Terence Tao's Coin Game: AI Did Four Things, Humans Did Four Things — I Checked My Own Division of Labor Against His

Contents

1. What this is about
2. The coin game
3. Then, who did which step
4. The line between the two lists
5. Holding a solution, hunting for its problem
6. One thing to take with you
7. Sources

He who learns alone, without friends, remains narrow and ill-informed.
— Book of Rites, “Record on Learning” (Warring States to Western Han period)

What this is about

Last week I wrote about Terence Tao calling AI mathematicians “slightly drunk geniuses” whose scores come with numerators but no denominators. This week the same series (AI 101 channel, uploaded 2026-08-26, about 14 minutes) dropped another episode. No metaphors this time — one real case, a coin game, with every step named: which ones humans did, which ones AI did.

The coin game

Alice splits a big pile of coins into n stacks, heights up to her. Bob takes away some stacks — but the ones he picks must run strictly upward or strictly downward in height, never zigzag. Bob picks the combination that gets him the most; Alice arranges heights to lose the least. The question: what entry fee should Alice charge Bob to make it fair?

Someone on a forum ran the small cases and made a lovely conjecture: when the number of stacks is a perfect square k², Bob can take 1/k of the total. With 16 stacks, a quarter. The conjecture sat unproven for two months.

Then, who did which step

Someone fed the conjecture to an automated prover called Aristotle — and it worked, producing a proof and translating it into Lean, a language that lets a machine check a proof line by line. Its trick: convert the coin problem into packing small squares into a big square. The video notes the move comes from an obscure 1959 paper, and the problem itself had been solved by other means in 2016 — few remembered.

When the stacks grew too many to compute, Tao switched to AlphaEvolve, ran it up to 16 piles, stared at the patterns, and made a conjecture of his own. Boris simplified it; Lawrence Wu recognized the simplified function as identical to one from a “square packing” problem solved two years earlier. The pieces snapped together.

Tao compresses the episode into two lists. AI did four things: searched literature, filled proof steps, computed tables, translated into Lean. Humans did four things: posed the problem, made the conjecture, understood the proof, noticed two problems were the same one. His words: AI by themselves are already great, but there’s far more potential in human-AI collaboration.

And the denominators I complained about last week — this episode provides some: of the 1,000-odd Erdős problems tracked, 699 remain unsolved and about 480 are solved, a large share dug out of old literature where they’d been solved decades ago and forgotten; Aristotle’s automated proving succeeds only about 1–2% of the time.

The line between the two lists

AI’s four tasks share one trait: verification can be handed to a machine. Literature checks against the source, Lean verifies line by line, tables can be recomputed, a bad translation won’t compile — garbage gets caught on the spot. The human four are the opposite: whether a problem is good, a conjecture beautiful, a proof truly understood, two problems one — the output is judgment itself, and no machine can grade it.

That’s the same line I use when delegating to AI. Fetching data, converting files, batch rewrites — handed over without worry, because a script can check the result. Whether to buy a stock, whether an article’s conclusion holds — work whose output is the conclusion itself I don’t outsource, because nothing can check it for me. Mathematicians have Lean as referee, so they can let AI charge ahead and flail; those of us making investment judgments don’t, so we keep AI outside the judgment room. The difference isn’t how smart the AI is — it’s whether your field has a referee a machine can be.

Holding a solution, hunting for its problem

One more detail keeps growing on me. Aristotle’s move ran in the reversed order: not holding a problem and hunting for a solution, but holding an old 1959 solution and finding the new problem it fits. I have a drawer of such old solutions myself — the technical indicators I’ve collected over the years. I used to ask, “can this indicator pick winning stocks?”, and the answer kept disappointing. Now the stocks are chosen by other means, and I walk around holding the indicators, looking for the problems they actually fit — timing entries, trimming drawdowns. The indicators didn’t change; they finally met the right problem.

One thing to take with you

The evening I finished the video I did one small thing, and you could try it today: write on a sticky note the last three tasks you were about to hand to AI, and ask of each — when this is done, can a machine or script tell me right from wrong? If yes, delegate freely. If no, the output is your judgment; let AI be a staff officer. One of my three failed the question, and I changed it on the spot from “ask AI to write the conclusion” to “ask AI to lay out the materials.”

Sources

• AI 101 channel, “Terence Tao demonstrates how AI solves math: a coin game, and which steps humans and AI each took,” uploaded 2026-08-26: youtu.be/llGxnS34pz8
• Last week’s piece: Numerators Without Denominators: Tao’s Slightly Drunk Genius

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