HN Theater @HNTheaterMonth

The best talks and videos of Hacker News.

Hacker News Comments on
The Map of Mathematics

Domain of Science · Youtube · 28 HN points · 9 HN comments
HN Theater has aggregated all Hacker News stories and comments that mention Domain of Science's video "The Map of Mathematics".
Youtube Summary
The entire field of mathematics summarised in a single map! This shows how pure mathematics and applied mathematics relate to each other and all of the sub-topics they are made from.

#mathematics #DomainOfScience

If you would like to buy a poster of this map, they are available here:
North America: https://store.dftba.com/products/map-of-mathematics-poster
Everywhere else: http://www.redbubble.com/people/dominicwalliman/works/25095968-the-map-of-mathematics
French version: https://www.redbubble.com/people/dominicwalliman/works/40572671-the-map-of-mathematics-french-version?asc=u
Spanish Version: https://www.redbubble.com/people/dominicwalliman/works/40572693-the-map-of-mathematics-spanish-version?asc=u

I have also made a version available for educational use which you can find here: https://www.flickr.com/photos/95869671@N08/32264483720/in/dateposted-public/

To err is to human, and I human a lot. I always try my best to be as correct as possible, but unfortunately I make mistakes. This is the errata where I correct my silly mistakes. My goal is to one day do a video with no errors!

1. The number one is not a prime number. The definition of a prime number is a number can be divided evenly only by 1, or itself. And it must be a whole number GREATER than 1. (This last bit is the bit I forgot).

2. In the trigonometry section I drew cos(theta) = opposite / adjacent. This is the kind of thing you learn in high school and guess what. I got it wrong! Dummy. It should be cos(theta) = adjacent / hypotenuse.

3. My drawing of dice is slightly wrong. Most dice have their opposite sides adding up to 7, so when I drew 3 and 4 next to each other that is incorrect.

4. I said that the Gödel Incompleteness Theorems implied that mathematics is made up by humans, but that is wrong, just ignore that statement. I have learned more about it now, here is a good video explaining it: https://youtu.be/O4ndIDcDSGc

5. In the animation about imaginary numbers I drew the real axis as vertical and the imaginary axis as horizontal which is opposite to the conventional way it is done.

Thanks so much to my supporters on Patreon. I hope to make money from my videos one day, but I’m not there yet! If you enjoy my videos and would like to help me make more this is the best way and I appreciate it very much. https://www.patreon.com/domainofscience

Here are links to some of the sources I used in this video.

Links:
Summary of mathematics: https://en.wikipedia.org/wiki/Mathematics
Earliest human counting: http://mathtimeline.weebly.com/early-human-counting-tools.html
First use of zero: https://en.wikipedia.org/wiki/0#History http://www.livescience.com/27853-who-invented-zero.html
First use of negative numbers: https://www.quora.com/Who-is-the-inventor-of-negative-numbers
Renaissance science: https://en.wikipedia.org/wiki/History_of_science_in_the_Renaissance
History of complex numbers: http://rossroessler.tripod.com/ https://en.wikipedia.org/wiki/Mathematics
Proof that pi is irrational: https://www.quora.com/How-do-you-prove-that-pi-is-an-irrational-number
and https://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational#Laczkovich.27s_proof

Also, if you enjoyed this video, you will probably like my science books, available in all good books shops around the work and is printed in 16 languages. Links are below or just search for Professor Astro Cat. They are fun children's books aimed at the age range 7-12. But they are also a hit with adults who want good explanations of science. The books have won awards and the app won a Webby.

