
In Search of Proofs from “The Book” - digital55
https://www.quantamagazine.org/gunter-ziegler-and-martin-aigner-seek-gods-perfect-math-proofs-20180319/
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tacomonstrous
As a working mathematician, I'm uncomfortable with this apotheosis of 'the
proof'. While there's always room for aesthetics, this might support the
rather misleading premise that mathematics is about digging up chiseled
beauties, when it is really about hours, days and months of flailing around,
trying to understand one thing, or even what it means to understand that
thing. And it's rarely pretty.

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ggm
I think Davis and Hersh say this. Ruben Hersh "what is mathematics really"
felt like it was opening the door to the sausage factory.

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yantrams
Brilliant book that. The way he explains how a polished rigorous proof hides
the process(compared with frontend and kitchen views of a restaurant) by which
a mathematician has arrived at it changed my perception of how mathematics is
done.

I notice the same phenomena in programming too. The final piece of code that
works doesn't reflect all the failed attempts at solving a problem. This is
why I tend to not delete/clear cells at all from my jupyter notebooks. :) It
is always informative/fun to refer to them at a later point in time to relive
that problem solving experience.

PS: In case you haven't, you should try Proofs and Refutations by Lakatos.

Edit: Fixed name of the book mentioned and added some text.

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ggm
Do you mean "proof and refutations" ?

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yantrams
Ah yes, thanks for correcting me :)

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wolfkill
As a mathematician and a believer in God, I get uncomfortable when people
start attributing math to God. I see math as being very much a construct of
the human psyche and as astounding as it is, there are enormous gaps between
mathematical models and physical observations. So in my mind math is to
reality as human is to Divine.

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User23
It logically follows that any faith that believes God to be a unitary creator
is going to attribute math to Him.

Your absolutely correct observation about gaps notwithstanding, the driving
question for me here is this: why does math work so well? I personally exclude
any explanation that doesn't involve the Logos in some form as incoherent, but
I don't have a specific answer and probably never will.

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Retra
Math works so well because we consistently abandon any math that doesn't work
well.

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hyperpallium
And where the math of reality seems ugly or awkward or contrived, we invent
notation to make it look neat and simple.

The reason why math education takes so many years is to learn all the
complexity, conventions and abuse of notation. As in speech and image
interpretation, the adept cannot see the complexity.

You can make anything simple by inventing a language to state it in. Use
custom entities instead of multiplying them.

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mgamache
I have a feeling they really mean Spinoza's God (like Einstein), but this use
of 'God' causes confusion for a lot of readers. Some readers might think they
are referring to the God of the Bible or Koran.

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beojan
Spinoza's God couldn't have a book of anything.

Then again, the Abrahamic God (being omniscient) wouldn't need a book either,
but would simply _know_ the perfect proof (and every imperfect proof) for
every theorem.

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Koshkin
Well, God _is_ the word (i.e. the proof).

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extr
> It’s a powerful feeling. I remember these moments of beauty and excitement.
> And there’s a very powerful type of happiness that comes from it.

I always try to explain to people this is the reason I love math so much.
There is no feeling like getting to the bottom of something and it makes sense
in such a perfect way, you can hardly believe the universe works like that. I
am no believer but I think it's the closest I can feel to God.

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ythn
> I am no believer but I think it's the closest I can feel to God.

It's a shared sentiment:

"Mathematics is the language with which God wrote the universe." \-- Galileo

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dang
This fine article was flagged; I'm betting because of the word "God" in the
title. That word has triggering effects independently of what it is used to
refer to.

To assuage the sensitive, we've degodded the title and replaced it with the
usual Erdős reference.

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montrose
This is an interesting point:

"To do these short and surprising proofs, you need a lot of confidence. And
one way to get the confidence is if you know the thing is true. If you know
that something is true because so-and-so proved it, then you might also dare
to say, "What would be the really nice and short and elegant way to establish
this?" So, I think, in that sense, the ugly proofs have their role."

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yantrams
This book is a must have for anyone who loves Mathematics or problem solving
in general. You'll find many celebrated problems attacked using concepts from
seemingly disparate domains.

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combatentropy
Paul Graham explored why different fields --- like math, art, and engineering
--- all use the word "beautiful,"
[http://www.paulgraham.com/taste.html](http://www.paulgraham.com/taste.html)

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johnsonjo
The book talked about in the article is on Springer Link. Luckily my
University is subscribed to Springer Link, so I just had to login to my
University's VPN and I was able to download this book for free; score!

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tromp
> The sixth edition will be the final one.

And so will the seventh.

