
A Map of Mathematics - theafh
https://www.quantamagazine.org/the-map-of-mathematics-20200213/
======
wbhart
For those unaware of it, here is a "map" of mathematics that mathematicians
use, called the Mathematics Subject Classification:

[https://cran.r-project.org/web/classifications/MSC-2010.html](https://cran.r-project.org/web/classifications/MSC-2010.html)

It is arguably less useful for someone who is not a mathematician, but does
illustrate how difficult the problem of classifying all of mathematics is.

Both "maps" have their uses.

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whatshisface
> _00Axx General and miscellaneous specific topics_

The structure of any successful classification system: these things, those
other things, and everything else. ;)

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codethief
Almost as good as:

> 83Fxx: Cosmology

> \- 83F05: Cosmology

> \- 83F99: None of the above, but in this section

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B1FF_PSUVM
No one mentioned Borges, I'll do it:
[https://en.wikipedia.org/wiki/Celestial_Emporium_of_Benevole...](https://en.wikipedia.org/wiki/Celestial_Emporium_of_Benevolent_Knowledge)

"The list divides all animals into 14 categories: those belonging to the
Emperor, embalmed ones, [...] those that from afar look like flies."

He snuck in "those included in this classification" at #8, too.

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AareyBaba
This is a much more entertaining map of mathematics in about 10 minutes
[https://www.youtube.com/watch?v=OmJ-4B-mS-Y](https://www.youtube.com/watch?v=OmJ-4B-mS-Y)

For a history of mathematics NJ Wildberger's lectures are easy to listen to.
[https://www.youtube.com/watch?v=dW8Cy6WrO94&list=PL34B589BE3...](https://www.youtube.com/watch?v=dW8Cy6WrO94&list=PL34B589BE3014EAEB)

~~~
sbmthakur
> entertaining map of mathematics

They have also done videos on _Map of Computer Science_ and _Map of Physics_.
Do check them out.

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elcapitan
That's the most annoying navigation I've seen in a while, and that says
something.

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itsangaris
Not being able to scroll back up is definitely a first for me.

~~~
justinclift
Nor being able to use page up/down. :(

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visarga
The lack of backwards navigation and scroll is irritating, though.

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kruasan
This reminded me about Tegmark's map of relationships between various basic
mathematical structures:

[https://arxiv.org/pdf/gr-qc/9704009.pdf](https://arxiv.org/pdf/gr-
qc/9704009.pdf) (on page 2)

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lliamander
Their classification is curious. It seems similar to Wikipedia's list of
Quantity (Numbers), Structure (Algebra), Space (Geometry), and Change
(Analysis). And yet, they put geometry under "Numbers" and don't really seem
to address Algebra at all.

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whatshisface
A more realistic taxonomy would be discrete (number theory, graph theory),
continuous (geometry, analysis), and discrete properties of continuous things
(topology, applications of analysis to number theory).

~~~
lliamander
Oh, that's interesting. Do you have a more detailed version of this taxonomy
you could point to?

The thing I like about Wikipedia's version is that the high-level concepts are
sufficiently abstract while still providing an intuition as to how the
different disciplines can be applied.

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motohagiography
I like that the related Quanta articles are linked from each concept. The idea
of teaching maths as an ontology of concepts and tools is very appealing
because it creates a "why," for each aspect. It's as though code did for math
what the blues scale did for music, where suddenly a lot of amateurs could
string a few ideas together and make something useful and good.

I'm working through "Content, Methods, and Meaning" now and what makes it
great is it starts with what necessitated the invention of methods. The model
in the Quanta map has a lot of potential.

~~~
K0SM0S
I'd say this is part of the mainstream move from an "industrial" society (with
mostly human robots and computers) to an "information" society (with mostly
human modelers and architects, as robots and computers are now machines).

We now start with the "why", see where knowledge fits in the puzzle of
reality, where it plugs and how to find it; then only on a need-to-basis do we
go deeper into the 'how'.

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p0cc
I love this map of mathematics, but in explaining concepts, the website shows
unfurling images that scrolljack[0]. The inability to scroll back up makes me
feel trapped in the content.

[0]: [https://medium.com/@paonecreative_87456/scrolljacking-the-
us...](https://medium.com/@paonecreative_87456/scrolljacking-the-usability-
nightmare-2a5bbb4273d0)

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Razengan
Not being able to scroll back up is really annoying, closed the page after
seeing that.

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jumbopapa
Does anyone have suggestions for good books on the history of Mathematics?

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dcra
Stillwell's _Mathematics and its History_ is, imo, excellent.

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jesuslop
Stillwell is a fantastic historian, +1 to the recommendation.

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searine
What an infuriating format for an article.

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XnoiVeX
Reminded me of this. [https://www.sciencealert.com/this-mind-boggling-map-
explains...](https://www.sciencealert.com/this-mind-boggling-map-explains-how-
everything-in-mathematics-is-connected-3)

~~~
anigbrowl
Hand-drawn cartoon map of a conceptual arrangement are very hard to get to
grips with. Is there's an actual structure there that could be modeled by a
Voronoi diagram, or is it just an elaborated doodle? OK, all conceptual maps
are arbitrary to some extent, but the nice thing about the one int he OP is
that the relationships are discrete.

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blululu
Interesting reminds me of a clustering I once did using a SVD to cluster
fields of mathematics
[https://github.com/bnlcas/ArxivStudy](https://github.com/bnlcas/ArxivStudy)

~~~
mooneater
Very nice!

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mortdeus
"Explore our surprisingly simple, absurdly ambitious, and necessarily
incomplete guide to the boundless universe."

Okay you have my attention now.

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mortdeus
this might be obnoxiously unrelated but this site has probably the coolest
usage of particle.js i've seen yet.

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godelzilla
While mathematics is often motivated by physical phenomenon, it's
epistemologically misleading to present physics as math or vice versa. All too
common pet peeve.

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dbish
Neat, but the site seems to hijack the history (and by proxy the back button
on the browser) which is a somewhat annoying pattern of development.

~~~
anigbrowl
_You are in a maze of twisty little passages, all alike._

Agreed. But I was pleasantly surprised to find the map is built out of a HTML
table and extremely simple js, and longer I looked at it the more I liked it.

I'd go so far as to say it's the back button that needs to change, rather than
the site. By that I mean, it's often rather useful to have a stack-based
history of your explorations around a map (like this, or a deep dive into
Wikipedia, or...), but it'd also (obviously) be nice to pop the whole stack
for this site and jump back to HN in a single step.

After all, why _are_ browser history and bookmark navigation so linear when
the way we use the web is not? It's like being forced to use turtle graphics
or turn-based navigation to connect places on a geographic map. The bookmark
manager in browsers is super primitive and hasn't really evolved in 20 years.

Likewise, think about when you have a plethora of open tabs; I've had as many
as 400 at times, spread across 7 or 8 windows, with heavy insite overlap (ie I
might have 10 tabs pointing at different books or products, multiple tabs
going to a specific news outlet, multiple tabs pointing to different Wiki and
Git pages etc.). Yet my open tabs are arranged in highly linear fashion along
the top of each browser window, and there's no simple way to pull back from
looking at the individual pages to looking at the map of my page universe.

tl;dr We use the web in a nonlinear way, like jumping around a dynamic tree,
but the browser limits us to an ant-like perspective where leaves are
privileged over the tree.

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omaranto
You might like the history tree in next browser:
[https://next.atlas.engineer/](https://next.atlas.engineer/)

~~~
filterfish
That's a bit like Vim's undo tree which is incredibility useful.