Frontiers of Space: http://nobrow.net/shop/professor-astro-cats-frontiers-of-space/
Atomic Adventure: http://nobrow.net/shop/professor-astro-cats-atomic-adventure/
Intergalactic Activity Book: http://nobrow.net/shop/professor-astro-cats-intergalactic-activity-book/
Solar System App: http://www.minilabstudios.com/apps/professor-astro-cats-solar-system/

Find me on twitter, instagram, and my website:
http://dominicwalliman.com
https://twitter.com/DominicWalliman
https://www.instagram.com/dominicwalliman
https://www.facebook.com/dominicwalliman
HN Theater Rankings

Hacker News Stories and Comments

All the comments and stories posted to Hacker News that reference this video.
This is a good map of Mathematics to get an overview of where you can go... https://www.youtube.com/watch?v=OmJ-4B-mS-Y

Then Giles McMullen-Klein has an awesome recommended list for data science (your mileage may vary). https://www.youtube.com/watch?v=V2aIDbpESyU

Jan 27, 2021 · lamename on A Map of Mathematics
The educational youtube channel Domain of Science has a pretty wide-scope Map of Mathematics, depending on your background https://youtu.be/OmJ-4B-mS-Y
Dec 31, 2020 · 2 points, 0 comments · submitted by ColinWright
Dec 03, 2020 · 4 points, 0 comments · submitted by ColinWright
> shift this burden to the medium

This is beautifully expressed. Knowledge consists of connections across concepts but those connections are rarely shown explicitly in textbooks. Even wikipedia, while allowing you to traverse the connections back and forth easily, does not do a great job of giving you the bird's eye view of a subject or a field. Check out this "map" of mathematics: https://www.youtube.com/watch?v=OmJ-4B-mS-Y Every subject needs a similar map.

Besides visualizing the connections, we'd also need interactivity to the topic that helps with forming new mental models - which is the core aspect of learning. Jupyter notebooks, ObservableHQ, Mathigon are some of the good projects working on this aspect.

Disclaimer: I am building the open-source project https://github.com/learn-awesome/learn/ which is attempting to build the complete map of knowledge/skills. So I too am biased against books and in favor of digital/interactive tools.

activatedgeek
> Check out this "map" of mathematics: ... Every subject needs a similar map.

I often find this sort of approach to be rather counter-productive. If I am learning something, I'd be happy with my local part of the graph, the things that I specifically care about. It is much easier to make multi-hop connections in knowledge when one is really familiar with their local knowledge cluster. I, for one, find an absolute knowledge graph of everything quite intimidating and feel lost in the sea.

LearnAwesome looks interesting. Good luck!

marcosdumay
An actual map (navigable, instead of a presentation) would be kinda of as useful as a world map. You can look at it and say "This time I'll travel here!", and get an idea of what the travel would require.
Aug 01, 2020 · 11 points, 1 comments · submitted by ColinWright
seesawtron
I like the summary poster: https://www.flickr.com/photos/95869671@N08/32264483720/in/da...
Feb 14, 2020 · AareyBaba on A Map of Mathematics
This is a much more entertaining map of mathematics in about 10 minutes 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...

lemmonii
Even in this mostly excellent lecture Wildberger manages to inject some of his finitist nonsense in the end (48m)
sbmthakur
> entertaining map of mathematics

They have also done videos on Map of Computer Science and Map of Physics. Do check them out.

I suggest this "Map of mathematics" as a starting point that gives you a reasonable birds-eye view of the field. https://www.youtube.com/watch?v=OmJ-4B-mS-Y
Aug 18, 2018 · 1 points, 0 comments · submitted by ColinWright
Jun 26, 2018 · 2 points, 0 comments · submitted by ColinWright
This is a general issue i have seen as well.

We live in 2018 and there is no open source course for everything. Instead there are probably 10-30k universities who have similar courses and professors who give the same lecture every year.

They get paid often enough by countries to create and do those courses. In germany most of our unversities are paid by all of us germans anyway.

And what do you find online? Always the starter verion like 101 computer science or videos with bad audio or video, no proper exercises, no solution helper etc. Nothing. You have to go to different sites to sometimes pay or sometimes not.

there are no local locations to meet up with people.

There should be a global initiative for global free and open access learning. Sponsored and supported by companies and countries. Build upon a core of a knowledge graph based on topics or 'snippets of knowledge'. Like for example: math -> add -> sub

Something like 'The Map of Mathematics' (https://www.youtube.com/watch?v=OmJ-4B-mS-Y)

And when you wanna get the global accepted math 101 level, you have to take specific topics / snippets.

