Conjecture Institute president Logan Chipkin and fellow Paul Raymond-Robichaud hosted an X Space to discuss the recent letter published by various Fields Medal winners about AI use in mathematics.
Note: I drafted this post a few days after listening to the conversation it mentions, but I only got to publish it now, more than a month later. Since then, Conjecture Institute published an official write-up of the conversation which I recommend reading.
The topic is worth exploring regardless of how interested one might be in arcane mathematical problems, because the reaction of these prominent mathematicians reveals a misconception about knowledge creation with consequences that spans far beyond the field.
Titled A Severe Misalignment of AI in Mathematics, the letter argues that AI represents a “threat to intellectual work” because it can produce results without developing underlying understanding.
In many fields and activities, years of training have traditionally served not only to produce a final answer or product, but also to develop understanding and the ability to formulate new questions and ideas. However, building on a vast body of previous human work, AI systems are becoming increasingly capable of producing the results of such work directly, and these goals cease to align. The issues the mathematical community faces now are similar to issues that other scientific and creative professions are facing, and indicate issues that all of humanity might face: how to make sure that, as AI changes the way work is done, we do not lose sight of what that work was meant to achieve in the first place.
On the surface, the concern seems legitimate. In leaning on AI to solve our problems, are we forfeiting deeper understanding? I have argued the same with less eloquence: Are you delegating work or delegating thinking?
But if one examines what LLMs have recently contributed to mathematics through our best understanding of epistemology, as Logan and Paul did, these prestigious mathematicians’ concern shrinks considerably.
To worry that using AI will result in generating proofs without developing understanding implies that once the proof is obtained, no one will care to understand its implications. This is somewhat surprising coming from a field that purports to value understanding above all else.
In practice, the introduction of AI doesn’t seem to impair understanding. On the contrary, it can help grow it.
In chess, engines had the opposite effect to the one the Fields medalists fear. Understanding of the game has been increasing since machines became able to beat humans. As Game Changer: AlphaZero’s Groundbreaking Chess Strategies and the Promise of AI by Matthew Sadler and Natasha Regan shows, inquiry into the products of AI is producing increased understanding.
In my world of software development, the sudden collapse of the cost of writing code has resurfaced decades-old best practices that many had been ignoring. Techniques like walking skeletons and tracer bullets, domain languages and design patterns, formerly discarded by some as too academic, are being rediscovered and their practical value better understood. It turns out that when you can move very fast, being able to channel that speed without derailing is rather valuable. In this way, AI is helping develop our understanding of what it takes to write “good” software.
Whether in mathematics, software, or chess, the introduction of AI has given practitioners more ways to develop understanding, not less.
But there’s a catch. As always, it’s up to us people, with our creativity and agency, to go look for that understanding. AI doesn’t rob the curious mind of the ability to understand the world; it only reduces the toil involved.
As Paul observed in the X Space, the consequences of less toil in knowledge creation can be very positive. When agricultural techniques result in more productivity, we need fewer farmers to produce the same amount of food. But theorems are not carrots. Increasing our ability to solve certain mathematical problems does not mean we’ll need fewer mathematicians. There’s an infinite number of mathematical problems to solve.
Appreciating that knowledge creation, the engine of progress and the economy, starts with problems, and that problems are inevitable, greatly reduces the concern about the medium- to long-term impact of AI, or of any other technological innovation.
The reaction of these illustrious mathematicians is worrying because it foments a growing AI doomerism. Demands to slow down AI and regulate the frontier are dangerous. It is not hyperbole to say that our survival depends on solving ever more problems ever more rapidly. We don’t know what we don’t know, and it’s what we don’t know that has the potential to harm us — badly. Any effort to slow down the rate of knowledge creation, including formalizing arcane mathematical proofs, robs us and our children of a better future.
We’ve seen what bad ideas about technology can do. The nuclear doomers of the ‘70s and ‘80s were very effective in pulling the brake on the adoption of nuclear energy. As a result, we’ve been stuck with lesser forms of energy production, such as burning coal. So, in a perverse turn of events, the same environmental concerns that were a strong component of the anti-nuclear push led to further damage to the environment by forcing countries into burning more fossil fuels.
In the same way a rational environmentalist should endorse nuclear energy instead of campaigning against it, people who care about increasing our understanding of the world should endorse AI improvements instead of demanding a slowdown.
This is not to say that LLM vendors are beyond criticism, or that we should proceed willy-nilly without any regard for safety or privacy. In fact, it is exactly because we need to approach AI development with care and responsibility that vague, emotionally loaded calls to “regulate the frontier” are so counterproductive.