Related papers: The Lean mathematical library
As developers of libraries implementing interval arithmetic, we faced the same difficulties when it comes to testing our libraries. What must be tested? How can we devise relevant test cases for unit testing? How can we ensure a high (and…
The fast-paced development of machine learning (ML) methods coupled with its increasing adoption in research poses challenges for researchers without extensive training in ML. In neuroscience, for example, ML can help understand…
Viewing formal mathematical proofs as logical terms provides a powerful and elegant basis for analyzing how human experts tend to structure proofs and how proofs can be structured by automated methods. We pursue this approach by (1)…
To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary…
The prevalence of software systems has become an integral part of modern-day living. Software usage has increased significantly, leading to its growth in both size and complexity. Consequently, software development is becoming a more…
The challenge of formal proof generation has a rich history, but with modern techniques, we may finally be at the stage of making actual progress in real-life mathematical problems. This paper explores the integration of ChatGPT and basic…
We present Qiskit Machine Learning (ML), a high-level Python library that combines elements of quantum computing with traditional machine learning. The API abstracts Qiskit's primitives to facilitate interactions with classical simulators…
Discrete mathematics is the foundation of computer science. It focuses on concepts and reasoning methods that are studied using math notations. It has long been argued that discrete math is better taught with programming, which takes…
We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…
Typeclasses provide an elegant and effective way of managing ad-hoc polymorphism in both programming languages and interactive proof assistants. However, the increasingly sophisticated uses of typeclasses within proof assistants, especially…
Neurosymbolic approaches leveraging Large Language Models (LLMs) with formal methods have recently achieved strong results on mathematics-oriented theorem-proving benchmarks. However, success on competition-style mathematics does not by…
We present several steps towards large formal mathematical wikis. The Coq proof assistant together with the CoRN repository are added to the pool of systems handled by the general wiki system described in \cite{DBLP:conf/aisc/UrbanARG10}. A…
Formalized mathematics has recently garnered significant attention for its ability to assist mathematicians across various fields. Premise retrieval, as a common step in mathematical formalization, has been a challenge, particularly for…
The Python ecosystem represents a global, data rich, technology-enabled network. By analyzing Python's dependency network, its top 14 most imported libraries and cPython (or core Python) libraries, this research finds clear evidence the…
Formal theorem proving with TLA+ provides rigorous guarantees for system specifications, but constructing proofs requires substantial expertise and effort. While large language models have shown promise in automating proofs for tactic-based…
Mathematical research thrives on the effective dissemination and discovery of knowledge. zbMATH Open has emerged as a pivotal platform in this landscape, offering a comprehensive repository of mathematical literature. Beyond indexing and…
This paper describes the technical and conceptual development of the LuminLab platform, an online tool that integrates a purpose-fit human-centric AI chatbot and predictive energy model into a streamlined front-end that can rapidly produce…
Mathematical reasoning remains a significant challenge for Large Language Models (LLMs) due to hallucinations. When combined with formal proof assistants like Lean, these hallucinations can be eliminated through rigorous verification,…
The paper examines the construction of a course in mathematical analysis at a pedagogical university, aimed at developing the ability of future mathematics teachers to detect and solve problems related to finding proofs. Key words: teaching…
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…