The Case Against Formal Verification, 50 Years Later - Ivan Gavran

Prediction: AI will make formal verification go mainstream — Martin Kleppmann’s blog

Much has been said about the effects that AI will have on software development, but there is an angle I haven’t seen talked about: I believe that AI will bring formal verification, which for decades has been a bit of a fringe pursuit, into the software engineering mainstream.

What Functional Programmers Get Wrong About Systems - Ian Duncan

Type systems verify properties of programs. Production correctness is a property of systems. The gap between these is where the interesting failures live.

What It Now Takes to Establish a Fact

Hilke Schellmann & Mihir Kshirsagar from Princeton CITP on findings from a convening on information integrity, authentication and verification in the age of AI.

Experts Argue Whether Computers Could Reason, and if They Should (Published 1977)

Computer world is in midst of fundamental dispute over question of computer intelligence since MIT Prof Joseph Weizenbaum wrote book arguing that machines can never be made to reason like people and should not be; Weizenbaum por (M)

Formal Verification Reference - Aura

This document describes the formal verification infrastructure that provides mathematical guarantees for Aura protocols through Quint model checking, Lean theorem proving, and Telltale session type verification.

AI agents are checking the scientific literature — and spotting decades-old errors

The technology is proving adept at finding faults in decades-old papers and reference databases.

On AI and building your own GIS software

Of the thousands of essays over the past two years surrounding AI and its implications are some very thought provoking ones with enormous implications for GIS. Some of the essays are around the the…

Mathematics with large language models as provers and verifiers

During 2024 and 2025 the discussion about the theorem-proving capabilities of large language models started reporting interesting success stories, mostly to do with difficult exercises (such as problems from the International Mathematical Olympiad), but also with conjectures [Feldman & Karbasi, arXiv:2509.18383v1] formulated for the purpose of verifying whether the artificial intelligence could prove it. In this paper we report a theorem proving feat achieved by ChatGPT by using a protocol involving different prover and verifier instances of the gpt-5 model working collaboratively. To make sure that the produced proofs do not suffer from hallucinations, the final proof is formally verified by the lean proof assistant, and the conformance of premises and conclusion of the lean code is verified by a human. Our methodology is by no means complete or exact. It was nonetheless able to solve five out of six 2025 IMO problems, and close about a third of the sixty-six number theory conjectures in [Cohen, Journal of Integer Sequences, 2025].

Mathematics with large language models as provers and verifiers

During 2024 and 2025 the discussion about the theorem-proving capabilities of large language models started reporting interesting success stories, mostly to do with difficult exercises (such as problems from the International Mathematical Olympiad), but also with conjectures [Feldman & Karbasi, arXiv:2509.18383v1] formulated for the purpose of verifying whether the artificial intelligence could prove it. In this paper we report a theorem proving feat achieved by ChatGPT by using a protocol involving different prover and verifier instances of the gpt-5 model working collaboratively. To make sure that the produced proofs do not suffer from hallucinations, the final proof is formally verified by the lean proof assistant, and the conformance of premises and conclusion of the lean code is verified by a human. Our methodology is by no means complete or exact. It was nonetheless able to solve five out of six 2025 IMO problems, and close about a third of the sixty-six number theory conjectures in [Cohen, Journal of Integer Sequences, 2025].

Falsehoods Programmers Believe About Names | Kalzumeus Software

Classic essay about how software routinely bumbles human names.

Establishing trust in automated reasoning - MetaROR

Since its beginnings in the 1940s, automated reasoning by computers has become a tool of ever growing importance in scientific research. So far, the rules underlying automated reasoning have mainly been formulated by humans, in the form of program source code. Rules derived from large amounts of data, via machine learning techniques, are a complementary approach currently under intense development. The question of why we should trust these systems, and the results obtained with their help, has been discussed by early practitioners of computational science, but was later forgotten. The present work focuses on independent reviewing, an important source of trust in science, and identifies the characteristics of automated reasoning systems that affect their reviewability. It also discusses possible steps towards increasing reviewability and trustworthiness via a combination of technical and social measures.