arXiv AI
Navier-Stokes lost in translation: Why Lean verification of AI autoformalisation does not guarantee correct natural language proofs
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arXiv AI
Jun 16
The Faithfulness Gap: Certifying Semantic Equivalence Between Natural-Language and Formal Mathematical Statements
arXiv:2606. 16541v1 Announce Type: new Abstract: Autoformalization, translating natural-language mathematics into formal proof assistants, is bottlenecked not by translation fluency but by \emph{faithfulness}: a formal statement can typecheck and be provable, yet still encode a different theorem than the source intended.
arXiv AI
Jun 16
Evaluating the Robustness of Proof Autoformalization in Lean 4
arXiv:2606. 14867v1 Announce Type: cross Abstract: Proof autoformalization aims to translate a mathematical informal proof written in natural language into a formal proof in a formal language such as Lean~4.
arXiv AI
Jun 2
Formally Solving Answer-Construction Problems in Lean
arXiv:2505. 18492v5 Announce Type: replace Abstract: Mathematical competition problems fall into two broad types: theorem proving, which asks for a proof of a given statement, and answer construction, which requires constructing a property-satifying object with proofs.
arXiv AI
Aug 18
Does the Proof Prove It That Way? Faithful Formalization of Elements Proofs
arXiv:2608. 15432v1 Announce Type: new Abstract: In formal verification, both the autoformalization of statements and automated proof search have been studied extensively.
arXiv AI
Aug 28
FaithSieve: Fine-Grained Evaluation of Math Proofs with Faithful Formal Evidence
FaithSieve is a Lean‑assisted framework that fine‑grains natural‑language mathematical proofs into local reasoning units, extracts typed proof obligations, and verifies them with formal evidence gated by semantic alignment. It introduces two expert‑verified datasets—ProofLoc‑Olympiad and ProofLoc‑University—to benchmark first‑error localization. On these benchmarks, FaithSieve outperforms direct‑judging baselines, achieving 81.43% and 84.5% exact first‑error accuracy respectively.
arXiv AI
22h ago
Formalizing inverse problems in the age of AI: possibilities, pitfalls, and an invitation
arXiv:2611.06962v1 Announce Type: new Abstract: Proof assistants such as Lean check mathematical proofs down to the axioms, and AI agents have recently made writing such proofs cheap. We describe Aut...