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A Map of Mathematics
- dbish 7y agoNeat, 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.
- J5892 7y agoIt took me like 3 minutes to get back here.
- MrZander 7y agoAnd you can't scroll back up once you've scrolled down which is insanely annoying
- anigbrowl 7y agoYou 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.
- omaranto 7y agoYou might like the history tree in next browser: https://next.atlas.engineer/ https://next.atlas.engineer/
- anigbrowl 7y agoI might indeed. I am not a big fan of console driven applications, but it's intriguing so I am installing it on my linux box now. Thanks for the suggestion!
- filterfish 7y agoThat's a bit like Vim's undo tree which is incredibility useful.
- XnoiVeX 7y agoReminded me of this. https://www.sciencealert.com/this-mind-boggling-map-explains-how-everything-in-mathematics-is-connected-3 https://www.sciencealert.com/this-mind-boggling-map-explains...
- anigbrowl 7y agoHand-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.
- lliamander 7y agoTheir 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.
- whatshisface 7y agoA 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 7y agoOh, 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.
- p0cc 7y agoI 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-usability-nightmare-2a5bbb4273d0 https://medium.com/@paonecreative_87456/scrolljacking-the-us...
- deleted 7y ago[deleted]
- blululu 7y agoInteresting 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 7y agoVery nice!
- _ylmx 7y agoDoes anyone have suggestions for good books on the history of Mathematics?
- phaemon 7y agoFrom the Birth of Numbers. ISBN 9780393040029
- dcra 7y agoStillwell's _Mathematics and its History_ is, imo, excellent.
- jesuslop 7y agoStillwell is a fantastic historian, +1 to the recommendation.
- spenuke 7y agoFor a very informal tour, The Three Body Problem by Cixin Liu is a science fiction novel where the history of mathematics, physics, and computation play a large role. So much so that I think it puts many people off the book and its entire trilogy.
- chadcmulligan 7y agoI recommend this a lot "A History of Vector Analysis: The Evolution of the Idea of a Vectorial System (Dover Books on Mathematics)" by Michael Crowe. It's a page turner.
- btilly 7y agoThe Mathematical Experience is not a history of mathematics per se, but there is a lot of history and context in it. Highly recommended. https://www.amazon.com/Mathematical-Experience-Phillip-J-Davis/dp/0395929687 https://www.amazon.com/Mathematical-Experience-Phillip-J-Dav... is a link to Amazon.
- Someone 7y ago“A Concise History of Mathematics” by D.J. Struik apparently (I have read only a tiny part of it) is good, but being 70+ years old, it is getting more and more dated. It also doesn’t discuss the mathematics itself in much depth; it more connects topics and has references (plenty of them) for those who want to learn about those topics. “The World of Mathematics” by J.R. Newman isn’t a history, but more a sample of pure and, mostly, applied (“How to hunt a submarine” is the title of a chapter on operations research) mathematics. I think it is worth mentioning, though, certainly for “tourists” who aren’t aiming for full coverage of the subject, but just want to visit nice viewpoints. Also, I think it’s quite readable for non-mathematicians, as it doesn’t do much ‘real’ math (Stillwell's _Mathematics and its History_, mentioned elsewhere, has more of that in its first 25 pages than this 1000+ page work), and its chapters can be read in isolation.
- mortdeus 7y agothis might be obnoxiously unrelated but this site has probably the coolest usage of particle.js i've seen yet.
- mortdeus 7y ago"Explore our surprisingly simple, absurdly ambitious, and necessarily incomplete guide to the boundless universe." Okay you have my attention now.
- godelzilla 7y agoWhile mathematics is often motivated by physical phenomenon, it's epistemologically misleading to present physics as math or vice versa. All too common pet peeve.
- wbhart 7y agoFor 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.
- whatshisface 7y ago>00Axx General and miscellaneous specific topics The structure of any successful classification system: these things, those other things, and everything else. ;)
- codethief 7y agoAlmost as good as: > 83Fxx: Cosmology > - 83F05: Cosmology > - 83F99: None of the above, but in this section
- B1FF_PSUVM 7y agoNo one mentioned Borges, I'll do it: https://en.wikipedia.org/wiki/Celestial_Emporium_of_Benevolent_Knowledge https://en.wikipedia.org/wiki/Celestial_Emporium_of_Benevole... "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.
- 725686 7y ago6,200 Lines just to list all fields!
- waynecochran 7y agoWow. I have a degree in Math, and I am mostly aware of how little I know, but that chart really intimidates me.
- codethief 7y ago
- searine 7y agoWhat an infuriating format for an article.
- motohagiography 7y agoI 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 7y agoI'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'.
- visarga 7y agoThe lack of backwards navigation and scroll is irritating, though.
- Razengan 7y agoNot being able to scroll back up is really annoying, closed the page after seeing that.
- deleted 7y ago[deleted]
- kruasan 7y agoThis 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)
- elcapitan 7y agoThat's the most annoying navigation I've seen in a while, and that says something.
- itsangaris 7y agoNot being able to scroll back up is definitely a first for me.
- justinclift 7y agoNor being able to use page up/down. :(
- mojomark 7y agoIt's like taking a tour of the Smithsonian, but only being allowed to view it through a paper towel tube.
- hammerbrostime 7y agoI'm not sure why they don't start with the navigation map, instead of the wonky scrolling experience. You have to hunt for the map, but the link to it is just below the title screen. The map is actually well designed!
- AareyBaba 7y agoThis 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=PL34B589BE3014EAEB https://www.youtube.com/watch?v=dW8Cy6WrO94&list=PL34B589BE3...