More Questions About Whether Researchers Can Trust OpenAI With Unpublished Math

You've got a proof that isn't finished. Maybe it isn't even written down properly yet — just a notebook full of steps that seem to work. You want to test a lemma, check a counterexample, or get a model to formalize a fragment in Lean. OpenAI's API is right there.

But here's the uncomfortable part: the moment you paste that fragment into a chat window or an API call, you've handed a private company a piece of unpublished mathematics. And unless you've changed a specific setting, you've also given them permission to train on it.

The Core Tip: Opt Out of Data Training Before You Share Anything

Key Takeaway: OpenAI's API uses your inputs for model training by default. You have to opt out manually — it is not the default. Do it before your first API call, not after.

OpenAI's API data usage policies are explicit: data submitted to the API may be used to improve services unless the user opts out. That's the whole problem in one sentence.

The opt-out process itself is short:

1. Sign in to your OpenAI account and go to Settings → Data Controls.
2. Find the toggle for "Improve the model for everyone" (or the equivalent API training consent setting, depending on your plan).
3. Turn it off. Confirm the change.
4. If you're on a Team or Enterprise plan, check whether your organization's admin has already set a data policy — individual settings can be overridden at the org level.
5. Verify. Send a test request, then check your data controls again. Settings have silently reset before.

Why does this matter for mathematicians specifically? If your unpublished lemma ends up in a training corpus, it doesn't come back out. There's no attribution mechanism, no citation, no way to prove the idea was yours. The model just gets a little better at a problem you were planning to publish on.

The Retention Problem Doesn't Go Away

Opting out stops training use. It does not stop retention.

OpenAI retains API data for 30 days for abuse monitoring even when you've opted out. If you haven't opted out and the data is used for training, retention can be indefinite. That's a meaningful difference for anyone working on a result they haven't posted to arXiv yet.

The concern isn't hypothetical. In a 2023 Nature survey, 38% of mathematicians said they would not share unpublished work with AI companies because of fears about idea theft. A separate 2023 Center for Data Innovation survey found 45% of AI researchers had similar worries about private companies' data policies. And a 2024 Pew study reported that 62% of academics think AI companies should be required to get explicit consent before using unpublished research.

There's also the Researcher Access Program. It's generous — OpenAI has handed out over $1 million in API credits since 2022 — but the terms allow OpenAI to use your data and feedback. If your work is sensitive, read that agreement line by line before signing up.

And remember: OpenAI has published on mathematical reasoning (the Lean theorem prover integration, math-focused reasoning work). That's not evidence of theft. It is evidence that your subfield overlaps with their commercial interests.

Other Precautions Worth Taking

Opting out is necessary. It isn't sufficient.

• Post a preprint first. If your idea is on arXiv, you've established priority. A timestamp beats a terms-of-service argument every time.
• Use NDAs for collaborations. If you're working with OpenAI or anyone adjacent to them, get confidentiality in writing. OpenAI has historically required researchers to sign NDAs — turnabout is fair.
• Anonymize or use synthetic examples. Swap in a toy version of your lemma. Test the structure, not the actual result.
• Consider open-source models. Llama, Mistral, and similar models can run locally. Nothing leaves your machine. For unpublished math, that's a real advantage.
• Watch the Azure angle. OpenAI's Microsoft partnership means data may sit on Azure servers, which brings its own data-sovereignty questions for university compliance offices.

FAQ

Can OpenAI use my unpublished mathematical research if I share it with them? Yes, under default settings. API inputs may be used for training unless you opt out. Chat inputs on consumer plans have similar defaults.

What is OpenAI's data retention policy for API inputs? 30 days for abuse monitoring if you've opted out. Indefinite if the data is used for training.

How can researchers protect unpublished math when using OpenAI? Opt out of training, use synthetic or anonymized examples, preprint early, and consider local open-source models for anything genuinely sensitive.

Does the Researcher Access Program require giving up rights to your research? The terms allow OpenAI to use your data and feedback. That's not the same as assigning copyright, but it's broad enough to warrant caution.

Are there alternatives to OpenAI for researchers who need to protect unpublished math? Yes — Llama, Mistral, and other open-weight models run locally with no data leaving your machine.

The Bottom Line

There's no public evidence that OpenAI has lifted unpublished proofs from researchers. But the governance is thin, the retention rules are loose, and the opt-out is buried. That combination is enough to justify caution.

Before your next API call, take two minutes to opt out of data training in your OpenAI account settings. Your unpublished proofs will thank you.