
The Aesthetic Beauty of Math - prostoalex
https://www.theparisreview.org/blog/2019/07/22/the-aesthetic-beauty-of-math/
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romwell
I've always been telling people: mathematics is art, just with a smaller
audience.

After all, beauty is the only criterion for a work of pure mathematics. People
might use other words, such as _elegant_ and _interesting_ , and also, quite
often, _surprising_ to highlight different aspects of that beauty. And quite
often, a math paper works in the way a mystery novel does (modern math papers,
for silly reasons, are often written backwards and give away the name of the
murdered on the first page -- and yet still work in the same way).

In the end, a mathematician would go in a certain direction because it is
_interesting_ , and the results will be appreciated if they are _beautiful_.

The article mentions _equations_ , but quite often, equations are only there
out of necessity. The ideas, often better expressed with diagrams, examples,
and conversations might still _need_ some algebra to be pinned down, but often
enough, they are considered "ugly" and shoved under the rug. The
mathematicians' word for this ugliness is _technical_ ; during the talks,
they'll say somethings likes this:

>And so the limiting distribution of the number of sides in a single cell in a
tesselation given by a geodesic curve on a hyperbolic manifold is given by a
Poisson process. The proof is _quite technical_ , so I'll skip it...

Which translates to the following:

>Here are two ideas that come from different worlds. It turns out that they
are the same in this setting: like two lines in a poem that rhyme. The beauty
of the poem is readily seen, but the rhyme is difficult to spell out with the
alphabet of proofs and equations - so I will not do it.

~~~
recursive
> beauty is the only criterion for a work of pure mathematics

I'm no mathematician, but I think correctness and consistency must factor in
somewhere.

~~~
j7ake
The beauty implicitly assumes the math is correct and consistent, but
expresses something much deeper.

Analogous to how music adheres to certain rules and structures (these rules
and structures are allowed to vary across genres).

Another analogy is how a “beautiful play” in basketball should adhere to the
rules of the game. For example, a beautiful dunk during a game implies that
the player wasn’t travelling or carrying the ball.

My third analogy would be a “beautiful move” in chess. It’s implied you
followed the chess rules to make that move otherwise it wouldn’t be beautiful.

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melling
Anyone recommend the essay mentioned in the article?

[https://en.m.wikipedia.org/wiki/A_Mathematician's_Apology](https://en.m.wikipedia.org/wiki/A_Mathematician's_Apology)

[https://archive.org/details/hardy_annotated/page/n1](https://archive.org/details/hardy_annotated/page/n1)

~~~
romwell
I'd recommend starting with the (much, much) shorter, modern sequel: Paul
Lockhart's "Mathematician's Lament"[1]

It addresses a different side of the question. Namely, why, if mathematics is
about beauty, most people perceive it as an instrument of torture?

(The TL;DR is: the way we teach math _is_ often a nonsencial torture, to the
extent that what we teach _is not math_ ).

[1]Lockhart's Lament:
[https://www.maa.org/external_archive/devlin/LockhartsLament....](https://www.maa.org/external_archive/devlin/LockhartsLament.pdf)

~~~
hackermailman
There's a guy who teaches math that makes sense from the bottom up if anybody
is interested
[https://m.youtube.com/playlist?list=PL5A714C94D40392AB](https://m.youtube.com/playlist?list=PL5A714C94D40392AB)

If you supplement his rational math with those books from AOPS (art of problem
solving curriculum) to practice, it's actually quite easy. Their intro to
number theory book is a good example of exploring the 'beauty' (in quotes so I
don't sound like a cringeworthy pseudophilosopher)

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jejones3141
It's not just mathematicians who see it. Edna St. Vincent Millay saw it.
[https://www.poetryfoundation.org/poems/148566/euclid-
alone-h...](https://www.poetryfoundation.org/poems/148566/euclid-alone-has-
looked-on-beauty-bare)

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agumonkey
I wonder if people did partially abstract geometry before persistent (clay,
wall paint or else) writing happened.

Basically how primitive tribes did think mathematically and did they start by
accounting with pebbles or levers or ..

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dlkf
Was anyone else put off by the tautological title?

~~~
chmaynard
The adjective "Aesthetic" seems unnecessary.

