
This is your brain on mathematics - greydius
https://anthonybonato.com/2016/04/20/this-is-your-brain-on-mathematics/
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jordigh
A pet peeve of mine is when mathematics itself is described as a language,
instead of distinguishing mathematics from mathematical language. It's like
saying Neuromancer is just a language, that Neuromancer is just English.

There is content in mathematics that is independent of the language used to
express it. Mathematical notation is also incidental. It is not mathematics
itself.

~~~
goldenkey
It might be incidental but the history of mathematics is rich with dissent and
conflicting methodologies and syntaxes. Just even the initial mathematical
symbols that started to be used were quite the ambitious effort by Peano. [1]
That reading will take you down the wormhole of efforts for a "universal
language" between mathematicians based on latin. And then you'll end up
reading about 20 different other takes on the ideas. No, it's not just
incidental -- there were international congresses of mathematicians about
these issues and the adopted solutions were mostly elegant and looked upon
favorably. There are always going to be some dissenters though, and they have
some validity - but well, conventions are usually a compromise between
effectiveness and majority opinion. There is still huge rift in mathematics on
the issue of constructive proofs vs intuitionistic proofs. There are a lot of
camps in formal mathematics. Kinda like functional programmers and the
constant "tripes" they'll knack on. Whimsical stuff :-)

[1]
[https://en.wikipedia.org/wiki/Giuseppe_Peano](https://en.wikipedia.org/wiki/Giuseppe_Peano)

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lumberjack
This will probably sound wacky but here's what I think:

There are two steps to conveying a thought in a language:

1\. recall the grammar rules and vocabulary 2\. form the sentence

The steps are fundamentally different in that the first one is an exercise in
recollection whereas the second one is a "creative" process of some sort.

To prove a mathematical fact you go through the same two steps:

1\. you recall all the past mathematical knowledge 2\. you deduce the fact in
a creative process of meshing together the facts you just recalled

So conveying a thought in a language is sort of analogous to proving a
mathematical fact.

But clearly when doing math step 2 is given the spotlight whereas when you are
talking in a foreign language step 1 is by far the hardest.

~~~
senthil_rajasek
just out of curiosity, how many human languages do you speak fluently?

~~~
raddad
English, Canadian, Australian and American English.

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kusmi
Doesn't surprise me. I spent my youth thinking math was impenetrable, and only
when I started programming later in life I realized that mathematicians
shouldn't be naming things.

~~~
goldenkey
Mathematics is a lot more rigorous than programming. But considering I'm
learning Group and Ring Theory with the 1999 textbook 'Learning Abstract
Algebra with Mathematica [Library]' I don't exactly disagree. Working with
abstract structures in a more concrete way is a crystal-shattering way to
intuit them -- I don't know if it will be an ultimate downfall though yet. As
a programmer it just seemed natural to me to be able to manipulate these
structures as if they are instances of an abstraction -- of a type. If it
peels out for me, I will have a unique perspective among mathematicians. I
just see a large sect between those who appreciate the abstractions, and those
who bastardize them for utility. I didn't have love and enigmatic affinity for
mathematics until I realized that even up to Calc II, the number-crunching
utilitarian bastardization of mathematics was conveyed and taught to me -- not
the beauty or philosophy of mathematical approach and thinking. Unfortunately,
when only results and empirical justifications fill a programmers' mind, the
beauty is lost. I feel there is definitely a more mastered perspective by
being both a programmer and an inspired mathematician that is lost by being in
exclusively one camp or the other. Until education reform is had, this unique
perspective will just be for those who incidentally stroll down the path.

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gohrt
Without even looking I guarantee that the Periodic Table of Finite Simple
Groups is garbage --- there's no way that the space of finite simple groups
have the same structure as the space of atoms.

~~~
goldenkey
A little silly to speak with such overconfidence considering the only
similarity is the "table" paradigm. The actual periodic table is poor for its
use anyways, and there have been valid criticisms that call for a more
abstract grouping, like a spiral/ring table [1] [2] But in any case, the
properties of numbers are intrinsic to the relationship between space and time
- the ability to store a number physically [in memory] and then act on it at a
later time. You can try to claim that physics transcends mathematics -- but I
would argue that the properties of numbers, and hence algebras, are more
fundamental than even physical field theories are.

[1]
[http://www.chemistryland.com/CHM130W/03-BuildingBlocks/Chaos...](http://www.chemistryland.com/CHM130W/03-BuildingBlocks/Chaos/SpiralTable.jpg)
[2]
[https://upload.wikimedia.org/wikipedia/commons/6/6b/The_Ring...](https://upload.wikimedia.org/wikipedia/commons/6/6b/The_Ring_of_Periodic_Elements.svg)

