OpenAI's Astra model has solved a key problem in group theory, specifically regarding the existence of non-sofic groups. This breakthrough occurred this month, according to Dr Henry Bradford, a Fellow of mathematics at Christ’s College, University of Cambridge.
Astra's proof primarily consists of a slight twist on theorems previously developed by Gabor Kun and Andreas Thom. Dr Bradford noted that even a few months ago, the idea of AI achieving such a breakthrough would have seemed incredible.
The development has prompted mathematicians to reflect on the purpose of mathematical research. Dr Bradford suggests that if AI can produce research papers more quickly and affordably than humans, universities might be tempted to view human mathematical researchers as unnecessary. However, he highlights the view of mathematician Bill Thurston, who believed the value of mathematics lies in understanding and sharing ideas among people, rather than solely in proving new theorems.