Related papers: Is Mathematics Obsolete?
Over the past thirty years or so the authors have been teaching various programming for mathematics courses at our respective Universities, as well as incorporating computer algebra and numerical computation into traditional mathematics…
Mathematical reasoning is essential for problem-solving in education, science, and industry, serving as a crucial benchmark for evaluating artificial intelligence systems. As Large Language Models (LLMs) improve their reasoning…
This book provides a comprehensive and accessible introduction to the emerging field of AI for mathematics. It covers the core principles and diverse applications of using artificial intelligence to advance mathematical research. Through…
Math is constructed by people for people: just as natural language corpora reflect not just propositions but the communicative goals of language users, the math data that models are trained on reflects not just idealized mathematical…
Mastering one or more programming languages has historically been the gateway to implementing ideas on a computer. Today, that gateway is widening with advances in large language models (LLMs) and artificial intelligence (AI)-powered coding…
This article analyzes the existential risks artificial intelligence (AI) poses to humanity, tracing the trajectory from current AI to ultraintelligence. Drawing on Irving J. Good and Nick Bostrom's theoretical work, plus recent publications…
This paper reviews the historical development of AI and representative philosophical thinking from the perspective of the research paradigm. Additionally, it considers the methodology and applications of AI from a philosophical perspective…
This perspective piece calls for the study of the new field of Intersymbolic AI, by which we mean the combination of symbolic AI, whose building blocks have inherent significance/meaning, with subsymbolic AI, whose entirety creates…
This paper examines various methods and ideas for humanizing mathematics. The term 'humanizing mathematics' which includes elements of 'aesthetic mathematics' refers to approaches that emphasize the aesthetic, philosophical, and subjective…
The challenges of solving complex university-level mathematics problems, particularly those from MIT, and Columbia University courses, and selected tasks from the MATH dataset, remain a significant obstacle in the field of artificial…
We introduce FrontierMath, a benchmark of hundreds of original, exceptionally challenging mathematics problems crafted and vetted by expert mathematicians. The questions cover most major branches of modern mathematics -- from…
We consider state of the art applications of artificial intelligence (AI) in modelling human financial expectations and explore the potential of quantum logic to drive future advancements in this field. This analysis highlights the…
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 propositional version of the…
The tension between deduction and induction is perhaps the most fundamental issue in areas such as philosophy, cognition and artificial intelligence (AI). The deduction camp concerns itself with questions about the expressiveness of formal…
Recently, there is an increasing interest in understanding the performance of AI systems in solving math problems. A multitude of tests have been performed, with mixed conclusions. In this paper we discuss an experiment we have made in the…
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…
This essay examines how automation has reconfigured mathematical proof and labor, and what might happen in the future. It discusses practical standards of proof, distinguishes between prominent forms of automation in research, provides…
Computers have already changed the way that humans do mathematics: they enable us to compute efficiently. But will they soon be helping us to reason? And will they one day start reasoning themselves? We give an overview of recent…
Although language models demonstrate remarkable proficiency on mathematical benchmarks, it remains unclear whether this reflects true mathematical reasoning or statistical pattern matching over learning formal syntax. Most existing…
Mathematical reasoning, a core aspect of human cognition, is vital across many domains, from educational problem-solving to scientific advancements. As artificial general intelligence (AGI) progresses, integrating large language models…