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!<p>Here is my take on a concept map of math topics: <a href="https://minireference.com/static/tutorials/conceptmap.pdf" rel="nofollow">https://minireference.com/static/tutorials/conceptmap.pdf</a> (covers only high school math + calculus + linear algebra)
... And then someone more familiar with, y'know, mathematics went and made one: <a href="http://nada.kth.se/~axelhu/mapthematics.pdf" rel="nofollow">http://nada.kth.se/~axelhu/mapthematics.pdf</a>
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.<p>Maybe one could do an interactive version where the nodes can move in different dimensions like historic timeline, field of use, mathematical area.
Related - map of Physics: <a href="https://www.youtube.com/watch?v=ZihywtixUYo" rel="nofollow">https://www.youtube.com/watch?v=ZihywtixUYo</a>
Any chance of an international treaty whereby all parties agree to stop saying either "maths" or "math"?<p>No criticism here, I'll agree to either one.
"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"<p>Uhh... that's not the interpretation of the incompleteness theorems...<p>See also the Halting Problem
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.
It's a followup to the Map of Physics
<a href="https://www.youtube.com/watch?v=ZihywtixUYo" rel="nofollow">https://www.youtube.com/watch?v=ZihywtixUYo</a>
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).<p>The most beautiful part of math wasn't explained at all, which is <i>how the fields relate</i>! 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.<p>Instead, the video gave extremely high-level mathematical "buzzword soup" with artificial boundaries and an explanation that seems to be derived after the fact.<p>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.
Here's the map in case you don't want to watch the entire 11 min video:<p><a href="https://www.flickr.com/photos/95869671@N08/32264483720/in/dateposted-public/" rel="nofollow">https://www.flickr.com/photos/95869671@N08/32264483720/in/da...</a><p>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?