
The Map of Mathematics [video] - ghosh
http://www.openculture.com/2017/02/the-map-of-mathematics.html
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ivan_ah
I found this to be a nice summary of all the themes. I don't understand why
comments here are so critical—it's a youtube video not a PhD thesis!

Here is my take on a concept map of math topics:
[https://minireference.com/static/tutorials/conceptmap.pdf](https://minireference.com/static/tutorials/conceptmap.pdf)
(covers only high school math + calculus + linear algebra)

~~~
Someone
You have to be critical so that the real good stuff gets the attention it
deserves. This just makes too many glaring errors to justify its claim to be "
_the_ map of mathematics".

I think [http://www.math-atlas.org](http://www.math-atlas.org) was a way
better attempt and hope it will come back.

The last copy I could find on archive,org is
[http://web.archive.org/web/20150616152045/http://www.math-
at...](http://web.archive.org/web/20150616152045/http://www.math-atlas.org/)

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gooseh
... And then someone more familiar with, y'know, mathematics went and made
one:
[http://nada.kth.se/~axelhu/mapthematics.pdf](http://nada.kth.se/~axelhu/mapthematics.pdf)

~~~
pash
I've always like this tree [0] because it shows clearly which subjects are
prerequisite for learning others.

0\.
[http://space.mit.edu/home/tegmark/toe.gif](http://space.mit.edu/home/tegmark/toe.gif)

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0xdada
It's not a tree ;)

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pash
Whoops, you're right. Just a DAG.

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mxfh
A two dimensional projection of the space might imply too much distance
between fields that are otherwise incredibly close; like
vectors/versors/quaternions or combinatorics and with CS and optimization.

Maybe one could do an interactive version where the nodes can move in
different dimensions like historic timeline, field of use, mathematical area.

~~~
rawnlq
On some online learning sites there are interactive knowledge graph mapping
prerequisites such as:

[https://www.khanacademy.org/exercisedashboard](https://www.khanacademy.org/exercisedashboard)

[https://www.expii.com/map/0](https://www.expii.com/map/0)

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Sir_Cmpwn
Related - map of Physics:
[https://www.youtube.com/watch?v=ZihywtixUYo](https://www.youtube.com/watch?v=ZihywtixUYo)

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WhitneyLand
Any chance of an international treaty whereby all parties agree to stop saying
either "maths" or "math"?

No criticism here, I'll agree to either one.

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acchow
"called Godel's Incompleteness theorems, which for most people means that
mathematics does not have a complete and consistent set of axioms. Which means
that it's all kind of made up by us humans"

Uhh... that's not the interpretation of the incompleteness theorems...

See also the Halting Problem

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tempodox
This is a great visualisation. And quite instructive to find myself mostly
operating on the Pure Math side. Maybe that explains the gravitational pull I
feel in the direction of FP and the like.

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panglott
It's a followup to the Map of Physics
[https://www.youtube.com/watch?v=ZihywtixUYo](https://www.youtube.com/watch?v=ZihywtixUYo)

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dorianm
Wikipedia's version:
[http://i.imgur.com/zGcdMVl.png](http://i.imgur.com/zGcdMVl.png)

[https://en.wikipedia.org/wiki/Areas_of_mathematics](https://en.wikipedia.org/wiki/Areas_of_mathematics)

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reikonomusha
I watched the video and it definitely does not paint an accurate picture of
mathematics. Additionally, there's a heap of misinformation (e.g., "fractals
are scale invariant", "group theory is about groups [of things]", "Gödel's
incompleteness theorem leads to a mystery of why math is even useful", all of
which is not true whatsoever).

The most beautiful part of math wasn't explained at all, which is _how the
fields relate_! How do geometry and algebra come together? How about algebra
and topology? How about prime number theory and complex numbers? Many of the
most influential, important, deep, and illuminating theorems of mathematics
are precisely those that make such bridges.

Instead, the video gave extremely high-level mathematical "buzzword soup" with
artificial boundaries and an explanation that seems to be derived after the
fact.

I'm all for educating the masses on the magnificent landscape of higher
mathematics, but I think it's a disservice to do it non-factually.

~~~
carlob
These are the things I found I would have known to be wrong at the end of high
school:

The complex plane doesn't usually have the imaginary on the x axis.

Real numbers are not the only ones that have infinite digits, think 1/3.

e is not called 'the exponential'.

Also, why the hell is probability applied math?

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HiroshiSan
1/3 is a real number, did you mean irrationals?

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reikonomusha
The video described real numbers (beyond rationals, hence irrationals) as ones
with non-terminating decimal expansions.

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fxn
I have not watched the video, but for people reading only comments let me
clarify.

Numbers go naturals < integers < rationals < reals. Reals are the union of
rationals (quotient of integers) with irrationals.

Rationals may have an infinite decimal expansion, like 1/3 has, but it has a
repeating pattern at some point. Irrationals have an infinite decimal
expansion and has no repetition of that kind.

This characteristic of irrationals does not depend on the base, it is always
the same way. The finitude or infinitude of the representation of a rational
depends on the base, but if infinite, there is a repeating pattern.

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reinhardt1053
Great video, one mistake I spotted: he did include the number 1 among the
prime numbers.

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kol
Because 1 is not a prime: "A prime number (or a prime) is a natural number
greater than 1 that has no positive divisors other than 1 and itself."
[https://www.wikiwand.com/en/Prime_number](https://www.wikiwand.com/en/Prime_number)

~~~
rtpg
Funner definition is "positive number with exactly two divisors". This reduces
the amount of special casing

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chestervonwinch
Here's the map in case you don't want to watch the entire 11 min video:

[https://www.flickr.com/photos/95869671@N08/32264483720/in/da...](https://www.flickr.com/photos/95869671@N08/32264483720/in/dateposted-
public/)

I wonder if there are a set of features and distance metric that could
describe each field well enough to do hierarchical cluster analysis -- maybe
through scraping keywords from enough mathematics journals, etc?

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deepakkarki
Tangential, but what tools do people use to make such videos?

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ccvannorman
It really depends on how much effort you want to put in, and your existing
skills. I personally use Final Cut Pro. YouTube also has built-in editing
features for stitching, cutting, and possibly overlaying videos.

Final Cut Pro is quite high end so I only use 5-10% of the features to make
this video: [https://vimeo.com/73754523](https://vimeo.com/73754523)

It took a few hours of storyboarding and editing once I had the footage.

