Tanswell, Fenner Stanley and Berg, Ásgeir (2025) The Philosophical Prospects of Large Language Models in the Future of Mathematics. [Preprint]
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The Philosophical Prospects of Large Language Models in the Future of Mathematics 19.08.2025.pdf - Accepted Version Download (4MB) |
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The Philosophical Prospects of Large Language Models in the Future of Mathematics 19.08.2025.pdf Download (4MB) |
Abstract
In this article, we examine the philosophical implications Large Language Models might have on mathematical practice in the near future. Some prominent researchers argue that Large Language Models will soon have the ability to generate or check proofs, lifting a great burden of human mathematicians.
We claim, however, that the implementation of LLM technologies in mathematics is not merely a neutral tool that assists mathematicians to continue on as before, but instead entails a radical change to the practices of mathematics with important philosophical implications.
We will argue that we cannot be confident such tools will continue to work as expected, even if they become arbitrarily more reliable than they currently are, and that the kind of justification we get from LLM-generated proofs can never be properly mathematical. We will evaluate solutions to this problem involving either computer verification or human checking and argue that these cannot fix the philosophical gap to give us proper mathematical justification.
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