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This paper discusses digital online mathematics examinations -- a discussion ranging from high school to university level examinations. In particular, we consider the nature of mathematical writing, what is distinctive about mathematical…

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…

When beginners learn to speak a non-native language, it is difficult for them to judge for themselves whether they are speaking well. Therefore, computer-assisted pronunciation training systems are used to detect learner mispronunciations.…

The use of logical systems for problem-solving may be as diverse as in proving theorems in mathematics or in figuring out how to meet up with a friend. In either case, the problem solving activity is captured by the search for an…

Noting that lemmas are a key feature of mathematics, we engage in an investigation of the role of lemmas in automated theorem proving. The paper describes experiments with a combined system involving learning technology that generates…

The geometry automated theorem proving area distinguishes itself by a large number of specific methods and implementations, different approaches (synthetic, algebraic, semi-synthetic) and different goals and applications (from research in…

It is nowadays common to consider that proof must be part of the learning of mathematics from Kindergarten to University1. As it is easy to observe, looking back to the history of mathematical curricula, this has not always been the case…

Mathematical proofs are both paradigms of certainty and some of the most explicitly-justified arguments that we have in the cultural record. Their very explicitness, however, leads to a paradox, because the probability of error grows…

The material presented in this paper contributes to establishing a basis deemed essential for substantial progress in Automated Deduction. It identifies and studies global features in selected problems and their proofs which offer the…

Proof Designer is a computer software program designed to help Mathematics students learn to write mathematical proofs. Under the guidance of the user, Proof Designer assists in writing outlines of proofs in elementary set theory. Proof…

Teaching college students how to write rigorous proofs is a critical objective in courses that introduce formal reasoning. Over the course of several years, we have developed a mechanically-checkable style of calculational reasoning that we…

Geometry theorem proving forms a major and challenging component in the K-12 mathematics curriculum. A particular difficult task is to add auxiliary constructions (i.e, additional lines or points) to aid proof discovery. Although there…

This paper presents an intelligent tutoring system, GeoTutor, for Euclidean Geometry that is automatically able to synthesize proof problems and their respective solutions given a geometric figure together with a set of properties true of…

Mathematics is a highly specialized domain with its own unique set of challenges that has seen limited study in natural language processing. However, mathematics is used in a wide variety of fields and multidisciplinary research in many…

PIE is a Prolog-embedded environment for automated reasoning on the basis of first-order logic. It includes a versatile formula macro system and supports the creation of documents that intersperse macro definitions, reasoner invocations and…

Grammar checking is the task of detection and correction of grammatical errors in the text. English is the dominating language in the field of science and technology. Therefore, the non-native English speakers must be able to use correct…

The ever-growing complexity of mathematical proofs makes their manual verification by mathematicians very cognitively demanding. Autoformalization seeks to address this by translating proofs written in natural language into a formal…

We present a prototype of an integrated reasoning environment for educational purposes. The presented tool is a fragment of a proof assistant and automated theorem prover. We describe the existing and planned functionality of the theorem…

We propose a novel system, MathMistake Checker, designed to automate step-by-step mistake finding in mathematical problems with lengthy answers through a two-stage process. The system aims to simplify grading, increase efficiency, and…

The sequent calculus is a formalism for proving validity of statements formulated in First-Order Logic. It is routinely used in computer science modules on mathematical logic. Formal proofs in the sequent calculus are finite trees obtained…