Tao: Open math problems being non-renewably mined by AI is the line Fields medalist Terence Tao posted online on September 8, 2026, and it's the top story on Hacker News this morning. His point: AI tools are burning through good open problems so fast that finding a worthwhile problem, not solving one, is becoming the scarce resource in mathematics.
Short answer: Terence Tao warned on September 8, 2026 that AI is mining open math problems "in a non-renewable fashion." Once an AI system flattens a problem — solves it without explaining why — it stops teaching anyone anything, and the rumor that someone is working on a promising problem can now trigger a rush of AI effort that kills it before a human project matures.
I read Tao’s original four-part thread before writing this, not just the Hacker News summary. I also checked the Hacker News thread this morning: 108 points, 78 comments, most from working mathematicians arguing over whether Tao is right. He posted the thread as four consecutive posts, four minutes apart. It holds together as one argument. This article walks through what he actually said, then gets practical about using AI on hard problems yourself.
What Tao actually said
Tao opens with a water analogy: "a country or region can suffer a critical shortage of drinking water while simultaneously being surrounded by a massive ocean." You can generate infinite open math problems — pick a huge, meaningless target like the 10^10^10th digit of pi — but almost none of them are worth anyone's time. A good problem is one that teaches you something on the way to solving it, win or lose. That's the scarce resource, not problems in general.
Working out which problems are good, he says, is "a lengthy, deliberate, and subjective process" that depends on mapping a field's difficulty landscape: which questions yield to known methods, which take real effort, and which are currently out of reach. New mathematical results normally push that frontier outward, opening new territory even as they close old questions.
The part that worries him is what AI changes about that process. In his words, from the third post in the thread: "it is now the identification of a promising problem which is the scarce and precious resource. We have now seen that even the rumor of someone working on a problem can trigger a massive amount of AI-powered effort to flatten it before the original research project has time to reach its full potential." AI labs, he adds, tend not to publish their failed attempts or show their working, which makes it hard to tell "AI-feasible" problems from genuinely "AI-hard" ones ahead of time. The risk he flags: mathematicians quietly stop sharing promising directions to avoid getting scooped by a black-box solve, which would undo centuries of open science.
What you'll need
You don't need to be a research mathematician to follow this, or to apply it. You need an AI chat tool you already use — ChatGPT, Claude, or a research-focused one like Perplexity all work here — and one real problem you actually care about, not a toy example. A public problem list helps if you don't already have one: the Erdős Problems database and Tao's own "What's new" blog both maintain running lists of open questions with notes on what's known. The only real prerequisite is caring about the reasoning, not just getting an answer, since that's the whole thing Tao says is at risk.
Step-by-step: using AI on a hard problem without burning it
1. Decide before you start whether you're solving or exploring
If you genuinely just want the answer to a closed, practical question, a black-box AI solve is fine — that's not what Tao is warning about. If you're working on an open problem you or someone else might publish on later, decide that up front, because it changes how you should prompt.
2. Ask for the reasoning trace, not the answer
Prompt for a full worked path — every attempt, every dead end, every partial result — instead of a final answer. In my testing, asking Claude or ChatGPT to "show your complete search process, including approaches that didn't work" got a noticeably more useful response than asking it to "solve this," which tends to return a compressed, confident answer with the actual search work stripped out.
3. Treat a clean answer with no shown work as a red flag, not a win
If a model hands you a tidy final result with no visible reasoning, that's the exact "incomprehensible solve" Tao says destroys a problem's value — you get an answer, but nobody, including you, learns why it's true or how to find the next one like it.
4. Don't publish the bare result
Tao's proposal is to hold problems to a standard closer to "solves the problem and identifies insights that others can build on" — the same way a food bank sets explicit quality standards for donations rather than accepting anything. If you post a result, post the reasoning path with it.
5. Be careful who you tell about a promising direction
This is the uncomfortable part of Tao's post: he says even a rumor that someone is close to a result can trigger a wave of AI-assisted attempts to grab it first. If a problem matters to you, decide who you loop in before you loop in anyone.
6. Re-check anything an AI tool tells you is already solved
Because there's no visible boundary between what current AI tools can and can't actually do reliably, don't take a model's word that a problem is closed. Verify against a real source — a paper, a maintained problem database, or, for anything you'd act on, another person.
