[HN Gopher] A Map of Mathematics
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A Map of Mathematics
Author : theafh
Score : 170 points
Date : 2020-02-14 17:51 UTC (5 hours ago)
(HTM) web link (www.quantamagazine.org)
(TXT) w3m dump (www.quantamagazine.org)
| [deleted]
| kruasan wrote:
| This reminded me about Tegmark's map of relationships between
| various basic mathematical structures:
|
| https://arxiv.org/pdf/gr-qc/9704009.pdf (on page 2)
| blululu wrote:
| Interesting reminds me of a clustering I once did using a SVD to
| cluster fields of mathematics
| https://github.com/bnlcas/ArxivStudy
| searine wrote:
| What an infuriating format for an article.
| mortdeus wrote:
| "Explore our surprisingly simple, absurdly ambitious, and
| necessarily incomplete guide to the boundless universe."
|
| Okay you have my attention now.
| XnoiVeX wrote:
| Reminded me of this. https://www.sciencealert.com/this-mind-
| boggling-map-explains...
| anigbrowl wrote:
| Hand-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.
| visarga wrote:
| The lack of backwards navigation and scroll is irritating,
| though.
| godelzilla wrote:
| While mathematics is often motivated by physical phenomenon, it's
| epistemologically misleading to present physics as math or vice
| versa. All too common pet peeve.
| lliamander wrote:
| Their 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 wrote:
| A 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 wrote:
| Oh, 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.
| dbish wrote:
| Neat, 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.
| anigbrowl wrote:
| _You 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.
| J5892 wrote:
| It took me like 3 minutes to get back here.
| MrZander wrote:
| And you can't scroll back up once you've scrolled down which is
| insanely annoying
| motohagiography wrote:
| I 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 wrote:
| I'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'.
| jumbopapa wrote:
| Does anyone have suggestions for good books on the history of
| Mathematics?
| LanceH wrote:
| The Princeton Companion to Mathematics. More an Encyclopedia of
| mathematics with history in it.
| ivan_ah wrote:
| I have two recommendations that I don't see mentioned by anyone
| else yet:
|
| 1. __An Introduction to Mathematics __by Alfred North
| Whitehead, 1911 available
| athttp://www.gutenberg.org/ebooks/41568
|
| It not specifically about history, but I found it nice how it
| builds up concepts from first principles, e.g. "We had problem
| X, so we invented math concept Y to help with problem X, and
| then extended the idea concept Z that handles more general
| class of problems."
|
| 2. __Mathematics 1001: Absolutely Everything That Matters About
| Mathematics in 1001 Bite-Sized Explanations Hardcover __by
| Richard Elwes, 2010. (non free)
|
| This one doesn't go into any details on any topics, but it
| gives you a bird's eye overview of many topics and based on the
| "sampling" I did for the few concepts that I know, I found the
| bite-size explanations to be fairly good (i.e. mathematician
| explains things in plain language, and not science journalist
| simplistic analogy).
| Someone wrote:
| "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.
| btilly wrote:
| _The 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-Dav...
| is a link to Amazon.
| billfruit wrote:
| I don't know how helpful it is to the common reader, L.E
| Dickson's 3-volume 'History of the Theory of Numbers' is
| mentioned frequently as a definitive history of that branch of
| Mathematics.
| dcra wrote:
| Stillwell's _Mathematics and its History_ is, imo, excellent.
| jesuslop wrote:
| Stillwell is a fantastic historian, +1 to the recommendation.
| spenuke wrote:
| For 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.
| phaemon wrote:
| From the Birth of Numbers. ISBN 9780393040029
| chadcmulligan wrote:
| I 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.
| p0cc wrote:
| I 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-
| us...
| [deleted]
| elcapitan wrote:
| That's the most annoying navigation I've seen in a while, and
| that says something.
| wbhart wrote:
| For 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
|
| 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.
| 725686 wrote:
| 6,200 Lines just to list all fields!
| whatshisface wrote:
| > _00Axx General and miscellaneous specific topics_
|
| The structure of any successful classification system: these
| things, those other things, and everything else. ;)
| Razengan wrote:
| Not being able to scroll back up is really annoying, closed the
| page after seeing that.
| mortdeus wrote:
| this might be obnoxiously unrelated but this site has probably
| the coolest usage of particle.js i've seen yet.
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(page generated 2020-02-14 23:00 UTC)