A Map of Mathematics

https://www.quantamagazine.org/the-map-of-mathematics-20200213/

by theafh • 6 years ago

414 55 6 years ago

dbish• 6 years ago

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.

J5892• 6 years ago

It took me like 3 minutes to get back here.

MrZander• 6 years ago

And you can't scroll back up once you've scrolled down which is insanely annoying

anigbrowl3• 6 years ago

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.

omaranto• 6 years ago

You might like the history tree in next browser: https://next.atlas.engineer/

XnoiVeX• 6 years ago

Reminded me of this. https://www.sciencealert.com/this-mind-boggling-map-explains...

anigbrowl3• 6 years ago

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.

lliamander2• 6 years ago

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.

whatshisface2• 6 years ago

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).

lliamander2• 6 years ago

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.

p0cc• 6 years ago

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...

blululu• 6 years ago

Interesting reminds me of a clustering I once did using a SVD to cluster fields of mathematics https://github.com/bnlcas/ArxivStudy

mooneater• 6 years ago

Very nice!

_ylmx• 6 years ago

Does anyone have suggestions for good books on the history of Mathematics?

phaemon• 6 years ago

From the Birth of Numbers. ISBN 9780393040029

dcra• 6 years ago

Stillwell's _Mathematics and its History_ is, imo, excellent.

jesuslop• 6 years ago

Stillwell is a fantastic historian, +1 to the recommendation.

spenuke• 6 years ago

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.

chadcmulligan• 6 years ago

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.

Someone• 6 years 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.

billfruit• 6 years ago

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.

ivan_ah• 6 years ago

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 at http://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).

btilly• 6 years ago

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.

LanceH• 6 years ago

The Princeton Companion to Mathematics. More an Encyclopedia of mathematics with history in it.

AareyBaba2• 6 years ago

NJ Wildberger's lectures are online https://www.youtube.com/watch?v=dW8Cy6WrO94&list=PL55C7C8378...

xkgt• 6 years ago

"A Cultural History of Physics" by Karoli Simonyi is a brilliant book on the history of Science and math from antiquity to recent past. Even though the title reads as history of physics, the book touches upon everything from Math to Philosophy as they were all under one umbrella until recent past.

https://www.amazon.com/Cultural-History-Physics-K%C3%A1roly-...

jostylr• 6 years ago

Nature and Growth of Modern Mathematics by Edna Kramer. If you love history and mathematics, this is a good combination from what I remember, sort of alternating between historical placements and biographies with actual mathematical content explained.

I read this decades ago before I learned advanced mathematics and I found it enlightening and inspiring at the time though I have not revisited it since though it is a cherished memory. The book's age prevents it from covering the many modern innovations since.

mortdeus2• 6 years ago

this might be obnoxiously unrelated but this site has probably the coolest usage of particle.js i've seen yet.

mortdeus2• 6 years ago

"Explore our surprisingly simple, absurdly ambitious, and necessarily incomplete guide to the boundless universe."

Okay you have my attention now.

godelzilla• 6 years ago

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.

wbhart• 6 years ago

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.

whatshisface2• 6 years ago

00Axx General and miscellaneous specific topics

The structure of any successful classification system: these things, those other things, and everything else. ;)

codethief2• 6 years ago

Almost as good as:

83Fxx: Cosmology
- 83F05: Cosmology
- 83F99: None of the above, but in this section

725686• 6 years ago

6,200 Lines just to list all fields!

waynecochran• 6 years ago

Wow. I have a degree in Math, and I am mostly aware of how little I know, but that chart really intimidates me.

codethief2• 6 years ago

If only I had discovered that list back when I was still an undergraduate. The hardest part about finding a good research area seems to be knowing it exists in the first place.

nilaykumar• 6 years ago

A less intimidating and slightly more practical approach might be to look at how we classify our own work on the arXiv: https://arxiv.org/archive/math

The MSC is of course quite useful for catalog and reference purposes.

dylan604• 6 years ago

Is this really a map, or just a table of contents?

searine• 6 years ago

What an infuriating format for an article.

visarga• 6 years ago

The lack of backwards navigation and scroll is irritating, though.

motohagiography• 6 years ago

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• 6 years ago

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'.

Razengan• 6 years ago

Not being able to scroll back up is really annoying, closed the page after seeing that.

ryugarden• 6 years ago

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)

elcapitan• 6 years ago

That's the most annoying navigation I've seen in a while, and that says something.

itsangaris• 6 years ago

Not being able to scroll back up is definitely a first for me.

justinclift• 6 years ago

Nor being able to use page up/down. :(

mojomark• 6 years ago

It's like taking a tour of the Smithsonian, but only being allowed to view it through a paper towel tube.

hammerbrostime• 6 years ago

I'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!

AareyBaba2• 6 years ago

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...

sbmthakur• 6 years ago

entertaining map of mathematics

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

lemmonii• 6 years ago

Even in this mostly excellent lecture Wildberger manages to inject some of his finitist nonsense in the end (48m)

A Map of Mathematics

Related Stories