Advancements in Research Mathematics through AI: A Framework for Conjecturing

Abstract: 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 has increasingly sought the assistance of computers to bolster these tasks. This paper is a testament to that pursuit; it presents a robust framework enabling a computer to automatically generate conjectures - particularly those conjectures that mathematicians might deem substantial and elegant. More specifically, we outline our framework and provide evidence in the mathematical literature demonstrating its use in generating publishable research and surprising mathematics. We suspect our simple description of computer-assisted mathematical conjecturing will catalyze further research into this area and encourage the development of more advanced techniques than the ones presented herein.