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The Map of Mathematics [video]
- tempodox 10y agoThis 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.
- reikonomusha 10y agoI 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 10y agoThese 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?
- HiroshiSan 10y ago1/3 is a real number, did you mean irrationals?
- reikonomusha 10y agoThe video described real numbers (beyond rationals, hence irrationals) as ones with non-terminating decimal expansions.
- fxn 10y agoI 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.
- carlob 10y agoThe video says the difference between reals and rationals is that reals can have infinite decimal expansions. But I concede you're right (if a bit pedantic), the complement of reals and rationals is irrationals.
- bsaul 10y agoThe video does mention that "how the field relate" can't be drawn properly on the same 2d map. So maybe the next step is now to make other maps using different projections to show those relations ? Using the same pictograms would help people visualize better, and it would make an interesting collection of maps.
- ccvannorman 10y agoDo you have a better source? I would love to see something that focuses on the relations, such as what Langland tried to do, in video form.
- hackermailman 10y agoThe book "Elements of Mathematics: From Euclid to Gödel" by Stillwell does this in terms of identifying what is considered advanced in a survey of elementary math topics and showing how they fit together or don't, like how Groups drop commutativity of multiplication from the ring http://press.princeton.edu/titles/10697.html http://press.princeton.edu/titles/10697.html
- vog 10y agoIndeed, it would have been better if they had one or more mathematicians in their team. I'm pretty sure that most mathematicians would have loved to support them, at least to proofread their script and to review their animations.
- deepakkarki 10y agoTangential, but what tools do people use to make such videos?
- ccvannorman 10y agoIt 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.
- deleted 10y ago[deleted]
- mxfh 10y agoA 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.
- k__ 10y agoOr computer science, which also deals with sets, logic, coplexity and groups.
- Angostura 10y agoThe presenter does explicitly call out the problem with 2D presentation.
- rawnlq 10y agoOn 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
- chestervonwinch 10y agoHere'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/dateposted-public/ https://www.flickr.com/photos/95869671@N08/32264483720/in/da... 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?
- Sir_Cmpwn 10y agoRelated - map of Physics: https://www.youtube.com/watch?v=ZihywtixUYo https://www.youtube.com/watch?v=ZihywtixUYo
- reinhardt1053 10y agoGreat video, one mistake I spotted: he did include the number 1 among the prime numbers.
- kol 10y agoBecause 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
- panglott 10y agoIt's a followup to the Map of Physics https://www.youtube.com/watch?v=ZihywtixUYo https://www.youtube.com/watch?v=ZihywtixUYo
- gooseh 10y ago... 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
- nicocourts 10y agoI registered here to share this image exactly. Saw it over on /r/math and while any such endeavor is doomed from the start to be unrealistic or incomplete, this one didn't anger me quite as much.
- rayuela 10y agoI'd never seen this before. This is fucking great. Much better than the parent post. Thanks for sharing it!
- pash 10y agoI'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
- 7373737373 10y agoA 2d-map of arxiv papers: http://paperscape.org/ http://paperscape.org/
- ivan_ah 10y agoI 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)
- reikonomusha 10y agoA good presentation style doesn't make something correct. The correctness is what folks are critical of, not the medium.
- Someone 10y agoYou 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-atlas.org/ http://web.archive.org/web/20150616152045/http://www.math-at...
- WhitneyLand 10y agoAny 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.
- dorianm 10y agoWikipedia'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
- acchow 10y ago"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