Can maths survive AI? Fields medallist Terence Tao calls for a ‘Maths 2.0’ world

Advanced artificial-intelligence models are transforming mathematics at an astonishing speed. In the past few months, AI-aided proofs — logical arguments that demonstrate why a mathematical result is correct — have been released for hundreds of long-standing maths problems.

Mathematicians might need several months to fully understand the underlying arguments and implications of these automatically derived solutions. As a mathematician who uses AI tools for my own research, I can see that the field has fundamentally transformed. We now urgently need to establish a ‘Maths 2.0’ era, in which ‘proof scarcity’ is no longer a defining feature of the field.

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The challenges associated with this new way of doing maths are already evident. Many AI-generated results are not described clearly enough to meet quality standards for publication. Some researchers using AI tools simply move on to the next problem once they have a minimally presentable proof, leaving results that can be difficult for other mathematicians to assess. And it still remains unclear how extensively AI models are drawing on the previous work of mathematicians without providing proper attribution.

The centuries-old practice of openly sharing maths problems is under serious threat because mathematicians are increasingly fearful that disclosing their research directions will lead to their work being ‘scooped’ by a rival who is equipped with a frontier AI model. Graduate students and junior mathematicians used to develop their skills and gain early recognition from their peers by solving such problems. On 6 October, technology firm OpenAI dumped hundreds of solutions to such problems online in one go. It disrupted countless research programmes overnight.

Perhaps the most counter-intuitive consequence is that human understanding of mathematics is falling behind, because AI systems generate results faster than mathematicians can digest and absorb them. Confined to pure mathematics, this ‘proof indigestion’ might be a minor concern. But AI-generated mathematical models deployed in the real world without a matching understanding of their mechanisms could have serious consequences. For example, complex AI-generated models are already used to some extent to determine who qualifies for a bank loan and to measure financial risk in markets. If the complexity of these models outpaces the capacity for humans to understand when they might malfunction, the risks of unforeseen mistakes will grow, affecting the general public.

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These negative impacts are not inevitable. Used creatively, and with the right incentives, AI tools could enhance human understanding. It is still possible to change course, through a radical reassessment of the conventional incentive structure of mathematics and by introducing more-responsible practices around AI use.

Competing Interests

The author declares no competing interests.