I could fit the early stages of AI progress into a familiar story: first a model could summarize a document, then write some code, then help investigate a problem. Each step made work I understood faster or easier.

Research-level mathematics makes that story harder to hold onto.

The question I keep returning to is what happens when AI can reason beyond the reach of our best minds. Would its discoveries still make sense to us?

That is a question about a possible future, not a claim that we have arrived there. Impressive results deserve close inspection. But mathematics gives us a concrete place to start thinking about the distinction between extending human reasoning and moving beyond it.

Mathematics puts the question of insight in view

Epoch AI's FrontierMath tests models on difficult mathematics, including research-level problems. Work like this interests me because it pushes the discussion beyond how fluent an answer sounds and toward whether it is correct.

There are also results outside benchmarks. In May 2026, OpenAI reported that a reasoning model had disproved a conjecture concerning the planar unit distance problem, a problem originating with Paul Erdős in 1946. External mathematicians checked the proof. That is a specific achievement, and it matters more than a vague claim that a model is now “good at math.”

Hard mathematics demands choices about how to think. A mathematician has to find a useful abstraction, notice which assumptions matter, and recognize when two apparently distant ideas belong together. Trying more possibilities helps, but choosing what to try is part of the difficulty.

An AI contribution can still fit within reasoning we understand. Perhaps the model explored a construction a human could have found with more time, connected material from another field, or persisted through a search that would have exhausted a person. Those possibilities are already consequential. They give us more opportunities to find insight.

They also leave open a deeper question: how far can this process go?

A tireless collaborator is already a major change

It is tempting to put an IQ number on a model and locate it somewhere in the human distribution. I find the underlying comparison more useful than the number: imagine a very capable collaborator who can search widely, use tools, and keep trying long after you need a break.

Even that picture understates the effect of scale. Many such collaborators, working on different approaches, could accomplish far more than one unusually smart person. A system would not have to surpass every human in every respect to transform research.

I can still picture how that work might happen. One attempt finds a promising construction. Another connects a citation trail. A third discovers the flaw everyone else missed. The individual steps are recognizable, even if their combined speed and reach are unfamiliar.

That makes the next possibility harder to separate from the first. Perhaps what we call artificial superintelligence, or ASI, would emerge from enough of these advantages compounded together. More memory, more attempts, better tools, and more reliable checking might be sufficient.

It could remain understandable step by step while becoming impossible for any person to match as a whole.

Science adds a constraint that thought alone cannot remove

Physics is an obvious place to extend this thought experiment. A powerful system might propose new mathematical structures, identify experimental signatures we missed, or design instruments that make an old question measurable.

But the universe still gets a vote. A promising theory has to survive observations and experiments. The same broad constraint applies to biology and materials science: more reasoning can suggest where to look, but a convincing explanation cannot substitute for evidence.

I can imagine an ASI operating like a research organization: developing theory, running simulations, designing experiments, and criticizing its own results. That would make many more paths worth exploring, while leaving real limits on how quickly discoveries could be tested.

Even this enormous possibility is fairly easy to describe. It uses the categories of work we already know.

There may be kinds of thought we cannot picture

The possibility I find harder to imagine is that greater intelligence changes the questions themselves.

Human thought has a particular shape. We use language, diagrams, equations, stories, and analogies. Our working memory is limited, our training takes years, and our attention is attached to bodies that eventually need lunch.

A more capable system might overcome those limits by holding more variables in view, maintaining competing explanations for longer, or combining fields without needing a separate apprenticeship in each. Those are differences of degree that I can at least gesture toward.

But perhaps some insights require forms of representation we simply do not have. The comparison that comes to mind is calculus and a dog: more facts alone will not close that gap. I do not know whether anything similar would separate us from an ASI. I also do not know how we would rule it out.

I can picture a better battery, a new proof technique, or an experiment no human thought to propose. I have a much harder time picturing a discovery whose underlying concepts we cannot grasp. Even describing it seems to require borrowing from the ideas we already have.

That is where my imagination runs out.

The uncertainty cuts both ways

I want to leave room for that possibility without treating every benchmark improvement as evidence that it is imminent. A result on a hard problem tells us something about the system that produced it. It does not, by itself, establish a general ranking against every human mind.

I also do not want to assume that human thought sets the limit of what intelligence can be. There is no comfort in dismissing a possibility just because it is difficult to imagine.

For now, I can follow much of the proposed path: better training, more compute, stronger tools, more persistence, and better verification. What I cannot see is whether that path eventually leads to ideas that feel unfamiliar in a much deeper way.

That prospect is exciting and unsettling. I keep trying to imagine the first truly non-human idea, and every example I come up with still looks suspiciously human.

If you have a way of thinking about that gap, I would love to hear it.