
What is it like to understand advanced mathematics? - vinchuco
https://www.quora.com/What-is-it-like-to-understand-advanced-mathematics-Does-it-feel-analogous-to-having-mastery-of-another-language-like-in-programming-or-linguistics/answers/873950?share=1
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jzl
There are many wonderful passages in the book "Genius" by James Gleick that
describe Richard Feynman's deep intuitive understanding of calculus. He also
talks about it a bit in his own works such as Surely You're Joking Mr.
Feynman. Highly recommend if you want to see lots of interesting answers to
this question. His key approach was that he always wanted to understand things
based on "first principles". So he would usually take on a new mathematical
frameworks by breaking them down and re-deriving them on his own from scratch.

Reminds me of how Ben Franklin taught himself to write by reading famous
passages and then attempting to write them from memory, comparing his version
to the original version afterward and seeing what he did differently and why.

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paultopia
Interestingly, this reads like the experience of expert knowledge in almost
anything.

Like, I have expert knowledge in law, and I'm working toward at least more
advanced (though far far from expert) knowledge in coding-things, and it very
nicely matches how I interact with legal problems and can dimly see glimmers
off at the end of a long tunnel in coding problems.

But at the same time, it's inspiring as all hell, because mathematics from the
outside doesn't seem like the kind of thing that could ever produce the same
satisfying and effective experiences of cognition.

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swayvil
It's like being really good at a video game that only you and maybe 2 other
guys play.

You talk about the dungeons, monsters, level-bosses, etc but nobody can
relate.

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nopinsight
I somehow feel like this is written by Terence Tao, based on the quality,
style, and length that are similar to what's on his blog. Anyone else shares
the feeling or has a different guess?

Edit: In a later part, the answer says "Terence Tao is very eloquent about
this here: ..." so likely not (based on factors like typical personality of a
mathematician, but I could be wrong since I don't know him personally).

~~~
vinchuco
[https://en.wikipedia.org/wiki/Stylometry](https://en.wikipedia.org/wiki/Stylometry)

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moocowtruck
to understand advanced mathematics, is to start reading books on philosophy

~~~
KGIII
Pretty much.

Mathematics is a language. Most people only learn arithmetic, and then only by
rote. Sometimes, it is disheartening. I've had people who refused to accept
that Ph.D. is Doctor of Philosophy.

I like to point out that nobody has successfully brought me a bucket of
negative apples.

Err... I'm a mathematician. I am an applied mathematician. I am not smart
enough to be a philosopher of mathematics, though I have my Ph.D.

Anyhow, math is a language that is capable of telling stories, truths, and
even falsehoods.

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dgut
That PhD means "Doctor of Philosophy" is just an artifact of the fact that all
doctoral degrees were once subcategories of "Philosophy".

Philosophy today is pretty useless.

~~~
pmoriarty
_" Philosophy today is pretty useless."_

Studying philosophy teaches you how to think. If you consider that useless...

~~~
webnrrd2k
If philosophy (and only philosophy) teaches people how to think, then who
taught the first philosopher?

~~~
pmoriarty
No one claimed only philosophy taught people how to think.

