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Only for ChatGPT, if the user hasn’t opted out. Would mathematicians be using ChatGPT for this kind of work? Genuinely asking, I know nothing about this!
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If I am reading your question correctly you are asking about chat interface Vs Codex/Claude code? If so, in my experience Codex/Claude code use is widespread for mathematicians who are seriously using these tools.
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Yes, mathematicians are. And yes, most of my colleagues did not even know the opt-out was an option.
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It isn't relevant whether they were promised that. Indeed I think the assumption must be that they were not promised that, since otherwise the author asking if they were would not make much sense.

If OpenAI did use the conversations from Buckmaster and Alpoge, then not disclosing it, explicitly, is plagiarism. If they planned to use that plagiarism to pressure the authors to publish, that is even more unethical. What the terms of use say does not make it any more or less ethical.

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