Related papers: Advancements in Research Mathematics through AI: A…
We introduce a novel framework for human-AI collaboration in prediction and decision tasks. Our approach leverages human judgment to distinguish inputs which are algorithmically indistinguishable, or "look the same" to any feasible…
Combinatorics is a fundamental mathematical discipline as well as an essential component of many mathematical areas, and its study has experienced an impressive growth in recent years. One of the main reasons for this growth is the tight…
[Taken from the "README" in the book] My goal with this book is to provide some kind of bridge for mathematics between the high-school-level and college-level for physics students. From my perspective, our job as physicists is to observe…
The advent of computers has allowed mathematicians to do increasingly more difficult computations that used to be practically impossible. Peer reviewers will seldom look at any code attached to a math paper, however. In this article, we…
This survey paper is an expanded version of an invited keynote at the ThEdu'22 workshop, August 2022, in Haifa (Israel). After a short introduction on the developments of CAS, DGS and other useful technologies, we show implications in…
Computational philosophy is the use of mechanized computational techniques to unearth philosophical insights that are either difficult or impossible to find using traditional philosophical methods. Computational metaphysics is computational…
Reasoning with defeasible and conflicting knowledge in an argumentative form is a key research field in computational argumentation. Reasoning under various forms of uncertainty is both a key feature and a challenging barrier for automated…
Scientific discovery is a complex cognitive process that has driven human knowledge and technological progress for centuries. While artificial intelligence (AI) has made significant advances in automating aspects of scientific reasoning,…
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…
The traditional foundation of science lies on the cornerstones of theory and experiment. Theory is used to explain experiment, which in turn guides the development of theory. Since the advent of computers and the development of…
In scientific research, ``limitations'' refer to the shortcomings, constraints, or weaknesses of a study. A transparent reporting of such limitations can enhance the quality and reproducibility of research and improve public trust in…
The pursue of what are properties that can be identified to permit an automated reasoning program to generate and find new and interesting theorems is an interesting research goal (pun intended). The automatic discovery of new theorems is a…
When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…
We present an overview of how certain computational tools currently interact with mathematical practice, and reflect on the implications for research mathematics in the short to medium term, as the field navigates the emerging age of AI and…
In the recent years, we have linked a large corpus of formal mathematics with automated theorem proving (ATP) tools, and started to develop combined AI/ATP systems working in this setting. In this paper we first relate this project to the…
Insightful interdisciplinary collaboration is essential to the principled governance of technology. When such efforts address the interaction between computation and society, they often focus on modeling, the process by which computer…
Electronic exams (e-exams) have the potential to substantially reduce the effort required for conducting an exam through automation. Yet, care must be taken to sacrifice neither task complexity nor constructive alignment nor grading…
This paper explores the application of automated planning to automated theorem proving, which is a branch of automated reasoning concerned with the development of algorithms and computer programs to construct mathematical proofs. In…
Good problems grab us. They invite us to find patterns, make conjectures, and prove-or perhaps disprove-a conjecture. When I first taught, I saw my work as tantalizing students with structures just beyond their reach, so that I could elicit…
Mathematical models implemented on a computer have become the driving force behind the acceleration of the cycle of scientific processes. This is because computer models are typically much faster and economical to run than physical…