most recent 30 from http://mathoverflow.net 2013-05-22T15:51:31Z http://mathoverflow.net/feeds/question/2437 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/2437/is-there-an-image-for-you-that-epitomizes-mathematics Kim Greene 2009-10-25T07:30:25Z 2010-07-22T13:42:28Z

<p>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?</p> <p>For instance, some look at Hokusai's "Great Wave" as evoking a notion of fractals. <a href="http://en.wikipedia.org/wiki/File:Great_Wave_off_Kanagawa2.jpg" rel="nofollow">http://en.wikipedia.org/wiki/File:Great_Wave_off_Kanagawa2.jpg</a></p> <p>There is some interesting discussion of this here, <a href="http://www.squarecirclez.com/blog/math-in-art-hokusais-the-wave/595" rel="nofollow">http://www.squarecirclez.com/blog/math-in-art-hokusais-the-wave/595</a></p>

http://mathoverflow.net/questions/2437/is-there-an-image-for-you-that-epitomizes-mathematics/2440#2440 Alon Amit 2009-10-25T08:14:05Z 2009-11-04T07:23:48Z

<p>"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. </p> <p>Still, given your example, one of course thinks of Escher, for example his hyperbolic plane tilings:</p> <p><img src="http://britton.disted.camosun.bc.ca/escher/circle%5Flimit%5FI.jpg" alt="Escher's hyperbolic plane tiling" /></p> <p>and the less well-known art of <a href="http://skonieczna.wordpress.com/2007/10/31/mathematical-impressions-by-anatoly-t-fomenko/" rel="nofollow">Anatoly Fomenko</a>. 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...</p> <p>Another picture that is frequently associated with mathematical research is Durer's <a href="http://en.wikipedia.org/wiki/Melencolia%5FI" rel="nofollow">Melancolia</a>. I can't say it really epitomizes anything for me, but it's a pretty picture.</p>

http://mathoverflow.net/questions/2437/is-there-an-image-for-you-that-epitomizes-mathematics/2468#2468 Anna Varvak 2009-10-25T13:11:10Z 2009-10-25T13:11:10Z

<p>Almost any of the <a href="http://images.google.com/images?hl=en&amp;source=hp&amp;q=escher&amp;um=1&amp;ie=UTF-8&amp;ei=OE7kSor3Gtrg8AbI8ZGIBw&amp;sa=X&amp;oi=image%5Fresult%5Fgroup&amp;ct=title&amp;resnum=1&amp;ved=0CBYQsAQwAA" rel="nofollow">Escher sketches</a>.</p>

http://mathoverflow.net/questions/2437/is-there-an-image-for-you-that-epitomizes-mathematics/2469#2469 aorq 2009-10-25T13:13:21Z 2009-10-25T13:13:21Z

<p>The top of page 1199 (page 4 of 17 of the PDF) in the article "<a href="http://www.ams.org/notices/200410/fea-grothendieck-part2.pdf" rel="nofollow">Comme Appelé du Néant</a>" in the Notices of the AMS.</p>

http://mathoverflow.net/questions/2437/is-there-an-image-for-you-that-epitomizes-mathematics/4012#4012 James 2009-11-03T22:31:30Z 2010-06-02T16:19:11Z

<p><a href="http://en.wikipedia.org/wiki/The_School_of_Athens" rel="nofollow">Raphael's <em>School of Athens</em></a></p> <p><img src="http://upload.wikimedia.org/wikipedia/commons/9/94/Sanzio_01.jpg" height="450"> </p>

http://mathoverflow.net/questions/2437/is-there-an-image-for-you-that-epitomizes-mathematics/4020#4020 Richard Kent 2009-11-04T00:32:21Z 2009-11-04T00:32:21Z

<p>I think <a href="http://en.wikipedia.org/wiki/The%5FScream" rel="nofollow">this</a> sums it up most of the time.</p>

http://mathoverflow.net/questions/2437/is-there-an-image-for-you-that-epitomizes-mathematics/4078#4078 Pasha Zusmanovich 2009-11-04T13:28:28Z 2009-11-04T13:28:28Z

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

http://mathoverflow.net/questions/2437/is-there-an-image-for-you-that-epitomizes-mathematics/26780#26780 Cam McLeman 2010-06-02T03:58:10Z 2010-06-02T03:58:10Z

<p>Hm, would a picture of Serre count?</p>

http://mathoverflow.net/questions/2437/is-there-an-image-for-you-that-epitomizes-mathematics/26784#26784 Henry Segerman 2010-06-02T04:09:18Z 2010-06-02T04:09:18Z

<p>The <a href="http://en.wikipedia.org/wiki/Lorenz_attractor" rel="nofollow">Lorenz attractor</a> 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.</p>

http://mathoverflow.net/questions/2437/is-there-an-image-for-you-that-epitomizes-mathematics/26793#26793 Victor Protsak 2010-06-02T06:12:54Z 2010-06-02T06:23:38Z

<p><img src="http://upload.wikimedia.org/wikipedia/commons/2/21/Mandel_zoom_00_mandelbrot_set.jpg" alt="Mandelbrot set"></p>

http://mathoverflow.net/questions/2437/is-there-an-image-for-you-that-epitomizes-mathematics/26796#26796 Roland Bacher 2010-06-02T07:24:06Z 2010-06-02T07:24:06Z

