‘The development of AI will stimulate debate about the value of mathematics as practised by human beings.’ Photograph: Igor Mojzes/AlamyView image in fullscreen‘The development of AI will stimulate debate about the value of mathematics as practised by human beings.’ Photograph: Igor Mojzes/AlamyLettersSurprising AI breakthroughs raise soul-searching questions for mathematiciansWhether mathematics thrives or perishes in the age of AI depends on what it is that society values in the human intellect, writes Dr Henry Bradford I share Kasra Rafi and Bruce Schneier’s impression that recent mathematical breakthroughs by AI consist in clever recombination of existing ideas, not development of truly novel theory (No, AI doesn’t mean the end of mathematics – at least not yet, 25 August). The question is: what happens to mathematics if this changes?Like many mathematicians, I have done much soul-searching in recent weeks, especially since a key problem in my own field of group theory (the existence of non-sofic groups) was solved this month by OpenAI’s Astra model. Astra’s proof consists largely in a slight twist on theorems by my colleagues Gabor Kun and Andreas Thom. That said, even a few months ago I would have found the idea that AI was capable of such a breakthrough incredible, so it seems foolhardy now to bet against AIs achieving superhuman capabilities in all areas of mathematical thought in the coming years.This forces the question: what is the purpose of mathematical research? Is it simply to prove new theorems (at which task future AIs may be far better than humans)? The great American mathematician Bill Thurston thought not: in his 1994 essay On Proof and Progress in Mathematics, he wrote that mathematicians “discover ... that what they really want is usually not some collection of ‘answers’ – what they want is understanding”. In other words, mathematics consists in the ideas living in human brains, with new theorems serving as markers for our progress in understanding and sharing these ideas.This matters, because the development of AI will stimulate debate about the value of mathematics as practised by human beings. If AI can churn out research papers faster and cheaper than humans, then administrators within cash-strapped universities will surely be tempted to regard their mathematical researchers as superfluous. On Thurston’s view, this would be a mistake, because the value of those researchers’ work consists less in the papers they write than in their contributions to the preservation and furtherance of mathematical knowledge among people.Whether mathematics thrives or perishes in the age of AI is not merely a technical question about the capabilities of future machine intelligences. It is a collective decision that society makes about what it is in the human intellect that we choose to value.Dr Henry BradfordFellow of mathematics, Christ’s College, University of CambridgeExplore more on these topicsMathematicsAI (artificial intelligence)lettersShareReuse this content