Perspective
The Bottleneck Moved — And Most Businesses Haven't Noticed
The world's most famous mathematician just described a shift happening at the frontier of research. The same shift is happening in your business, and it changes what you should be worried about.
On 24 July 2026, at the International Congress of Mathematicians in Philadelphia, Terence Tao gave a talk called "Mathematics in the Age of AI."
Tao is a Fields Medallist and, by most accounts, the greatest living mathematician. When he speaks about the direction of his field, the field listens.
He described an experiment called First Proof. Four AI systems were tested against ten novel research-level mathematics problems — genuinely new problems, under controlled conditions, in May 2026. Seven of the ten were solved at publication-level quality by at least one of the systems. Expert referees checked the results for correctness and for how well they were explained. The compute cost ranged from about ten to a thousand US dollars per problem.
Then Tao said the thing that matters, and it wasn't "look what AI can do."
He said mathematics is moving from an era of proof scarcity to an era of proof abundance.
For centuries, the hard part of mathematics was producing a proof. That was the bottleneck — the scarce thing, the reason a single result could make a career. Tao's argument is that this is ending. Proofs are becoming abundant. And when the scarce thing stops being scarce, the hard part moves somewhere else.
In his framing, it moves to what comes after: verifying that a proof is actually correct, explaining it so others can use it, publishing it, and eventually settling it into the body of knowledge that gets taught. AI is strong at the first stage and improving at the second. The rest still needs people.
The bottleneck moved. It didn't disappear.
Why a township business owner should care about any of this
Because the same shift has already happened to you, and almost nobody has said it out loud.
Think about what it used to take to get a booking system into a small business. You needed a developer. A developer cost more than the business made in a month, sometimes more than it made in a quarter. So you didn't get one. Not because you didn't want one, and not because you didn't understand what it would do — because the thing was scarce and it was priced for businesses much larger than yours.
Same for a proper website. Same for a costing model built by someone who actually knew how to build one. Same for a customer database. Same for a designed brand.
All of it was scarce. All of it was expensive. And the constraint on your business was straightforward: you could not get these things built.
That constraint is gone.
Not "getting easier." Gone. A working booking system can now be built in an afternoon by the person who will use it, with no code, for a fraction of what it cost two years ago. Building has become abundant, in exactly the way Tao says proofs have become abundant.
So what's the hard part now?
Here is where the parallel gets useful, and slightly uncomfortable.
When Tao says proofs will be abundant, he isn't celebrating. Most of his talk is about the problem this creates. If AI can generate more proofs than mathematicians can check, then the scarce thing becomes verification and judgement — knowing which results matter, whether they're actually right, and what to do with them.
Abundance doesn't remove the hard problem. It relocates it.
For your business, the hard problem has relocated in exactly the same way. It is no longer can this be built. It is:
Which one should you build first?
Because you can now build all of it, and you still only have so many hours. A business owner who builds a beautiful website while their real leak is enquiries going unanswered for six hours has built something abundant and solved nothing. The website works. The business doesn't improve. Effort was spent, and the actual constraint is untouched.
This is the failure we see most often. Not businesses that can't build. Businesses that build the wrong thing well, then conclude that the technology doesn't work for businesses like theirs. It's the same reason we're careful about what AI agents can and can't actually do today.
Cheap doesn't mean free
There's a second thing worth taking from Tao's talk, and it's the part most coverage skipped.
He didn't say AI has solved mathematics. He said it's strong at one stage, improving at another, and that the remaining stages need people. The judgement didn't get automated. The responsibility didn't move.
The same holds here. AI will build you a pricing model in twenty minutes. It cannot tell you whether the number is one your customers will actually pay, or whether the supplier you're costing against is about to raise prices, or whether the neighbour undercutting you is running at a loss and won't last the year.
That knowledge is yours. It always was. The tools have become abundant; your judgement hasn't, and it's now the scarcer half of the pair. That's the argument we make at length in AI plus kasi wisdom.
What this actually means for the next six months
If you take one thing from a Fields Medallist's assessment of his own field, take this:
Stop asking whether you can build it. Start asking what to build first.
The answer is rarely the thing that feels most urgent, and it's rarely the thing that would look most impressive. It's almost always the thing quietly costing you the most money right now — which, for most businesses, is not the absence of a website. It's enquiries that go unanswered, money owed that never gets chased, and prices set by feel rather than by cost.
Those are unglamorous. They're also where the money is.
The one question worth answering
Tao's whole argument rests on a shift in what's scarce. In mathematics, generating proofs was scarce and became abundant. In small business, building systems was scarce and became abundant.
In both cases, what became scarce instead is knowing which of the many things you could now do is the one that matters.
That's the entire reason our Business Diagnostic exists. Not to tell you AI can help — you already suspect that. To tell you, specifically, for your business, which three systems to build and in what order. Because in a world where you can build almost anything, building in the wrong order is the expensive mistake.
Find out what kind of business you're running — free, 4 min →
Frequently asked questions
What was Terence Tao's talk actually about?
Delivered at the International Congress of Mathematicians on 24 July 2026, it argued that AI is shifting mathematics from a period where proofs were scarce to one where they are abundant — and that this creates new problems around verifying, explaining and making sense of results, rather than solving all problems at once.
Does this mean AI can now run a business on its own?
No, and Tao's own framing is a useful check on that idea. He described AI as strong at generating results and improving at checking them, with later stages still requiring people. The same pattern applies in business: tools can build systems quickly, but deciding what to build, and whether the output is right for your market, remains yours.
If building is now cheap, why do I need training at all?
Because the constraint moved. When building was expensive, the skill worth having was access to someone who could build. Now that building is cheap, the skill worth having is knowing what to build first — which is a judgement about your specific business, not a technical skill.
Sources: Terence Tao, "Mathematics in the Age of AI," International Congress of Mathematicians, Philadelphia, 24 July 2026; First Proof benchmark results, May 2026.