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Can you think of an image, whether technical or nontechnical, available for viewing online that says a lot about what you think mathematics or a particular field of mathematics is all about?

For instance, some look at Hokusai's "Great Wave" as evoking a notion of fractals. http://en.wikipedia.org/wiki/File:Great_Wave_off_Kanagawa2.jpg

There is some interesting discussion of this here, http://www.squarecirclez.com/blog/math-in-art-hokusais-the-wave/595

edited Jul 19 2010 at 11:09

François G. Dorais♦

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3 revisions, 3 users
Kim Greene 100%

I'm voting to close; this question is now several months old and is rather stale. Moreover, none of the answers so far are good. – Kevin Lin Jun 3 2010 at 3:42

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I don't know whether MO questions can get stale, as long as there are new MO users who haven't seen them before. Or are new users supposed to familiarize themselves with all previous questions? – John Stillwell Jun 3 2010 at 4:38

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Moreover, who is really capable of judging if "none of the answers is good" when talking about a soft-question (and be confident that he could convince the rest of the people about him being right)? I learned some things from these answers, and I am pretty sure that there probably is at least one person that found good any particular answer - namely, its poser! – Jose Brox Jul 22 2010 at 13:03

Scott Morrison · Accepted Answer · 2009-11-04 07:23:48Z UTC

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"Epitomizing mathematics" is a tall order, and even representing what a single field is about (rather than just giving a cool glimpse of the subject matter) is pretty hard to imagine.

Still, given your example, one of course thinks of Escher, for example his hyperbolic plane tilings:

Escher's hyperbolic plane tiling

and the less well-known art of Anatoly Fomenko. I believe one of Fomenko's drawings is on the first page of one of Springer's GTM books - now I just need to remember which one...

Another picture that is frequently associated with mathematical research is Durer's Melancolia. I can't say it really epitomizes anything for me, but it's a pretty picture.

edited Nov 4 2009 at 7:23

Scott Morrison♦

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Alon Amit 77%

re: Fomenko, you're thinking of Shiryaev's "Probability" – Erik Davis Nov 23 2009 at 3:28

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Or perhaps GTM 58, Koblitz, $p$-adic Numbers, $p$-adic Analysis, and Zeta-Functions, which features Fomenko's conception of the 3-adic unit disk. Or GTM 97, Koblitz, Introduction to Elliptic Curves and Modular Forms, with a Fomenko drawing depicting the family of elliptic curves that arises in the congruent number problem. – Gerry Myerson Jun 2 2010 at 4:21

Curiously, in the Russian translations of Koblitz's books, they have been transposed. – Victor Protsak Jun 2 2010 at 6:00

I'm quite partial to this variation by Henry Segerman and Paul-Olivier Dehaye: segerman.org/autologlyphs/Poincaredisk_small.gif – Mark Meckes Jun 2 2010 at 13:45

Victor, the Russian translation of Koblitz's book on p-adic analysis has Fomenko's drawing of the 2-adic solenoid (both on the cover and inside the book), not a family of elliptic curves. That I checked directly. By a web search I find that the picture in the ell. curves book is the same in the translated volume as in the original one too. – KConrad Jul 7 2010 at 23:01

Richard Kent · Answer 2 · 2009-11-04 00:32:21Z UTC

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I think this sums it up most of the time.

answered Nov 4 2009 at 0:32

Richard Kent

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aorq · Answer 3 · 2009-10-25 13:13:21Z UTC

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The top of page 1199 (page 4 of 17 of the PDF) in the article "Comme Appelé du Néant" in the Notices of the AMS.

answered Oct 25 2009 at 13:13

aorq

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It's probably not a good thing that I knew what you were referring to before I even clicked the link... – Harrison Brown Oct 28 2009 at 17:26

John Stillwell · Answer 4 · 2010-06-02 08:31:42Z UTC

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$hyperbolic space$

answered Jun 2 2010 at 8:31

John Stillwell

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Wow, this takes me back. <i>Not Knot</i> completely changed my impression of mathematical visualization and what it could do; to my mind it still sets the standard for expository mathematics video, and it's a shame that more aren't trying to reach for the bar it sets. – Steven Stadnicki Jul 7 2010 at 0:14

Victor Protsak · Answer 5 · 2010-06-02 16:19:11Z UTC

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Raphael's School of Athens

edited Jun 2 2010 at 16:19

Victor Protsak

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Victor Protsak 57%

	Link appears to be broken; try en.wikipedia.org/wiki/The_School_of_Athens – JBL Jun 2 2010 at 15:51
	Fixed by imbedding the image. – Victor Protsak Jun 2 2010 at 16:09

Victor Protsak · Answer 6 · 2010-06-02 06:23:38Z UTC

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Mandelbrot set

edited Jun 2 2010 at 6:23

Victor Protsak

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2 revisions

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Check out the mandelbulb too. skytopia.com/project/fractal/mandelbulb.html – Dan Piponi Jun 2 2010 at 23:30

The Mandelbulb is just great! – Jose Brox Jul 7 2010 at 0:09

Roland Bacher · Answer 7 · 2010-06-02 07:24:06Z UTC

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What about the five platonic solids?

answered Jun 2 2010 at 7:24

Roland Bacher

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babubba · Answer 8 · 2010-07-22 13:42:28Z UTC

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answered Jul 22 2010 at 13:42

babubba

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Jon Awbrey · Answer 9 · 2010-06-02 17:44:07Z UTC

