What Is the Value of One-Shotting Moonshots?

Human beings no longer occupy an uncontested position at the top of the theorem-proving food chain. OpenAI’s release of more than 700 mathematical manuscripts earlier this month made that prospect difficult to ignore. The collection contains proposed advances across mathematics and theoretical computer science, at different stages of verification. What has stayed with me almost as much as the results themselves is the discomfort surrounding how they arrived.

I can understand some of that discomfort. A difficult problem gives researchers something to struggle with. We try an approach, get stuck, realize that we were asking the wrong question, and occasionally discover something useful while trying to do something else entirely. The original problem might remain unsolved, but the effort can leave behind techniques, connections, and a better sense of which questions are worth pursuing.

Some of this finds its way into papers. Much of it travels through conference talks, seminars, conversations over coffee, and the explanations we give our students or colleagues. A polished proof rarely contains everything that was learned in producing it. Maybe the real treasure is, at least in part, the connections made along the way.

A frontier AI model can now carry out much of this exploration internally and hand us a finished argument. The community then faces the considerable task of figuring out what happened and what can be learned from it. Terence Tao’s phrase “proof indigestion” captures the possibility that results arrive much faster than people can understand and absorb them.

The same concern extends to people using AI. Someone might prompt a model into solving a difficult problem, check the argument carefully, and release a preprint. They may understand how every step follows from the previous one while still having relatively little to say about how the ideas developed.

I can see why short-circuiting this process might seem pernicious. But I also find myself hesitant to make the journey more important than the destination in every setting.

Suppose AI discovers a treatment for a particular cancer, and independent testing establishes that it is safe and effective. We would still want to understand how it works, how to improve it, and what it might teach us about other diseases. Yet the benefit to patients could be enormous even while our understanding of the research process remained incomplete. In that situation, the weight I would attach to the destination changes considerably.

Even within mathematics, people reasonably value different things. Some are especially drawn to solving difficult problems. Others care more about developing concepts and ways of thinking. Timothy Gowers makes this point in explaining his own position on AI and mathematics. There is a spectrum of mathematical temperaments. I am unsure that we should expect everyone along that spectrum to reach the same judgment about what AI is doing to research.

This is the tension I wanted to think through more carefully. I try to give some formalism in my paper, What Is the Value of One(Few)-Shotting Moonshots?.

I started with a simple picture. Imagine a landscape of ideas laid out on a grid. Each point is a concept or result. Research establishes connections between neighboring points, allowing us to reach places we could not previously reach. Every discovery opens several directions for further investigation. Some connections come easily. Others require repeated attempts, and progress becomes harder as we move farther from familiar territory.

Both humans and AI can explore many routes. AI may explore considerably more of the landscape internally. The distinction I am interested in concerns how much of that exploration becomes available to everyone else.

In one extreme, the human community shares its explored map. In the other, AI shares one successful route to its deepest discovery. A reader learns how to reach that result, but much of the surrounding exploration remains private.

These are generous assumptions about human communication and demanding assumptions about AI communication. Human researchers leave plenty unspoken, and AI-assisted research can be communicated thoughtfully. I chose the extremes because I hoped they would help me understand what matters in the much messier middle.

The model gives research two sources of value. One comes from the best breakthrough it achieves. The other comes from the collection of ideas it makes available for future work. A communicated concept receives credit regardless of whether a human or an AI discovered it. We can then compare deeper discoveries and broader knowledge on a similar scale.

Under this setup, there is a range in which AI is better at discovery but human research creates more total value. AI gets farther, yet the extra value of its deepest result falls short of the broader knowledge that human researchers communicate. Once AI’s discovery advantage becomes sufficiently large, the value reverses. The greater the value we attach to public knowledge, the greater the advantage AI needs to compensate for communicating less of it.

There is something useful, to me, about making this dependence explicit. A mathematician critical of the OpenAI release might believe that the surrounding knowledge carries tremendous value and that current models have yet to compensate for what they leave uncommunicated. Someone more optimistic about AI might place greater weight on the discoveries themselves, or expect models to reach problems far beyond what humans could otherwise solve. Both positions can make sense within the same framework.

Actual research will, of course, live somewhere between these extremes. People can use AI to reach further and then explore the new territory around the result. A breakthrough might even give us a starting point from which we can ask questions that would previously have been out of reach. There is a hopeful possibility here that deserves as much attention as the concern about what gets lost.

This is why I found OpenAI’s October 26 announcement interesting. OpenAI describes its manuscripts as “raw research data” and outlines three approaches to further developing understanding around these new results. It also says researchers should receive recognition for the understanding and explanations they develop.

I read this as an acknowledgment that an important part of the work remains after the model produces its answer. It also gives a concrete example of the middle ground that motivated my comparison. We can take advantage of a distant discovery and organize further research around it.

What I keep coming back to, though, is scale. Organizing expert attention around a few prominent discoveries seems feasible. What happens when thousands of people can produce plausible research manuscripts with a few prompts? The ability to generate these papers can spread much faster than the expertise needed to assess and explain them. Even if only a fraction contain useful advances, they could demand enormous attention from a relatively small community.

I am glad that more people may be able to contribute to research. But wider participation in generating proposed discoveries also creates a collective problem of deciding what deserves attention. Some valuable ideas may remain buried in papers that nobody has time to understand. AI could help with explanation and synthesis too. How much that expands our capacity to absorb research is an important part of the question.

There is also an incentive problem. Suppose a young researcher spends several months extracting a useful technique from a difficult AI argument, finding its limitations, and writing something that others can learn from. How will that contribution be recognized? Will journals, hiring committees, and funding agencies value it enough to make the effort worthwhile? It seems optimistic to expect a growing amount of this work if announcing a result attracts substantially more recognition than making it understandable.

OpenAI’s announcement acknowledges recognition and commits support for work around the results. Those are welcome steps. I would like to think further about arrangements that could work at a much larger scale. Perhaps we need dedicated funding for explanation and synthesis, clearer ways to attribute these contributions, or publication formats that make them more visible. Each possibility brings questions about quality, independence, and how scarce attention should be allocated.

These seem like interesting questions to mull over, model, and try to find workable solutions to. How do we support people who turn a difficult argument into something others can use? How do we encourage exploration around a breakthrough when the headline result has already been claimed? And how can AI help with that work as well as with producing the next discovery?

I would like AI to help us reach places we could never have reached on our own. I also hope we leave enough of a map for someone else to wander off in a direction none of us had thought to explore.

Acknowledgements

AI assistance was used in drafting this blog post.