The Bottleneck Has Two Ends
Terence Tao says that's the same crisis we found in enterprise research — almost.
Direction and digestion aren't one job. They're the two ends of it.
On May 20, 2026, an internal OpenAI model refuted the unit-distance conjecture — an 80-year-old open problem in combinatorial geometry posed by Paul Erdős in 1946. The proof cost about $2,000 in tokens. It connected the geometry problem to algebraic number theory, identified an infinite family of point constructions, and got the math right.
It also forgot to mention where the idea came from. Mathematicians noticed the paper never cited the closely related prior work of Ellenberg-Venkatesh, Golod-Shafarevich, and Hajir-Maire-Ramakrishna — three lines of research the AI's own argument depended on. To fix that, three human mathematicians — Melanie Matchett Wood, Noga Alon, and Will Sawin — spent the following weeks writing a companion paper: a "short, digested, human-verified" version that put the machine's idea back into its actual intellectual history.
That gap — a machine that can generate a valid, publishable result and still fail completely at situating it — is close to the exact center of the argument Terence Tao made two months later, in the biggest keynote of his career.
The Same Crisis, a Different Discipline
On July 24, 2026, Tao delivered "Mathematics in the Age of AI" at the International Congress of Mathematicians, an address he later expanded into an essay for the ICM Proceedings. His claim: mathematics is entering its first "crisis in foundations" since Russell's paradox and Gödel's incompleteness theorems, a century ago. But where that earlier crisis was about logical validity — what counts as a proof — Tao says this one is about values and practices: what the discipline should actually be optimizing for, now that AI has made one part of the job nearly free.
Tao breaks the work of mathematics into stages — generation, verification, and what he calls digestion: the labor of explaining a result, getting the community to accept it, and eventually folding it into the standard, teachable body of the field. Generation and verification, he argues, are becoming abundant. Digestion is not. And he invokes Goodhart's Law to explain why that's dangerous rather than merely inconvenient: once a measurable proxy — a solved problem, a published paper — becomes cheap to optimize, AI will optimize it relentlessly, at the expense of everything that used to travel alongside it for free.
If that sounds familiar, it should. It's the same shape as the argument in our own research on Minimum Viable Thesis (MVT): AI has automated most of the mechanical work of research, and the scarce thing left is human judgment about what matters. So we ran Tao's keynote through the same process we ran our own thesis through — two AI models, cast as opposites, set loose to find out whether "digestion" and "direction" are actually the same discovery, arrived at twice, or just two people reaching for a similar metaphor. They didn't agree. The disagreement is the interesting part.
Same Pipeline, or Two Different Pipelines?
The first model's case was direct: Tao's pipeline never names who chooses which theorem is worth proving in the first place. Generation, verification, exposition, peer review, canonicalization — all five stages assume a problem has already been selected. That's exactly what MVT found in enterprise research: three of four functions automated, with problem selection as the one holdout, still entirely human.
The second model pushed back, and its correction is the sharper piece of work here. Tao's digestion, it pointed out, happens after a result already exists — it's downstream integration, deciding what a finished output means and whether it deserves to last. MVT's direction happens before anything starts — it's upstream selection, deciding what's worth attempting in the first place. Those aren't the same operation wearing two names. They're opposite ends of the same pipeline.
That correction survives. Tao's own pipeline is the evidence for it: at no point does he insert "pick a worthwhile problem" as a stage, because in pure mathematics the discipline has a century-deep backlog of pre-selected open problems to draw from. The crisis he's describing starts downstream of that choice, not because problem selection doesn't matter, but because mathematics rarely runs out of problems worth pointing an AI at.
So "digestion equals direction" doesn't hold as a literal identity. What holds is broader and, honestly, more useful: both are instances of a function you could call objective governance — the human work of deciding what's worth optimizing for, and what's worth trusting once the optimization is done. AI is hollowing out the legible, measurable middle of every knowledge pipeline faster than it's replacing either end.
The Leiden Declaration makes that split explicit rather than just implicit in what it protects. Published June 2, 2026, and endorsed by the International Mathematical Union with Tao among its signatories, the declaration doesn't just defend peer review and attribution — it names the mathematical community's ability to "articulate new and significant research questions" and shape its own research direction as a core value under threat, separately from its concerns about unreliable results and improper citation. Mathematics is organizing to protect both ends of the pipeline at once, which is a strange thing to do if there were really only one scarce function left.
The Correction That Matters Most
Here's where the second model earned its keep. Tao's essay treats the coming pile-up — proofs generated and verified faster than they can be explained, reviewed, and canonicalized — largely as an active, present danger. But in the lecture itself, at the point where he catalogs the forms this "indigestion" could take, Tao says the specific scenario of a backlog of published AI proofs waiting on textbook canonicalization "isn't happening yet." It's an extrapolation, not a measurement.
