Related papers: Advancements in Research Mathematics through AI: A…
We argue how AI can assist mathematics in three ways: theorem-proving, conjecture formulation, and language processing. Inspired by initial experiments in geometry and theoretical physics in 2017, we summarize how this emerging field has…
Recent years have seen the dramatic rise of the usage of AI algorithms in pure mathematics and fundamental sciences such as theoretical physics. This is perhaps counter-intuitive since mathematical sciences require the rigorous definitions,…
Recent developments show that AI can prove research-level theorems in mathematics, both formally and informally. This essay urges mathematicians to stay up-to-date with the technology, to consider the ways it will disrupt mathematical…
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…
This overview article highlights the critical role of mathematics in artificial intelligence (AI), emphasizing that mathematics provides tools to better understand and enhance AI systems. Conversely, AI raises new problems and drives the…
Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in various fields, including science, engineering, finance, and everyday life. The development of artificial intelligence (AI) systems capable of solving…
Recent progress in artificial intelligence (AI) is unlocking transformative capabilities for mathematics. There is great hope that AI will help solve major open problems and autonomously discover new mathematical concepts. In this essay, we…
We review the recent programme of using machine-learning to explore the landscape of mathematical problems. With this paradigm as a model for human intuition - complementary to and in contrast with the more formalistic approach of automated…
This paper presents a comprehensive overview on the applications of artificial intelligence (AI) in mathematical research, highlighting the transformative role AI has begun to play in this domain. Traditionally, AI advancements have heavily…
The Graph Brain Project is an experiment in how the use of automated mathematical discovery software, databases, large collaboration, and systematic investigation provide a model for how mathematical research might proceed in the future.…
Mathematical information is essential for technical work, but its creation, interpretation, and search are challenging. To help address these challenges, researchers have developed multimodal search engines and mathematical question…
Mathematics is one of the most powerful conceptual systems developed and used by the human species. Dreams of automated mathematicians have a storied history in artificial intelligence (AI). Rapid progress in AI, particularly propelled by…
Conjecturing and theorem proving are activities at the center of mathematical practice and are difficult to separate. In this paper, we propose a framework for completing incomplete conjectures and incomplete proofs. The framework can turn…
AI for Mathematics (AI4Math) is not only intriguing intellectually but also crucial for AI-driven discovery in science, engineering, and beyond. Extensive efforts on AI4Math have mirrored techniques in NLP, in particular, training large…
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…
Can artificial intelligence truly contribute to creative mathematical research, or does it merely automate routine calculations while introducing risks of error? We provide empirical evidence through a detailed case study: the discovery of…
AI tools and agents are reshaping how researchers work, from proving theorems to training neural networks. Yet for many, it remains unclear how these tools fit into everyday research practice. This paper is a practical guide to AI-assisted…
Analogy has received attention as a form of inductive reasoning in the empirical sciences. However, its role in pure mathematics has received less consideration. This paper provides an account of how an analogy with a more familiar…
The highest level of mathematics has traditionally been seen as a solitary endeavour, to produce a proof for review and acceptance by research peers. Mathematics is now at a remarkable inflexion point, with new technology radically…
Combinatorics is a powerful tool for dealing with relations among objectives mushroomed in the past century. However, an more important work for mathematician is to apply combinatorics to other mathematics and other sciences not merely to…