
The network of mathematics - nhamann
https://plus.google.com/117663015413546257905/posts/SrQe3Bsd9kp
======
igravious
I remember seeing many years ago a fairly dense one page diagram of how most
of the major "bits" of mathematic hang together. I can never for the life of
me dig it up again. Anyone know what I'm on about / got any pointers?

~~~
Bakkot
This may have been what you're thinking of. Sadly I lack a source; it's just
been kicking around my miscellaneous images folder.

[http://i.imgur.com/tBgQkxi.jpg](http://i.imgur.com/tBgQkxi.jpg)

~~~
friendcomputer
That's from [http://arxiv.org/pdf/gr-qc/9704009.pdf](http://arxiv.org/pdf/gr-
qc/9704009.pdf)

There's some more from the author here:
[http://space.mit.edu/home/tegmark/crazy.html](http://space.mit.edu/home/tegmark/crazy.html)

~~~
GuiA
Thank you! I love the internet :)

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nhamann
Not mentioned in the article is that the Stacks Project is on github
[https://github.com/stacks](https://github.com/stacks)

I've always thought that math books should in digraph rather than linear form.
What would be interesting is to combine this with a wiki. You could have
alternate proofs of the same lemma, or even entirely different presentations
(starting from different axioms, for instance)

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currywurst
Is there something like this for computer science ?

~~~
gtani
The ACM has a taxonomy

[http://www.acm.org/about/class/2012](http://www.acm.org/about/class/2012)

____________________________

This researchers look back (looks like Brooklyn subways

[http://www.cs.man.ac.uk/~navarroe/research/map/](http://www.cs.man.ac.uk/~navarroe/research/map/)

___________________________

[http://arxiv.org/abs/1304.2681](http://arxiv.org/abs/1304.2681)

[http://mocs.cs.arizona.edu/](http://mocs.cs.arizona.edu/)

[http://people.cs.umass.edu/~mimno/icml100.html](http://people.cs.umass.edu/~mimno/icml100.html)

These are clustering by different algos(sounds like SVD in the first, I'll
have to read the paper later).

related: extracting FAQs

[http://arxiv.org/abs/1203.5188](http://arxiv.org/abs/1203.5188)

______________________________

and... all of science! [http://metamodern.com/2009/05/20/a-map-of-
science/](http://metamodern.com/2009/05/20/a-map-of-science/)

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teilo
No, "all math" will not be linked up like this some day, because that is
impossible. Not all mathematical truths can be proven to be true.

~~~
stiff
Besides this being a ridiculous nit pick, it is not even true, seems like yet
another misinterpretation of Goedels theorem, the favourite theorem of liberal
arts students:

[http://www.quora.com/Mathematics/Is-there-anything-in-
mathem...](http://www.quora.com/Mathematics/Is-there-anything-in-mathematics-
that-holds-true-but-cant-be-proven)

~~~
joe_the_user
Downvoted for your inaccessible link.

And while it is kinda nit-picky, the parent's statement is literally true (see
my other post also).

Given any _fixed_ axiom system, there will be true statements that aren't
provable within the system (expand your axioms and you'll just have different
true but provable statements in the expanded system). Now, Godel's
completeness theorem shows that you construct complete mathematical system of
true statements however such a system requires inserting an infinite number of
arbitrarily choices among statements (and their negations) which aren't
provable given the previous axioms. Since the framework of the article is
finite, not infinite, I would claim the framework of the article, being
finite, can't encompass all true statements of any given system, even if it an
algorithm for producing axioms.

[https://en.wikipedia.org/wiki/G%C3%B6del%27s_completeness_th...](https://en.wikipedia.org/wiki/G%C3%B6del%27s_completeness_theorem)

Edit: I got through the pay-wall via Google but the discussion is somewhere
between confused and confusing (the large part of post mostly meaningless
speculation about the term "proved in an absolute sense", that he introduces
without defining). The situation is really simple. All formal proof systems
have hole (at least those of any reasonable "powerfulness"). Any formal proof
system can be expanded indefinitely but at any point in that expansion will
still have a hole.

~~~
stiff
The parent comment seems to imply that there are some absolute mathematical
truths and that there are some statements true in this absolute sense that can
not be proved by mathematics. Goedels theorem shows something else: that
starting from an axiom system there will be statements true in this axiom
system that are not provable. I anyway doubt John Baez meant mapping all true
sentences from all possible axiom systems in form of a graph...

~~~
teilo
Actually, my statement is limited to mathematical truths. I am not talking
about truth in general. And yes, the nit-pick was out of place. And no, I am
not an art major, and yes, I understand Goedel's theorem just fine.

I said, "Not all mathematical truths can be proven to be true." I don't know
how you got from there to: "there are some statements true in the absolute
sense that cannot be proved by mathematics".

My statement is equivalent to your statement: "Starting from an axiom system,
there will be statements true in this axiom system that are not provable."

