I thought mine was when claude found a very subtle but important bug in some open source LBM code I was using. It ground at it for hours and didn't give up until it found it. (Back when claude was cheap!). I recently had a my ACTUAL moment at a conference where the presenter was pitching his book about "One shotting scientific code". He has cooked up 60+ prompts that get you functioning simulations and put them into a book [0]. It floored me to realize I could have just ask claude to write me a whole new LBM solver instead of finding that bug! That raised the bar for me a lot.

[0] https://www.taylorfrancis.com/books/mono/10.1201/97810037340...