REAL-Prover: Retrieval augmented Lean prover for mathematical reasoning. ~ Ziju Shen et als. https://arxiv.org/abs/2505.20613 #AI #TheoremProving #LeanProver #Math

The Department of Computer Science, University of Oxford has released recordings of the recent Strachey Series Lectures featuring Leo de Moura and Kevin Buzzard:

1️⃣ "Formalizing the Future: Lean's Impact on Mathematics, Programming, and AI" - Leo de Moura, Chief Architect of Lean

Leo discusses how Lean provides a framework for machine-checkable mathematical proofs and code verification, enabling collaboration between mathematicians, software developers, and AI systems. He also outlines the work the Lean Focused Research Organization does to expand Lean’s capabilities and support the community.

➡️ Watch Leo's lecture here: https://podcasts.ox.ac.uk/formalizing-future-leans-impact-mathematics-programming-and-ai

2️⃣ "Will Computers Prove Theorems?" with Kevin Buzzard, Professor of Mathematics, Imperial College

Kevin examines the potential for AI systems and theorem provers to assist in mathematical discovery, addressing whether computers might someday find patterns in mathematics that humans have missed, and discusses the integration of language models with formal verification systems.

➡️ Watch Kevin's lecture here: https://podcasts.ox.ac.uk/will-computers-prove-theorems

#LeanLang #LeanProver #FormalVerification #Mathematics #AI #TheoremProving #OxfordCS

The Department of Computer Science, University of Oxford has released recordings of the recent Strachey Series Lectures featuring Leo de Moura and Kevin Buzzard:

1️⃣ "Formalizing the Future: Lean's Impact on Mathematics, Programming, and AI" - Leo de Moura, Chief Architect of Lean

Leo discusses how Lean provides a framework for machine-checkable mathematical proofs and code verification, enabling collaboration between mathematicians, software developers, and AI systems. He also outlines the work the Lean Focused Research Organization does to expand Lean’s capabilities and support the community.

➡️ Watch Leo's lecture here: https://podcasts.ox.ac.uk/formalizing-future-leans-impact-mathematics-programming-and-ai

2️⃣ "Will Computers Prove Theorems?" with Kevin Buzzard, Professor of Mathematics, Imperial College

Kevin examines the potential for AI systems and theorem provers to assist in mathematical discovery, addressing whether computers might someday find patterns in mathematics that humans have missed, and discusses the integration of language models with formal verification systems.

➡️ Watch Kevin's lecture here: https://podcasts.ox.ac.uk/will-computers-prove-theorems

#LeanLang #LeanProver #FormalVerification #Mathematics #AI #TheoremProving #OxfordCS

Introducing #DeepSeekProverV2 - a new #opensource #LLM designed for formal theorem proving in Lean 4.

The model builds on a recursive #TheoremProving pipeline powered by the company's DeepSeek-V3 foundation model.

Learn more: https://bit.ly/3ZlTt7h

#InfoQ #GenerativeAI

Introducing #DeepSeekProverV2 - a new #opensource #LLM designed for formal theorem proving in Lean 4.

The model builds on a recursive #TheoremProving pipeline powered by the company's DeepSeek-V3 foundation model.

Learn more: https://bit.ly/3ZlTt7h

#InfoQ #GenerativeAI

The Lean FRO team met synchronously in Amsterdam last week for our annual team retreat, and to discuss upcoming work and our Year 3 roadmap! 🇳🇱✨

We had very productive discussions around Lean's future in mathematics, software and hardware verification, and AI for math. It was energizing to see our team's commitment to Lean's continued growth in each of these domains.

We're cooking up many exciting developments that will support both our mathematical community and our growing base of software verification users. Stay tuned for our full Y3 roadmap publication at the end of July!

#LeanLang #LeanProver #Lean4 #FormalVerification #Programming #Mathematics #TheoremProving

The Lean FRO team met synchronously in Amsterdam last week for our annual team retreat, and to discuss upcoming work and our Year 3 roadmap! 🇳🇱✨

We had very productive discussions around Lean's future in mathematics, software and hardware verification, and AI for math. It was energizing to see our team's commitment to Lean's continued growth in each of these domains.

We're cooking up many exciting developments that will support both our mathematical community and our growing base of software verification users. Stay tuned for our full Y3 roadmap publication at the end of July!

#LeanLang #LeanProver #Lean4 #FormalVerification #Programming #Mathematics #TheoremProving

Channeling some PhD vacancies from our 🇳🇱 friends:

Six fully-funded PhD positions (4 years) in the project "Cyclic Structures in Programs and Proofs – New Harmonies in Software Correctness by Construction"

Deadline: Friday, May 23, 2025

https://cyclic-structures.gitlab.io/vacancies/

#FormalMethods #TheoremProving #NWOnl

DeepSeek Releases Massive 671B Prover V2 Model For Mathematical Theorem Proving Ahead of R2 Release

#AI #ChinaAI #DeepSeek #OpenSourceAI #Math #TheoremProving #Lean4 #MachineLearning #DeepLearning #MathAI

https://winbuzzer.com/2025/04/30/deepseek-releases-massive-671b-prover-v2-model-for-mathematical-theorem-proving-ahead-of-r2-release-xcxwbn/