And those snippets can than be filled with different people who are making a lecture for that topic and you can choose whom you like more or who is better in explaining it to you.

What do i do instead? I ask around for the lecture scripts because they are always behind a simple password protected area or have multiple links to different pages of different universietses who offer different courses for free as videos for there students in sometimes/often bad quality and / or bad video players etc.

It sucks and this is stupid.

dpflan
Have you seen this? Does this meet your criteria/have enough sufficient resources/curriculum?

> http://datasciencemasters.org/

sigi45
Nope, not at all.

I'm not looking for the next github page with collections of tons of different sites with different courses.

I still hope for one platform where all those smart people out there are working together to optimize learning.

tyu100
I forget if its the Verge or some other popular podcast but they are always suggesting Apple just put together a fully open and accredited online university.

The problem is that there are a lot of people getting paid a lot of money all over the world to work in post-secondary education whom control the keys to accreditation and whom have proven very resilient at resisting any optimization efforts.

JoshMnem
Apple isn't open. Their stuff has tended to not work on Linux.
solarkraft
I don't see why one would need Apple to do it. A consortium would be much better and more likely.
Bombthecat
Apple is big enough to piss away one billion dollar and create a crazy good online University.

Also need done good pr I guess :)

YPBS
Here is a list of CS courses including many graduate level courses:

https://github.com/Developer-Y/cs-video-courses

Double_a_92
Check out khanacademy.
rmorey
>There should be a global initiative for global free and open access learning. Sponsored and supported by companies and countries. Build upon a core of a knowledge graph based on topics or 'snippets of knowledge'.

I like this idea and the framing of it a lot

I agree with other comments that "learn maths" is too broad. You can take a university degree in maths and still be just at the beginning of "learning maths." I recommend refining your goal somehow: perhaps to learn math related to certain applications that you're interested in, or learn math in a certain area (e.g. high-school algebra, geometry, probability, discrete math, graph theory, calculus, pure math, abstract algebra, topology, etc).

If you have not mastered high-school algebra and other pre-calculus subjects, you should start there; most other maths subjects will assume that you know these things. Calculus takes up a lot of space in upper high-school and early university courses -- but if you're a developer there may be other subjects that are more immediately useful to you (e.g. discrete math, linear algebra).

I set out to "learn maths" (that's verbatim what it says on my personal Kanban board). In the end I took some university classes. For me they provided the structure and teachers to help me learn. Also, there is a difference between having an idea about what some math-thing is, and being able to pass an 3 hour closed-book exam in that topic.

I agree that Khan Academy is a good learning resource that will provide structure to your learning:

https://www.khanacademy.org/

Purplemath is another good resource:

http://www.purplemath.com/

YouTube is full of videos of people running through problems on any conceivable topic. Definitely search there for help.

Once you've worked your way through the high school prerequisites, I'd recommend Linear Algebra as a good next course. It has many practical applications, and is also an entry point towards pure math subjects like Abstract Algebra. Also, you don't need to know any calculus to study linear algebra. I like Gilbert Strang's OCW course:

https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra...

Finally, mathematics is HUGE. The following will give you a bit of an idea:

The Map of Mathematics https://www.youtube.com/watch?v=OmJ-4B-mS-Y

I'd start with this video to get an overview of all the topics and areas that mathematics entails (some might be unknown to you) https://www.youtube.com/watch?v=OmJ-4B-mS-Y . Then you go ahead and research a bit what sounds interesting to you and then you might google that topic and add "foundations" to that google search. It's just that most school/university math is heavily focused on analysis and algebra but there is so much more!
Feb 26, 2017 · 2 points, 0 comments · submitted by partycoder
Feb 09, 2017 · 5 points, 0 comments · submitted by arangelov
Feb 07, 2017 · 1 points, 0 comments · submitted by CarolineW
HN Theater is an independent project and is not operated by Y Combinator or any of the video hosting platforms linked to on this site.
~ yaj@
;laksdfhjdhksalkfj more things
yahnd.com ~ Privacy Policy ~
Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.