Re:When Math Gets Impossibly Hard
by m3kw9 on Wednesday September 16, 2020 @03:12PM
(#24496288)
Math is hard for me because once a step of a proof is lost on me, the whole thing is lost unless I branch out into a rabbit hole, and learn what just happened
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That's part of what makes it such a rich subject. Even something as simple as writing y=sin(x) has so much more embedded into it than the "input x output y" notion of functions. Parametrization of the Unit Circle, right triangles, special angles, you name it. Diving into the rabbit hole enough to convince yourself the step is justified is part of the learning process, if you're engaging with it properly. You do need to be judicious sometimes with what you decide is important to dive further into. That comes with the context/goals and experience of the reader.
ok, but all of those rabbit holes have bottoms. It just may be that the space in between represents a year or more of learning.
They don't have bottoms, because at the bottom you have logical assumptions like e.g. classical logic. These only exist because of history, only because it was the easiest way for someone to say something "insightful". Going down the rabbit hole, you have to choose some arbitrary point to stop at; it would be a point at which you think that you can apply the knowledge you have gained so far, in a way that other people will "appreciate".
Or you can just not stop, and try to go even deeper. But then you stop being a mathematician, and you turn into a madman, a philosopher or a theologist.
The "rabbit hole" being discussed is just "understanding a step in an argument", not, providing a foundation for logic.
It's not impossible to gain understanding of a step in someone else's argument.
I agree. Not everyone thinks or solves problems in the same ways, and math notation has historically favored only one type of cognition. More visual approaches using touch screens or spatial / tactile ones using AR would be cool to see.
There may also exist types of math that are impossible to represent or reason about with current notation.
If you are interested in mathematical notations, check out Terry Tao's comment [0][1] on desirable properties of math notations. It was discussed not long ago [2].
[0] https://en.wikipedia.org/wiki/Terence_Tao
[1] https://mathoverflow.net/questions/366070/what-are-the-benef...