Medals for Machines
Can machines know mathematics? Is the fact that they solve mathematical problems producing knowledge? Can the progress of AI machines change the future of mathematical knowledge? In this discussion activity, we are exploring the questions above. It leads us to the discussion of what is mathematical knowledge.
On July 21, 2025, Google (Gemini Deep Think) and OpenAI (with a new experimental model) announced that their AI models won gold medals at the International Mathematical Olympiad (IMO) for high school students (Reuters.com). Both models solved 5 out of 6 mathematical problems “using general-purpose reasoning models that processed mathematical concepts using natural language” (Reuters.com) within a 4.5-hour competition time limit. The problems in the Olympiad were linked to algebra, combinatorics, geometry, and number theory (Deepmind.Google). While Google’s score was verified by IMO, confirming it was a gold medal score, OpenAI did not officially enter the competition.
Some experts view this achievement as a demonstration that we are on the verge of creating an AI model that can rival human intelligence in mathematics, making it a valuable tool for mathematicians to apply to currently unsolved mathematical problems (New York Times). In August, it was announced that a new National Science Foundation (NSF) Institute at Carnegie Mellon University will be opened to help mathematicians integrate AI into mathematical reasoning. As Prasad Tetali, professor and department head of Mathematical Sciences at Carnegie Mellon, said: “Mathematical reasoning is foundational to many branches of science and engineering. When human insight and ingenuity are paired with machine-assisted formal reasoning, the scope of the outcome is limitless” (CMU.edu)
Discussion Questions:
- If AI can solve complicated mathematical problems, does it mean that it knows mathematics?
- Can we call the output of AI processes knowledge?
- Does human mathematical ability differ from that of a machine? If so how?
- How may technology like AI change the way knowledge is produced?
Commentary:
Whether we consider AI-generated output as knowledge or not depends on what we take knowledge to be. But it would not currently satisfy either the Justified True Belief criterion (given that we can neither justify the outputs nor are they really beliefs in any meaningful sense), nor does it satisfy the reliablist conception of knowledge (since the output of gen AI is not reliable and cannot be given the nature of the systems that produce it - see the discussion here: Generative AI and Knowledge). In general, strings of text output from gen AI models do not qualify as knowledge, not because of technological or engineering limitations of the model, but rather because these models do not possess the general characteristics of living things that we take to be necessary for strings of text to be meaningful. On the page Generative AI and Knowledge, we discuss why it does not matter to an AI model whether its output is true or not. It does matter to a living system whether its ‘beliefs’ are true because, on the whole, true beliefs are necessary for survival. Note that even the most advanced AI model needs human beings to interpret its output. In the same vein, knowledge is more than arriving at the answer to a question. It requires understanding, explaining, generalising, being able to produce new examples never thought before, and supporting claims with evidence. Gen AI can generate strings of text in response to questions but it requires human input to get the process going and human interpretation to make sense of the output.
Perhaps, gen AI can solve mathematical puzzles in a way that is satisfactory to the human mathematicians – at least that is the claim about the Olympiad. Perhaps, mathematical problems (like playing chess) are a sufficiently restricted set of problems for a specially trained machine to tackle. But again there is a strong hint of collaboration here. Human beings need to design the system to do this kind of ‘reasoning’, and they need to check it and interpret the results. The Tetali quote suggests that the AI model can be a useful tool but there is no suggestion that human involvement is not required.
Can it change the future of mathematical knowledge, then? Experts say it may accelerate the process - AI can explore problems, test conjectures and verify thinking, but mathematicians need to pose questions, clarify definitions and training datasets, supply heuristics and verify what AI is producing. It needs to be a partnership.
To learn more about AI changing the knowledge landscape, head to the conversation with Sir Demis Hassabis on The Future of Knowledge: