相关论文: Number Theory and Axiomatic Geometry in the Diproc…

Understanding geometric relationships with little mathematical knowledge can be challenging for today's students and teachers. A new toolset is introduced that is able to create a proof without words by combining the benefits of the…

We introduce a novel task consisting in assigning a proof to a given mathematical statement. The task is designed to improve the processing of research-level mathematical texts. Applying Natural Language Processing (NLP) tools to research…

We present the Sequent Calculus Trainer, a tool that supports students in learning how to correctly construct proofs in the sequent calculus for first-order logic with equality. It is a proof assistant fostering the understanding of all the…

Proof autoformalization, the task of translating natural language theorems and proofs into machine-verifiable code, is a critical step for integrating large language models into rigorous mathematical workflows. Current approaches focus on…

We address generating theorems from a given set of axioms, without proof goal, aiming at value from a mathematical point of view or as lemmas for automated proving. As benchmark, we convert a fragment of the Metamath database set.mm. Our…

Debugging is often a challenging and infuriating experience for secondary school students learning their first text-based programming language. Many students resort to ineffective debugging strategies, making success with solving errors…

We outline an unified introduction to the evolution equations of classical and quantum systems intended for a high school students audience. The attempt consists in circumventing the lack of mathematical knowledge with the use of simplified…

Can we acquire apriori knowledge of mathematical facts from the outputs of computer programs? People like Burge have argued (correctly in our opinion) that, for example, Appel and Haken acquired apriori knowledge of the Four Color Theorem…

The Axiom-Based Atlas is a novel framework that structurally represents mathematical theorems as proof vectors over foundational axiom systems. By mapping the logical dependencies of theorems onto vectors indexed by axioms - such as those…

The goal of this paper is twofold. First, we present a unified way of formulating numerical integration problems from both approximation theory and discrepancy theory. Second, we show how techniques, developed in approximation theory, work…

This panel draws on research of the teaching of mathematical proof, conducted in five countries at different levels of schooling. With a shared view of proof as essential to the teaching and learning of mathematics, the authors present…

Access to quality education remains a global challenge, particularly in crisis-affected regions. This study examines the decline in students' mathematical proficiency and proposes an innovative Moodle-based testing system that incorporates…

Despite the success of large language models (LLMs), the task of theorem proving still remains one of the hardest reasoning tasks that is far from being fully solved. Prior methods using language models have demonstrated promising results,…

Proof Blocks is a software tool that allows students to practice writing mathematical proofs by dragging and dropping lines instead of writing proofs from scratch. Proof Blocks offers the capability of assigning partial credit and providing…

Zero-shot Event Detection (ED), the task of identifying event mentions in natural language text without any training data, is critical for document understanding in specialized domains. Understanding the complex event ontology, extracting…

We describe a "top down" approach for automated theorem proving (ATP). Researchers might usefully investigate the forms of the theorems mathematicians use in practice, carefully examine how they differ and are proved in practice, and code…

Automated deduction seeks to enable machines to reason with mathematical precision and logical completeness. Classical resolution-based systems, such as Prover9, E, and Vampire, rely on binary inference, which inherently limits multi-clause…

The present work has been designed for students in secondary school and their teachers in mathematics. We will show how with the help of our knowledge of number systems we can solve problems from other fields of mathematics for example in…

Proof Blocks is a software tool which enables students to write proofs by dragging and dropping prewritten proof lines into the correct order. These proofs can be graded completely automatically, enabling students to receive rapid feedback…

We introduce a method to derive theorems from Elementary Number Theory by means of relationships among formal languages. Using $\sigma$-algebras, we define what a proof of a number-theoretical statement by Language Theory means. We prove…