
The Unplanned Impact of Mathematics - memexy
https://www.nature.com/articles/475166a
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37r7u43urr
As much as we talk about math literacy here (compared to other platforms
anyway), I can't help but feel like the incomprehensibility of high level math
to laymen is a feature. It's not talked about outside of academia often,
because why would it be, but for a long time philosophy resisted efforts to
'mathmatecize' (my own word) the field because of concern that it would become
inscrutible to outsiders. As a result, academic philosophy is much more
politically polarized than math. Where would we be if every step forward in
mathematics was met with backlash for not paying adequate concern to some
arbitrary set of external implications? Anyone can disagree of course but just
looking at the political affiliation ratios of educators makes it clear that
one aspect of the hard sciences historically has been an ability to stay
focused on utility despite post-modernism. I'm probably being unfair though,
the humanities continue to produce persuasive arguments (persuasive emphasis
being one of the first things most lit and speech majors learn during critical
thinking and writing courses in college) they've just dropped the pretense of
being truth seeking persuits.

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joe_the_user
I might see it this way because I've been studying math for a long time
(though not professionally most of it) but I don't think modern math is ever
made more complicated or hard to understand just for the heck of it. That's
because math is already felt as extremely hard for most people.

I think anyone in professional math is working really hard to make the field
more comprehensible to themselves and so to the world - and the reason for
this is the more a mathematician understands and more compactly they can
understand it, the further they can go.

And certainly, the way a mathematician put things curtly makes it harder for
the laymen, I think the biggest harm to the layman's understanding of math is
a math education that gets people conditioned to not think abstractly and
think of math as a series of dull exercises.

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j7ake
I agree. If some mathematicians purposeful obfuscated or made more complicated
than necessary certain topics, it would create an arbitrage opportunity for
others to clarify and simplify the topic.

There are definitely tangible rewards for those who can clarify and simplify a
topic, because it can lead to discoveries and insights.

This gradual clarification of a topic hinges on the actual importance of the
topic. If a topic is not important, I can see people getting away with
obfuscating or complicating results.

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bonoboTP
Respectable, pro mathematicians don't obfuscate. But there are definitely math
professors in non-top universities who get kicks out of torturing students and
think "this is supposed to be _hard_ " etc. I'm definitely a math enthusiast
but I _have_ personally met people like that. Typically the exams are under
strong time pressure and are more about rote learning of fixed types of
exercises and remembering definitions.

On the other hand, I had math profs who radiated curiosity and fun and the
exams were just a few questions, but you had to think to solve them and you
weren't under much time pressure.

So while mathematicians aren't purposefully obscure, the math people
(teachers) the average person interacts with are sometimes purposefully
obscure.

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mathgenius
Working in theoretical physics (quantum computing) I think about this a lot:
the unreasonable effectiveness of mathematics. I see two ways of understanding
this. (1) That mathematicians are in the game of building powerful tools, and
therefore these tools inherently capture a wide range of phenomena. (2) When
confronted with a difficult problem we become the drunk person looking for
their keys under the street light, even if we know the keys are elsewhere. In
this case, the street light is whatever good calculations we have at hand, ie.
mathematics.

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augustt
A nice example is that Gauss realized in 1805 that Fourier transforms could be
made less tedious by subdividing the problem (n=12=3*4 in his case), 160 years
before Cooley-Tukey.

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memexy
Yes, but Gauss was also a perfectionist and he didn't publish anything that
weren't up to his standards. He even discovered non-euclidean geometry at some
point but didn't think it was worth publishing so Bolyai's son János (and also
Lobachevsky) had to re-discover it

> Bolyai’s son János was also a mathematician. In 1832, János published his
> brilliant discovery of non-Euclidean geometry. His father, overjoyed that
> his son might have achieved something worthy of praise from Gauss, the man
> he admired more than any other, asked Gauss for his view of the work.

There was a bit of a feud and I don't know if it was ever properly settled

> Whether Gauss actually fleshed-out non-Euclidean geometry as comprehensively
> as Bolyai and Lobachevsky is uncertain.

\--

[https://www.famousscientists.org/gauss-and-non-euclidean-
geo...](https://www.famousscientists.org/gauss-and-non-euclidean-geometry/)

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HeOfLittleBrain
As I said the first time this topic was posted:

This article is ironic coming from such a math phobic publication as Nature:

[http://www.dam.brown.edu/people/mumford/blog/2014/Grothendie...](http://www.dam.brown.edu/people/mumford/blog/2014/Grothendieck.html)

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memexy
Why is it ironic and why are they math phobic?