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A proof without words for the Pythagorean theorem (Zhou Bi Suan Jing).

edited Jun 2 2010 at 17:44

Jon Awbrey

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2 revisions, 2 users
hypercube 57%

You could add a link to this (or even copy the answer there!) to the question "Proofs without words", for completeness' sake. – Mariano Suárez-Alvarez Jun 2 2010 at 18:01

Jon Awbrey · Answer 10 · 2010-06-03 03:30:15Z UTC

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Some History

edited Jun 3 2010 at 3:30

Jon Awbrey

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Jon Awbrey 86%

	I've reduced the size to fit in a page. Feel free to roll back if inappropriate. – Victor Protsak Jun 2 2010 at 16:15
	An easier way to do that would have been to change the 600px parameter in the original url. – Jon Awbrey Jun 2 2010 at 16:45

Anna Varvak · Answer 11 · 2009-10-25 13:11:10Z UTC

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Almost any of the Escher sketches.

answered Oct 25 2009 at 13:11

Anna Varvak

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Cam McLeman · Answer 12 · 2010-06-02 03:58:10Z UTC

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Hm, would a picture of Serre count?

answered Jun 2 2010 at 3:58

Cam McLeman

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:) $ $ – Mariano Suárez-Alvarez Jun 2 2010 at 13:48

Jose Brox · Answer 13 · 2010-07-22 13:06:17Z UTC

For category theory, from Abstract and Concrete Categories: The joy of cats, by Adámek, Herrlich and Strecker, page 12:

(http://katmat.math.uni-bremen.de/acc/acc.pdf)

Categorists have developed a symbolism that allows one quickly to visualize quite complicated facts by means of diagrams.

For me, this represents the fact that most, if not all of mathematics, is about structures and relations: even the simplest of them, when combined and interrelated, can give birth to fairly complex behaviour.

Henry Segerman · Answer 14 · 2010-06-02 04:09:18Z UTC

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The Lorenz attractor would be the canonical image for chaos theory, and with only a little verbal explanation it demonstrates the sensitivity to dependence on initial conditions very well.

answered Jun 2 2010 at 4:09

Henry Segerman

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Interesting! My impression was that the bifurcation diagram for the logistic map, en.wikipedia.org/wiki/…, was more canonical. – Victor Protsak Jun 2 2010 at 6:06

@Victor: Good point! I was also thinking about the Mandelbrot set. Chaos theory/fractals have many of the most interesting images. – Henry Segerman Jun 2 2010 at 15:38

I confess: you've given me the idea of M set. – Victor Protsak Jun 2 2010 at 16:20

Pasha Zusmanovich · Answer 15 · 2009-11-04 13:28:28Z UTC

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Bernar Venet's paintings [http://www.bernarvenet.com/ ] - those with colored commutative diagrams (if I remember properly, there was also a Notices article about that).

answered Nov 4 2009 at 13:28

Pasha Zusmanovich

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ams.org/notices/200206/comm-hofmann.pdf – Dan Piponi Jun 2 2010 at 23:31

Idoneal · Answer 16 · 2010-06-02 08:59:53Z UTC

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Here is a more mathematical rendition of Richard Kent's answer:

http://math-art.net/2007/12/03/eternal-scream-a-droste-effect/

edited Jun 2 2010 at 8:59

Idoneal

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Looks more like a mathematical rendition of "This is Spartaaaaaaaaa"... – darij grinberg Jun 2 2010 at 10:20

Mariano Suárez-Alvarez · Answer 17 · 2010-07-07 00:36:06Z UTC

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There is a painting by Diego Rivera of René Paresce (1866-1937) (gotten from web address http://www.vf.utwente.nl/~jagersaa/D_R.html)

alt text El Matemático

edited Jul 7 2010 at 0:36

Mariano Suárez-Alvarez

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Will Jagy 61%

	No image. Oh, well. – Will Jagy Jul 6 2010 at 19:54
	I added the image. Great painting, btw. – Mariano Suárez-Alvarez Jul 7 2010 at 0:36
	Thanks, Mariano. How did you do that? – Will Jagy Jul 10 2010 at 18:34

Will Jagy · Answer 18 · 2010-07-06 22:19:48Z UTC

... and months after this question was posted, no mention of Sidney Harris?

Start with his "... and then a miracle occurs" and his "You want proof? I'll give you proof!" . Continue from there.

Gerhard "That's Enough Subconscious For Today" Paseman, 2010.07.06

The first one available for sale as prints, notecards, etc. http://www.newyorkerstore.com/All-Industry-Cartoons/I-think-you-should-be-more-explicit-here-in-step-two/invt/118181

Jose Brox · Answer 19 · 2010-07-07 00:31:01Z UTC

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Keizo Ushio's topological "impossible" sculptures on stone

answered Jul 7 2010 at 0:31

Jose Brox

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ardentMirage · Answer 20 · 2010-07-19 06:53:44Z UTC

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Voronoi diagrams and their respective Delaunay triangulations.

answered Jul 19 2010 at 6:53

ardentMirage

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Jon Awbrey · Answer 21 · 2010-06-02 17:36:07Z UTC

Mathematics sometimes evokes emotion, as does music, and sometimes other forms of art. The strongest emotion I remember was the first time I saw Euler's Identity. So my image is just Euler's Identity written on a chalk board.