That's a meaningful qualifier, and not a small one. There is real, present-tense evidence that generation is outrunning digestion in specific cases — the Erdős refutation is one, and mathematicians already report a backlog of AI-assisted proofs on the Erdős Problems site that no human has yet vouched for. But there is no discoverable field-wide dataset showing mathematics as a whole — submission rates, referee delay, canonicalization lag — has actually crossed into crisis. Tao identified the mechanism before anyone measured the macro effect. That's the exact caution our own research applied to METR's task-horizon numbers: don't turn an accelerating, real, local signal into a claim about the whole system until someone's actually measured the system.
Which Domains Actually Prove the Law
The strongest test of whether "objective governance" is a real, general law rather than a coincidence of two arguments is to look for a case where it should apply and doesn't.
Chess is that case. Engines have generated and evaluated more chess analysis than any human could absorb for over two decades, with no comparable "digestion crisis" — no backlog of unread engine lines demanding peer review, no institutional declaration protecting human judgment about which openings matter. The reason is structural: almost all of that machine output is query-driven. It answers one local question — what should I play right now — and then it's discarded. Nobody treats a chess engine's twentieth-best line as a permanent claim on the collective attention of the chess community. That's the missing variable. Abundance alone doesn't create a digestion crisis. Abundance creates a crisis only when the institution surrounding it treats the output as a persistent candidate for scarce human belief — a result that has to be checked, attributed, taught, and remembered. Mathematics does that. Enterprise research usually does too. Chess mostly doesn't.
And the reverse case is just as informative: digestion crises don't require AI at all. Biomedical research had already blown past its own reviewers' capacity by 2010 — an estimated 75 randomized trials and 11 systematic reviews were being published every single day, most of them never making it into a synthesis anyone could act on. AI didn't cause that. It's the same failure mode arriving decades early, for the same underlying reason: production scaled and the human attention layer around it didn't.
Where the Crisis Is Actually Measured
If you want to see this pattern with real numbers instead of an anticipated one, don't look at mathematics. Look at software engineering, where the identical structure is already fully quantified. GitClear's analysis of over two thousand developer-weeks found that regular AI users produced roughly 320% more code. LinearB's benchmarking found the predictable consequence: pull requests containing AI-assisted code waited two and a half times longer for human review than ordinary code — and five times longer where an AI agent wrote the code with no developer involved at all. Refactoring, the unglamorous work of actually digesting and improving existing code, dropped from a quarter of all changes to under a tenth over the same period, while duplicated, unreviewed code rose past it.
Mathematics gave this crisis its name. Software engineering already has the receipts.
The Sentence Worth Publishing
"Digestion and direction are the same last human function" doesn't survive the evidence. What survives, and matters more: AI first cheapens the legible, optimizable middle of a pipeline — the part with a clean measure of success. Scarcity migrates to both ends of what's left. Upstream, it shows up as direction: deciding what's worth attempting. Downstream, it shows up as digestion: deciding what's worth believing, once a machine says it's done. They're not the same job. They're the two boundaries holding the shape of every knowledge pipeline AI is currently hollowing out from the middle.
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}The complete reconciled package — thesis, longform, four-beat carousel, bundle, and social thread — as one self-contained file.
An AI model refuted an 80-year-old math conjecture in May for about $2,000 in tokens. It got the math right. It forgot to cite the three papers its own proof was built on.
Three human mathematicians then spent weeks writing a companion paper just to explain where the AI's idea actually came from.
We'd already found this pattern in enterprise AI research — the machine gets faster at answering, the scarce thing becomes deciding what's worth asking and what's worth believing. So when Terence Tao, the most famous living mathematician, gave a keynote arguing math is entering the same crisis, we ran his argument through the same two-AI-models-fighting process we used on our own thesis.
One model said: same pattern, confirmed. Tao's pipeline for mathematical research never names who picks the theorem worth proving — exactly like our research found. The other model pushed back hard: that's not the same function at all. Tao's "digestion" happens after a result exists. Our "direction" happens before anything starts. They're not identical.
They're right, and it makes the piece better, not worse. Direction and digestion are two ends of the same shrinking middle — upstream, deciding what's worth optimizing for; downstream, deciding what's worth trusting once a machine says it's done. AI is hollowing out that middle faster than it's replacing either end.
The clearest proof isn't even in math. It's in your own pull requests: AI-written code ships 320% faster and waits 5.3 times longer for a human to actually review it.
Full reconciled research — contextjamming.com.