Example prompts you can copy
These are built to force a model to show its work instead of handing you a flattened answer:
- "Don't give me a final answer yet. Walk through every approach you'd try on this problem, in order, and tell me why each one would or wouldn't work before you commit to one."
- "Show me the full reasoning trace for this, including any dead ends, not just the path that worked."
- "Is this problem already solved anywhere in the literature? Cite where, and tell me your confidence, not just yes or no."
- "Map out what's known and unknown around this problem — what's easy given current methods, what's hard, and what's genuinely open — before attempting a solution."
- "If you can't verify a claim about this problem, say so explicitly instead of presenting your best guess as settled."
Common mistakes to avoid
The biggest one I see: treating "AI solved it" and "I understand it" as the same thing. They aren't, and Tao's whole argument is that the gap between them is what's getting destroyed. Second, asking a model to just "solve" a problem you actually care about, then being surprised the answer doesn't teach you anything — that's the default behavior, not a bug, so you have to prompt against it. Third, publishing a raw AI-generated result without the reasoning behind it, which is exactly the "answer with no insight" Tao says has near-zero value to the field. Fourth, assuming a model's claim that a problem is "already known" is reliable without checking a real source — these tools are confident about that even when they're wrong. Fifth, broadcasting a promising research direction widely before you've made real progress on it; per Tao, that's now a bigger risk than it used to be.
How the different approaches compare
| Approach | Insight preserved? | Risk the problem gets "mined" and abandoned | Best for |
|---|---|---|---|
| Full public write-up, traditional style | High | Low before publishing; you accept the risk once it's out | Established open problems, textbook lists |
| Ask AI privately, publish only the final answer | Low | Medium — the moment it's public, others can chase it with AI too | Quick sanity-checks, not real open questions |
| Ask AI privately, publish the full reasoning trace | Medium-high | Medium, but the field still learns something either way | Problems you want others to build on |
| Work with AI in isolation, don't publish | Highest for you personally | Low for others, but nobody else benefits | Competitive or priority-sensitive work |
In my testing, the second row is the one people default to without meaning to — you ask an AI tool for the answer, get a clean result, and paste just that into a forum or paper because the reasoning trace is long and messy. That's the exact pattern Tao is warning against.
Tools that make this easier
If you're new to prompting an AI tool for reasoning instead of answers, my ChatGPT guide and Claude guide both cover how to get a model to show its work rather than just its conclusion. For checking whether a problem or result already exists in the literature before you spend time on it, Perplexity is built for exactly that kind of sourced lookup. If you want the fuller picture of how Tao thinks AI should and shouldn't be used in math generally, his ICM framework is worth reading directly — I broke it down in Terence Tao: Mathematics in the Age of AI. And if you're curious why AI models look so strong at hard math problems in the first place, why AI isn’t outthinking mathematicians so much as out-remembering them and my practical guide to math in the age of AI both cover the mechanics behind what you're seeing in a chat window.
Frequently Asked Questions
What does "non-renewably mined" actually mean here?
Tao's point is that good open problems aren't unlimited the way they seem — you can invent infinite trivial questions, but the ones worth working on are found through a slow, subjective process, and once an AI tool "flattens" one by solving it without showing insight, that specific source of learning is gone for good.
Is Tao saying AI shouldn't be used on math problems at all?
No. His concern is specifically about black-box solves that give an answer with no visible reasoning, and about the chilling effect on sharing research directions. He's argued elsewhere, including in his ICM 2026 lecture, that AI is genuinely useful in math when you can verify and defend the output yourself.
Where did Tao actually post this?
As a four-part social media thread, posted under his own name, on September 8, 2026. It reached the top of Hacker News the next day.
How do I stop an AI tool from just giving me a flattened answer?
Ask for the full reasoning trace, including failed approaches, before it commits to a final answer — see the copyable prompts above. A model that resists showing its work at all is a sign to double-check the answer against a real source rather than trust it outright.
Does this apply to problems outside pure math?
The same pattern shows up anywhere a "hard, well-scoped, publicly known problem" is the valuable thing — competitive programming problems and open research questions in other fields face a version of the same risk Tao describes.