/sci/ - Science & Math » Thread #12279850

9KiB, 240x240, Angery.jpg

View Same Google iqdb SauceNAO

Intuition

Anonymous Tue 27 Oct 20:11:26 2020 No.12279850 View Reply Original Report

Quoted By: >>12280058 >>12280066 >>12280133 >>12280181 >>12280242 >>12281063 >>12281363

Do we ever develop mathematical intuition or do we just store lemmas in the back of our heads that pop up time to time to help us make sense of what we're reading?

Anonymous

Anonymous Tue 27 Oct 2020 21:28:27 No.12280058 Report

Quoted By:

>>12279850
bump

Anonymous

Anonymous Tue 27 Oct 2020 21:30:27 No.12280066 Report

Quoted By:

>>12279850
The nature of a Heyoka Empath
https://videos.utahgunexchange.com/watch/the-nature-of-a-heyoka-empath_NVoSurjYpVvk8Nh.html

Anonymous

Anonymous Tue 27 Oct 2020 21:55:02 No.12280133 Report

Quoted By: >>12280188

>>12279850
I'd say that's a form of intuition. As Von Neumann once said, 'in mathematics you don't understand things, you get used to them'.

Anonymous

Anonymous Tue 27 Oct 2020 22:11:22 No.12280181 Report

Quoted By:

>>12279850
I don't think one stores any lemma - so what you think of by storing lemma is probably shortcuts and intuition to reconstruct the lemmas

Anonymous

Anonymous Tue 27 Oct 2020 22:13:07 No.12280188 Report

Quoted By:

>>12280133
So it's not intuition but a sort of mental callus

Anonymous

Anonymous Tue 27 Oct 2020 22:28:32 No.12280242 Report

Quoted By: >>12281063

>>12279850
Both.
A lot of theorems have a central idea that hold the entire proof together. Intuition is just acquiring a sense for what that central idea is probably gonna look like.
But there are lemmas and theorems that you just don't forget. Low-level examples are stuff like the fundamental theorem of arithmetic or Euler's formula.

Anonymous

Anonymous Wed 28 Oct 2020 02:29:38 No.12281063 Report

Quoted By:

>>12279850
I agree with >>12280242. Currently taking a cryptography course, and a lot of problems have a "trick" to them. For example, given a function $f(a, b)$ , construct two inputs $a_1, a_2$ so that for all $b$ , $f(a_1, b) = f(a_2, b)$ .

I know this is possible by the pigeonhole principle, because the domain of $f$ is smaller than its range. But that doesn't help me solve the problem. I have to think pretty hard about $f$ , do a bit of trial-and-error, and sort of fail my way to an answer. That has almost nothing to do with what I know, but intuition helps a lot.

Anonymous

Anonymous Wed 28 Oct 2020 05:00:24 No.12281363 Report

Quoted By:

>>12279850
The answer to this question in any field is obviously "both". Even physical/athletic fields. Some people will do more of one or the other, and the way you learn the field may affect it, but it's of course going to be both, especially once you've participated in the field for years.

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches