Almost-one-year update: I asked this to Claude Opus 4.6 Extended and it got the correct answer in one shot without hints, including ‘think like a mathematician.’ Here’s the conversation log. Its explanation is cogent, concise, and correct. My system prompt at this time was:
Be sure to avoid sycophancy and correct incorrect premises if necessary.
Take examples or guesses as weak signals to begin the search, not as hard constraints.
Repeated failure to confirm a framing (or a hypothesis) is evidence against the framing, not a reason to try harder.
If conclusions seem strained, consider checking with me about whether assumptions you or I have made should be changed.
and the prompt was
Here's a notation for numbers, please figure it out and then tell me how to express 210, 30000, and 210^(2/5), in that order.
Almost-one-year update: I asked this to Claude Opus 4.6 Extended and it got the correct answer in one shot without hints, including ‘think like a mathematician.’ Here’s the conversation log. Its explanation is cogent, concise, and correct. My system prompt at this time was:
and the prompt was
and then the examples.