Self Delusion

After I (think I) solved an interesting problem that I found online, say on a forum, I usually go back to that forum to see other people´s solutions. To check if I ´forgot´ some ideas and could´ve solved the problem differently, or how people jot down their solutions if they had similar ideas, etc. What I find remarkable, but maybe that´s my bad, is that it often happens that I have to conclude that my solution is just wrong. Although my ideas almost always coincide with (some of) the ´right´ ideas, I just don’t seem to be able to make things rigorous (although I think I did) or I made some stupid mistake in a standard calculation or so. Apparently I’m extremely sloppy on the details. And that would not be that big of a problem if I would realise that and would be able to fix it by thinking very hard about every step I take in a proof to make sure I didn’t make any mistakes. But the catch is, I think I do just that. But I guess that, when I have an idea that could work, I start to obsess with that idea so much, that I stop being objective and start thinking I’m right about anything related to that idea. And this is bad. Really bad.

On a different, but maybe not totally unrelated note, I love to work with actual numbers. So with, say, 1233 (which btw equals $12^2 + 33^2$), instead of a’s, b’s or x’s. Although I think it’s not directly a problem if I, for example, first calculate some values of a function to see how fast it grows, the more general issue of only being able to solve a problem unless it’s really specific and not thinking about generalizations unless they’re obvious, might be a problem.

But then I realised that Ramanujan was like this too.