Interesting Bill Thurston quote, sadly from his obituary:
I’ve always taken a “lazy” attitude toward calculations. I’ve often ended up spending an inordinate amount of time trying to figure out an easy way to see something, preferably to see it in my head without having to write down a long chain of reasoning. I became convinced early on that it can make a huge difference to find ways to take a step-by-step proof or description and find a way to parallelize it, to see it all together all at once—but it often takes a lot of struggle to be able to do that. I think it’s much more common for people to approach long case-by-case and step-by-step proofs and computations as tedious but necessary work, rather than something to figure out a way to avoid. By now, I’ve found lots of “big picture” ways to look at the things I understand, so it’s not as hard.
To prevent mis-interpretation, I think people often look at quotes like this (I’ve seen similar ones about Feynman) and think “ah yes, see anyone can do it”. But IME the thing he’s describing is much harder to achieve than the “case-by-case”/”step-by-step” stuff.
Interesting Bill Thurston quote, sadly from his obituary:
To prevent mis-interpretation, I think people often look at quotes like this (I’ve seen similar ones about Feynman) and think “ah yes, see anyone can do it”. But IME the thing he’s describing is much harder to achieve than the “case-by-case”/”step-by-step” stuff.