Related papers: Lectures on AI for Mathematics
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…
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 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…
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…
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 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…
AI for Mathematics (AI4Math) has emerged as a distinct field that leverages machine learning to navigate mathematical landscapes historically intractable for early symbolic systems. While mid-20th-century symbolic approaches successfully…
This chapter provides an overview of the different Artificial Intelligence (AI) systems that are being used in contemporary digital tools for Mathematics Education (ME). It is aimed at researchers in AI and Machine Learning (ML), for whom…
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…
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…
The main drawback of using generative AI models for advanced mathematics is that these models are not primarily logical reasoning engines. However, Large Language Models, and their refinements, can pick up on patterns in higher mathematics…
In the words of the esteemed mathematician Paul Erd\"os, the mathematician's task is to \emph{prove and conjecture}. These two processes form the bedrock of all mathematical endeavours, and in the recent years, the mathematical community…
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…
This draft book offers a comprehensive and rigorous treatment of the mathematical principles underlying modern deep learning. The book spans core theoretical topics, from the approximation capabilities of deep neural networks, the theory…
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…
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,…
This paper addresses the question of how able the current trends of Artificial Intelligence (AI) are in managing to take the responsibility of a full course of mathematics at a college level. The study evaluates this ability in four…
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…
Artificial intelligence (AI) is the name popularly given to a broad spectrum of computer tools designed to perform increasingly complex cognitive tasks, including many that used to solely be the province of humans. As these tools become…
We introduce the AI co-mathematician, a workbench for mathematicians to interactively leverage AI agents to pursue open-ended research. The AI co-mathematician is optimized to provide holistic support for the exploratory and iterative…