Comment by creatonez
11 hours ago
> It looks like OP's most recent post was deleted
Apologies, I had figured out what distinction you were getting at right after writing my reply, so didn't feel the need to keep my misunderstanding up. But thanks for the detailed explanation!
Edit: Actually, I'm confused again. To be clear, it sounded to me from the discussion in the Joe McCann video that there was no tweaking the answer to get the question, i.e. that doing anything other than verification in reverse would have been against their ethic, that the answer must truly follow the question for it not to be cheating. The integral is fixed in place, and then legitimately solved by a highly competent Reshetnikov who is good at this, afforded plenty of time by scheming in advanced (as opposed to the illusion of only taking 3 hours), but is too lazy to formalize their work or is interested to see a 'clean' solution unbiased by their own approach to the problem or by the software that aided their work. And then it's verified trivially using differentiation (something symbolic math software almost never fails at), as opposed to my original misunderstanding that there still would have been uncertainty. Right?
The video in question [0]
No, although he was certainly an integral enthusiast, the video does not claim that he was solving them from scratch. Rather, it says he was starting from integrals with known answers and tweaking them slightly to see if he could break the CAS. At that point, although he did apparently try to solve the resulting problems himself, he already knew roughly what the answer would look like (by comparing to the previous answer, and also to the previous solution path.)
Specifically step 5 in my previous post is more work than it sounds, he was doing some calculations by hand, but it's like he's starting 90% of the way there and trying to do the last 10% by hand to fool the CAS. And remember, he can try as many variants of the tweak+10% as he wants until he finds something that works.
[0] https://www.youtube.com/watch?v=7gQ9DnSYsXg&t=14s
I guess I'm over-selling by implying it's a solution from scratch. Thanks to the nearby integrals that the software is able to serve up results for instantly, the tool is what lets you quickly explore until you run into something that will support a slight modification, as well as still be beautiful even after the modification. And of course, selection of the interesting questions is perfectly permissible in the ethic they were going for. Thinking about it like this, I could probably do the trick myself... time to refresh on my rusty calculus.
Yeah! It sounds like a pretty interesting and rewarding design process, but very much searching for a variant of a known problem that works, as opposed to somehow finding a crazy expression from nowhere that also happens to have a beautiful, simple integral, and then solving it without help although even the computers can't.