I've been thinking about this lately. Do you think geniuses like John von Neumann seriously questioned the information they absorbed? Quotes like pic rel make it seem like what these geniuses have in common is ridiculous memorization skills
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No, it's that you see the proof, you absorb it, but you don't waste time understanding it. You just take the theorem and run with it.
A lot of higher math courses are like this. It's not a trivial thing to prove many things and to fully understand some proofs are entire courses in and of themselves.
Rote memorization has nothing to do with it, when you see a theorem you immediately start thinking of ramifications of the theorem and less so about actually understanding the mechanisms of the theorem. If you think like this, you'll be successful in math.
This tbh - just skim the proof for 'tricks' that might come in handy especially for GPAmaxxing tests.
I used to do this, and it's a very bad way of doing things. You'll fool yourself into thinking you understand things you don't.
If anything your intuition should be so stong that the truth of a theorem should be almost obvious to you.
Nope, it's objectively the best way to learn math. Math makes the most sense as cycles of understanding. You read a math text multiple times at multiple levels.
The first time you read math should be cursory. High level. Then work on a few problems, then come back with a finer comb. Things click much more quickly this way.
There's no fooling understanding, it's just objectively a waste of effort to try and fully understand everything, first time through. It really only works for low level math courses because the subjects are straightforward.
i like where this is going. any thoughts on polya's book "mathematical discovery"? ive always had the sense that if you cant "play", test, and stretch a theorem then you dont really understand it.
or Mathematical Problem Solving - schoenfeld
I think this is more a problem with mathematics, it went completely out of hand. Most of mathematics has no practical use, and probably never will. For example, 3D graphics is possibly the most math heavy field today, and I believe the most obscure math that they use are quaternions. This is doubly sad, as on the other hand there is probably a lot that could be done to speed up various calculations, but mathematicians waste time on arcane topics that nobody will ever use for anything except for generating even more math.
What? No it's not. There's a lot of heavy math all across the applied math fields. DEs, SDEs, control theory, machine learning, optimizations, etc. These all require quite a bit of high level math and understanding some very complex math.
Pick up the average SDE or control theory text and see for yourself. These are very hot fields of math as well, almost every math department has professors focusing into them. These fields have math that didn't even exist 100 years ago. All of them with major applications in science, finance, robotics, etc.
I don't necessarily disagree that many mathematicians waste their efforts on arcane math, but that doesn't mean that the majority of math departments have very applied groups working in them.
>Pick up the average SDE or control theory text and see for yourself.
And I guess we're going to have fully functioning walking robots two years after someone finally decides to throw all this garbage out, exactly like with speech interfaces.
Huh? No one is throwing any of this out. You already use it everyday when you plug your destination into your phone.
It's literally one of the most applied fields in math and enabled landing on the moon with the foundational Kalman Filter problem.
It's not just used in robotics despite the memes. Pretty much any time series or time series like data will apply aspects of control theory to it because it's foundational.
>Kalman Filter p
Not advanced math.
Where is all the progress from this?
You're conflating associative reasoning which is how we integrate and extend abstractions with lo-level rote memorization of atomic facts about the world/systems/bodies of knowledge.
Von Neumann in particular had an insane memory.
>von Neumann
What did he ever do?
he is a israelite so the jidf promotes him incessantly as an authority figure
I don’t think remembering literal things matters as much as instinctually realizing a certain “direction” or “approach” to take.
You don't have to be smart to memorise things. It just takes time. And it doesn't take you being smart to understand things. It just takes time.
It is also a skill. Memorising a few dozen formulas used to be hard for me. Then i had taxonomy, where i had to memorise a few thousand species. Now a few hundred formulas in maths or chemistry is nothing. I really believe it's all just a matter of effort. I'm a fricking idiot, an i graduated summa cum laude. Just work hard.
What did he mean?
>nta
can you homosexuals stop with the redditesque acronym-forming?
nta will not happen. stop trying to make nta happen.
You can question till you're blue in the face, but you are not going to get any further understanding by doing so.