Related papers: Is Mathematics Obsolete?
Argumentation is a central subarea of Artificial Intelligence (AI) for modeling and reasoning about arguments. The semantics of abstract argumentation frameworks (AFs) is given by sets of arguments (extensions) and conditions on the…
The world of mathematics is often considered abstract, with its symbols, concepts, and topics appearing unrelated to physical objects. However, it is important to recognize that the development of mathematics is fundamentally influenced by…
Computation has changed the world more than any previous expressions of knowledge. In its particular algorithmic embodiment, it offers a perspective, within which the digital computer (one of many possible) exercises a role reminiscent of…
Mathematical reasoning recently has been shown as a hard challenge for neural systems. Abilities including expression translation, logical reasoning, and mathematics knowledge acquiring appear to be essential to overcome the challenge. This…
As artificial intelligence (AI) advances in reasoning capabilities, most recently with the emergence of Large Reasoning Models (LRMs), understanding how children conceptualize AI's reasoning processes becomes critical for fostering AI…
Large Reasoning Models (LRMs) have made significant progress in mathematical capabilities in recent times. However, these successes have been primarily confined to competition-level problems. In this work, we propose AI Mathematician (AIM)…
This article, dedicated, with admiration to Reuben Hersh, for his forthcoming 90th birthday, argues that mathematics today is not yet a science, but that it is high time that it should become one.
This study explores the integration of generative artificial intelligence (AI), specifically large language models, with multi-modal analogical reasoning as an innovative approach to enhance science, technology, engineering, and mathematics…
We study mathematical discovery through the lens of neurosymbolic reasoning, where an AI agent powered by a large language model (LLM), coupled with symbolic computation tools, and human strategic direction, jointly produced a new result in…
With the rapid rise of generative AI in higher education and the unreliability of current AI detection tools, developing policies that encourage student learning and critical thinking has become increasingly important. This study examines…
While Large Language Models have achieved notable success on formal mathematics benchmarks such as MiniF2F, it remains unclear whether these results stem from genuine logical reasoning or semantic pattern matching against pre-training data.…
Interpolation is an important property of classical and many non-classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the the non-monotonic system of…
The unification of logic and probability is a long-standing concern in AI, and more generally, in the philosophy of science. In essence, logic provides an easy way to specify properties that must hold in every possible world, and…
One of today's most significant societal challenges is building AI systems whose behaviour, or the behaviour it enables within communities of interacting agents (human and artificial), aligns with human values. To address this challenge, we…
Artificial intelligence (AI) research enjoyed an initial period of enthusiasm in the 1970s and 80s. But this enthusiasm was tempered by a long interlude of frustration when genuinely useful AI applications failed to be forthcoming. Today,…
This paper seeks to provide a thorough account of the ubiquitous nature of the Bayesian paradigm in modern statistics, data science and artificial intelligence. Once maligned, on the one hand by those who philosophically hated the very idea…
The rapid development of artificial intelligence (AI), marked by breakthroughs like 'AlphaEvolve' and 'Gemini Deep Think', is beginning to offer powerful new tools that have the potential to significantly alter the research practice in many…
In recent years, artificial intelligence (AI) decision-making and autonomous systems became an integrated part of the economy, industry, and society. The evolving economy of the human-AI ecosystem raising concerns regarding the risks and…
This paper explores the relationship of artificial intelligence to the task of resolving open questions in mathematics. We first present an updated version of a traditional argument that limitative results from computability and complexity…
This article argues that the most important significance of the AI revolution, especially the rise of large language models, lies not simply in automation, but in a fundamental change in how complex information and human know-how are…