On October 16th, according to OpenAI, one of its systems produced an argument that could overturn a computer science conjecture dating to 1999. On October 26th, the company announced it publicly, alongside two other claimed breakthroughs. Two of the conjecture’s original proposers, Russell Impagliazzo and Ramamohan Paturi, joined Ryan Williams in leading the group that will examine and explain the work.
That is the detail I keep coming back to. A machine has produced an argument that could overturn an assumption these researchers have spent decades studying. Their response is to sit down and read it.
These claims still need independent verification. Agreeing to examine them is not the same as endorsing them. But the possibility deserves our attention: AI may be contributing original work at the frontier of knowledge, with the people best equipped to judge it still working through what it means.
What Makes This Important
The computer science claim concerns the Exponential Time Hypothesis. For nearly three decades, researchers have used it to establish conditional limits on what computers can do efficiently. It has functioned like a building code for hundreds of papers. If the claimed disproof holds up, some of those limits will have to be reconsidered. It would not make every hard problem easy, but it could change where researchers think useful answers are possible.
The other claims concern the behavior of waves and the mathematical foundations of quantum field theory. The physics collaboration, led by Nobel laureate David Gross, is holding back the machine’s output while its members prepare a human-written account.
Much of our experience with AI still involves asking it to summarize a report or explain something somebody else discovered. These claims raise the prospect of asking a machine a question whose answer nobody has supplied, and receiving something that advances the field.
Scientific progress changes the tools available to everyone else. A new method can eventually make something cheaper to produce or possible to do at all. We cannot yet say what these particular results would enable. A lender has reason to care long before a discovery appears in a borrower’s business plan.
A useful discovery can also improve the next round of research. If AI helps develop better tools for investigating difficult questions, some of its work could make subsequent work more productive. I would not trust a confident timetable for that process. I would watch whether each round leaves researchers better equipped to do the next one.
The Work After the Answer
The announcement included formal proofs in Lean for the mathematics and computer science claims. Lean checks whether a conclusion follows from the supplied statement and assumptions; researchers still need to inspect those assumptions, check for admitted gaps, and make sure the statement captures the question they intended to ask.
A valid novel proof can be real knowledge before its significance is widely understood. The next work is learning what follows from it. Researchers need to explain which assumption failed and whether the method helps with another problem. That is how an achievement becomes something other people can build on.
Michael Polanyi described science as a community of overlapping expertise. No individual has to understand everything. We already depend on knowledge we could not reproduce ourselves, trusting people whose judgment is open to criticism from others who know enough to challenge it. AI adds a new participant in producing that knowledge. It also puts more pressure on the arrangements through which we decide what deserves confidence.
Requiring a human to reconstruct every step of every useful answer would defeat much of the purpose. Machines can help check and explain the work, and cheaper assistance can reach people who previously had no expert help at all. The question is whether the people relying on an answer have good reasons to trust it and a way to challenge it when something goes wrong.
If candidate discoveries multiply faster than reliable review, I expect more influence to accrue to whoever decides which questions receive attention and which results are accepted. That might be a small group controlling access to review, or a much wider community using open proofs and inexpensive checking tools. The amount of output alone will not tell us which arrangement we are building.
OpenAI has committed conference support and funding through the Simons Foundation. That is welcome. Sustained understanding will also require people whose careers can advance through explanation and correction, and institutions willing to pay for that work after the announcement has passed. A community that celebrates the novel claim but treats its careful examination as overhead will get more claims than understanding.
The Two Bills
In my own work, I keep coming back to how much time a competent person needs to verify what the machine produces. Cheap output with expensive verification is expensive work wearing a disguise.
Consider an underwriting analysis assembled in minutes. If the reviewer has to reconstruct every calculation, locate every source, and determine which assumptions were invented, the time saving may disappear. If the figures are traceable and the uncertainty is clear, the reviewer can spend more time on the credit judgment. A lending decision cannot be settled like a theorem. Evidence informs a choice for which someone remains responsible.
But a firm has two bills to pay. One is checking today’s work. The other is developing the people who will be able to check tomorrow’s. It is possible to look very efficient while paying only the first, drawing on expertise that someone else spent years helping people acquire.
Junior assignments often did two jobs at once. They produced something the organization needed, and they gave an inexperienced person practice. Automating the assignment may be sensible. Assuming the education will somehow survive its removal is not. The loss may remain hidden until an experienced employee leaves or an unfamiliar case exposes what nobody learned to recognize.
That does not make every old apprenticeship worth preserving. Some were needlessly punishing or kept capable outsiders from getting a chance. AI could give more people access to patient instruction and realistic practice than an overstretched supervisor ever could. A beginner can form an initial view, compare it with an assisted answer, and work through the difference with someone who understands the field. We can preserve the learning without preserving every tedious task or making a customer bear the cost of avoidable mistakes.
My expectation is that organizations will begin to diverge here. A firm that uses AI to deepen its people’s understanding may become capable of handling work it could not attempt before. A firm that uses it to eliminate practice while relying on the judgment of its current experts may discover, years later, that it has been spending an inheritance. Both could report impressive productivity in the meantime.
The test will be what the next generation can do with an unfamiliar problem. Can they recognize when an answer is wrong? Can they explain their reasons and revise them? Those abilities require opportunities to try, make mistakes, and be corrected. Buying a tool does not discharge an employer’s responsibility to provide them.
For a student or someone early in a career, my advice is still to become the person who can read the proof. A summary may be exactly what a task needs. But getting through an argument and possessing its conclusion are different experiences. Sometimes the effort changes what you are capable of noticing next time. AI can help you stay with that difficulty rather than simply removing it.
What We Are Trying to Preserve
There is a limit to the argument that humans will remain valuable because we retain some task machines cannot do. Today we might call that task judgment. We should prepare for machines to become better at many forms of judgment too.
I do not think a person’s worth should depend on winning that contest. Someone does not become worth less because their work can be done more cheaply. Nor should we have to prove that a relationship, an education, or a quiet afternoon produces an economic return before we can regard it as worthwhile. Some of the time these tools save can simply be lived.
That conviction offers no excuse to dismiss displacement. A worker who loses a livelihood needs more than reassurance about human dignity. It gives us a reason to take the loss seriously and to ask what an employer or a community owes the people affected.
Greater intelligence can help us pursue an aim without settling whether the aim deserves pursuit. A machine may help decide how to increase a company’s output. That leaves the company with choices about the people doing the work and the uses of the gain. AI can contribute to those arguments, but capability alone does not confer the authority to decide what everyone else must accept.
This is why understanding matters beyond catching errors. People need enough knowledge, and enough standing, to question the decisions shaping their lives. A technically correct answer can still be used for a purpose they have good reason to reject. We should want the benefits of discovery without treating disagreement about its use as a defect to be optimized away.
I keep returning to Impagliazzo and Paturi. They have agreed to examine a claim that could overturn a conjecture closely associated with their own work. That takes a willingness to be wrong, but it also takes the expertise to find out. A healthy institution makes room for both.
If these results hold up, we will have more reason to believe that machines can help us discover things we did not know how to discover ourselves. I want that possibility. I also want the next generation to inherit the ability to question what it is given and a say in what gets built with it. We can welcome an answer from a machine without handing over the purposes of the people who will live with it.
These are the leadership questions I explore at The Fourth Turning Leader: how to make sound decisions, take responsibility, and lead people through change we’re still learning to understand.