71–80 of 92 posts
I think, with modern tools, you need math intuition more than computational skills. That's why my site is all about interactive experience. There are no proofs or problems but a lot of things to tweak and drag.
So if you're looking for intuition, you're looking for deep familiarity which means spending the time/effort it takes to get familiar.
Resources don't help much as they're almost always about someone else's "intuition". Struggle that leads into false turns and force you to backtrack help a lot more I think.
An example - some time ago, I told some colleagues that they've been dealing with convolution even before middle school .. which surprised them. Multiplying numbers is the same operation as convolving their digit sequences. But if you didn't fool around enough with multiplication, or try to relate it to algebra, polynomials, and such, this can be hard to see.
Edit:typo fixed
I feel you need to rethink your goal. it's like you're trying to finding missing chapters from an undefined book. Try to be around problems that requires a high degree of math skills to solve. let the problems drive you. intuition is usually built by spending hundreds of hours thinking, eating, and drinking the problems you're truly interested in to arrive to a solution. If you spend enough time doing this, you'll kn…
As a mathematician, I say: what you lack is not math intuition, but math knowledge. Read really hard math textbooks and solve exercises. This is the only way known to me to get better at math.
I think category theory will give you an unique point of view of math, also basic logic and philosophy are very important for a good and solid foundation on math intuition.
https://arxiv.org/abs/1803.05316 along with their youtube lectures.
very basic but refreshing:
https://www.youtube.com/playlist?list=PL8dPuuaLjXtNgK6MZucdY...
if you are a programmer or developer:
https://bartoszmilewski.com/2014/10/28/category-theory-for-p... https://blog.ploeh.dk/2017/10/04/from-design-patterns-to-cat...
Related question, anyone know any good resources for learning and developing intuition in Abstract Algebra? Especially ones that explain it well, like Calculus Made Easy did for Calculus. AA is a prereq for cryptography, category theory and and other areas of interest for CompSci. I asked this a few weeks ago but at an off peak time and not many folks saw the question. But I know HN probably has good recommendations…
Take a look at "A Book of Abstract Algebra" by Charles Pinter. It's published by Dover, so very affordable. I've seen it criticized as too verbose, but that worked for me.
I feel you need to rethink your goal. it's like you're trying to finding missing chapters from an undefined book. Try to be around problems that requires a high degree of math skills to solve. let the problems drive you. intuition is usually built by spending hundreds of hours thinking, eating, and drinking the problems you're truly interested in to arrive to a solution. If you spend enough time doing this, you'll kn…
There's a loophole. You read about people like Gauss who had insights long before they became math students. There's something to dig there.
If something is to dig here is that the earlier you start the better you will be.
I feel you need to rethink your goal. it's like you're trying to finding missing chapters from an undefined book. Try to be around problems that requires a high degree of math skills to solve. let the problems drive you. intuition is usually built by spending hundreds of hours thinking, eating, and drinking the problems you're truly interested in to arrive to a solution. If you spend enough time doing this, you'll kn…
There's a loophole. You read about people like Gauss who had insights long before they became math students. There's something to dig there.
I guess the loophole here is simply being born with talent :P