Dan PiponiDec 2

It's a blessing and a curse.

I don't feel I understand some mathematics until I think I could have invented it myself and I often work hard to reach that stage. Well that's an illusion so I should qualify it a lot - I need to feel like if I was suitably "primed" I could have invented it. There's no way I could have explicitly invented monads, say, without lots of clues from all the papers I tried to read.

I feel like a good textbook or paper should lead you to a point where you can see what the main "trick" is going to be just before the big reveal. It allows you to develop pattern recognition for the type of problem.

But it does mean I waste a lot of time on stuff people may think is trivial. Machine learning papers are full of derivations like "log(A) = log(A/B) + log(B), now apply Jensen's equality" where B has magically appeared out of a hat. I can easily follow the argument but unless I know why this B was chosen I haven't learnt a reusable skill.

Show threadShae Erisson
@dpiponi I'm feeling that as I slowly learn group theory with much help from @mjd
We gave up on two(?) documents before Mark found one with much better motivation and fewer of the surprises you describe.
Dec 2 at 8:12pmWeb
Show threadDan PiponiDec 2

@shapr @mjd Yeah. I think proofs can play many roles. Sometimes they're pedagogical. But sometimes they're just slick because slick proofs are an art form. And sometimes you want a proof that is just a proof, ie. something to make you confident it's true.

Good luck with the Group Theory. I struggled with that for a while as an undergrad. Then one day I woke up and realised that conjugation, ie. forming a*b*inverse(a), was a technique I'd used for many years with Rubik's cube. A lot came together after that.