Related papers: Beginners' Quest to Formalize Mathematics: A Feasi…
Formal theorem proving, a field at the intersection of mathematics and computer science, has seen renewed interest with advancements in large language models (LLMs). This paper introduces SubgoalXL, a novel approach that synergizes…
"Mathematicians, like physicists, are pushed by a strong fascination. Research in mathematics is hard, it is intellectually painful even if it is rewarding, and you would not do it without some strong urge." [D. Ruelle]. We shall give some…
This study presents a case study of active learning within the Investigative Science Learning Environment (ISLE), using the iOLab digital devices. We designed a pilot lab format to enhance student engagement and understanding through direct…
ProofPeer strives to be a system for cloud-based interactive theorem proving. After illustrating why such a system is needed, the paper presents some of the design challenges that ProofPeer needs to meet to succeed. Contexts are presented…
Recent work by Clark et al. (2020) shows that transformers can act as 'soft theorem provers' by answering questions over explicitly provided knowledge in natural language. In our work, we take a step closer to emulating formal theorem…
Informal mathematics has been central to modern large language model (LLM) reasoning, offering flexibility and enabling efficient construction of arguments. However, purely informal reasoning is prone to logical gaps and subtle errors that…
The class $\MIP^*$ of promise problems that can be decided through an interactive proof system with multiple entangled provers provides a complexity-theoretic framework for the exploration of the nonlocal properties of entanglement. Little…
Using an interactive theorem prover to reason about programs involves a sequence of interactions where the user challenges the theorem prover with conjectures. Invariably, many of the conjectures posed are in fact false, and users often…
Undergraduate students of artificial intelligence often struggle with representing knowledge as logical sentences. This is a skill that seems to require extensive practice to obtain, suggesting a teaching strategy that involves the…
Proof engineering efforts using interactive theorem proving have yielded several impressive projects in software systems and mathematics. A key obstacle to such efforts is the requirement that the domain expert is also an expert in the…
Formalised libraries of combinatorial mathematics have rapidly expanded over the last five years, but few use one of the most important tools: probability. How can often intuitive probabilistic arguments on the existence of combinatorial…
Despite significant advancements in the conception of (formal) integrated development environments, applying formal methods in software industry is still perceived as a difficult task. To make the task easier, providing tools that help…
Interactive Theorem Provers (ITPs) are an indispensable tool in the arsenal of formal method experts as a platform for construction and (formal) verification of proofs. The complexity of the proofs in conjunction with the level of expertise…
This text is addressed to mathematicians who are interested in generalized functions and unbounded operators on a Hilbert space. We expose in detail (in a "formal way" - as done by Heisenberg and Pauli - i.e. without mathematical…
The interoperability of proof assistants and the integration of their libraries is a highly valued but elusive goal in the field of theorem proving. As a preparatory step, in previous work, we translated the libraries of multiple proof…
Comparing provers on a formalization of the same problem is always a valuable exercise. In this paper, we present the formal proof of correctness of a non-trivial algorithm from graph theory that was carried out in three proof assistants:…
The formalization of existing mathematical proofs is a notoriously difficult process. Despite decades of research on automation and proof assistants, writing formal proofs remains arduous and only accessible to a few experts. While previous…
We give an overview of our formalizations in the proof assistant Isabelle/HOL of certain irrationality and transcendence criteria for infinite series from three different research papers: by Erd\H{o}s and Straus (1974), Han\v{c}l (2002),…
Scientific laboratories are among the most challenging course components to integrate into online instruction. Available technology restricts the design and nature of experiments and it can be hard to replicate the collaborative lab…
The purpose of this paper is to explore the question "to what extent could we produce formal, machine-verifiable, proofs in real algebraic geometry?" The question has been asked before but as yet the leading algorithms for answering such…