<p>What about the five platonic solids?</p>

http://mathoverflow.net/questions/2437/is-there-an-image-for-you-that-epitomizes-mathematics/26801#26801 John Stillwell 2010-06-02T08:31:42Z 2010-06-02T08:31:42Z

<p><img src="http://www.math.uiuc.edu/~nmd/classes/2004/191/hspace.gif" alt="hyperbolic space"></p>

http://mathoverflow.net/questions/2437/is-there-an-image-for-you-that-epitomizes-mathematics/26803#26803 Idoneal 2010-06-02T08:54:42Z 2010-06-02T08:59:53Z

<p>Here is a more mathematical rendition of Richard Kent's answer:</p> <p><a href="http://math-art.net/2007/12/03/eternal-scream-a-droste-effect/" rel="nofollow">http://math-art.net/2007/12/03/eternal-scream-a-droste-effect/</a></p>

http://mathoverflow.net/questions/2437/is-there-an-image-for-you-that-epitomizes-mathematics/26819#26819 hypercube 2010-06-02T13:20:32Z 2010-06-02T17:44:07Z

<p>A proof without words for the Pythagorean theorem (Zhou Bi Suan Jing).</p> <p><img src="http://upload.wikimedia.org/wikipedia/commons/c/c3/Chinese_pythagoras.jpg" height="450"></p>

http://mathoverflow.net/questions/2437/is-there-an-image-for-you-that-epitomizes-mathematics/26824#26824 Jon O. 2010-06-02T14:20:23Z 2010-06-02T17:36:07Z

<p>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.</p> <h2>Epi-graph</h2> <p><a href="http://mathoverflow.net/questions/3134/whats-your-favorite-equation-formula-identity-or-inequality/5680#5680" rel="nofollow">Chalk this up to Benjamin Peirce</a> &mdash;</p> <p><img src="http://mywikibiz.com/images/8/86/Benjamin_Peirce_--_e%5E%28i_pi%29.png" alt="Benjamin Peirce's script for e^(i pi)"></p>

http://mathoverflow.net/questions/2437/is-there-an-image-for-you-that-epitomizes-mathematics/26826#26826 Jon Awbrey 2010-06-02T14:22:38Z 2010-06-03T03:30:15Z

<p><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/18/D%C3%BCrer_Melancholia_I.jpg/600px-D%C3%BCrer_Melancholia_I.jpg" height="500"></p> <p><a href="http://www.metmuseum.org/toah/works-of-art/43.106.1" rel="nofollow">Some History</a></p>

http://mathoverflow.net/questions/2437/is-there-an-image-for-you-that-epitomizes-mathematics/26876#26876 Colin Pratt 2010-06-02T22:16:47Z 2010-06-02T22:16:47Z

<p>How about a lovely <a href="http://upload.wikimedia.org/wikipedia/en/f/f2/ImplicitHeart.png" rel="nofollow">heart curve</a>?</p>

http://mathoverflow.net/questions/2437/is-there-an-image-for-you-that-epitomizes-mathematics/30807#30807 Guilherme 2010-07-06T19:33:18Z 2010-07-06T20:47:56Z

<p>I really like this picture of Paul Erdos: <a href="http://www.ime.usp.br/~yoshi/palib.html" rel="nofollow">http://www.ime.usp.br/~yoshi/palib.html</a></p>

http://mathoverflow.net/questions/2437/is-there-an-image-for-you-that-epitomizes-mathematics/30810#30810 Gerhard Paseman 2010-07-06T19:45:20Z 2010-07-06T22:19:48Z

<p>... and months after this question was posted, no mention of Sidney Harris?</p> <p>Start with his "... and then a miracle occurs" and his "You want proof? I'll give you proof!" . Continue from there.</p> <p>Gerhard "That's Enough Subconscious For Today" Paseman, 2010.07.06</p> <p>The first one available for sale as prints, notecards, etc. <a href="http://www.newyorkerstore.com/All-Industry-Cartoons/I-think-you-should-be-more-explicit-here-in-step-two/invt/118181" rel="nofollow">http://www.newyorkerstore.com/All-Industry-Cartoons/I-think-you-should-be-more-explicit-here-in-step-two/invt/118181</a> </p>

http://mathoverflow.net/questions/2437/is-there-an-image-for-you-that-epitomizes-mathematics/30811#30811 Will Jagy 2010-07-06T19:53:44Z 2010-07-07T00:36:06Z

<p>There is a painting by Diego Rivera of René Paresce (1866-1937) (gotten from web address <a href="http://www.vf.utwente.nl/~jagersaa/D_R.html" rel="nofollow">http://www.vf.utwente.nl/~jagersaa/D_R.html</a>)</p> <p><img src="http://img88.imageshack.us/img88/8959/elmatematico.jpg" alt="alt text"> El Matemático</p>

http://mathoverflow.net/questions/2437/is-there-an-image-for-you-that-epitomizes-mathematics/30839#30839 Jose Brox 2010-07-07T00:31:01Z 2010-07-07T00:31:01Z

<p><a href="http://www2.memenet.or.jp/~keizo/0005.htm" rel="nofollow">Keizo Ushio's topological "impossible" sculptures on stone</a></p> <p><img src="http://www2.memenet.or.jp/~keizo/060830017s.jpg" height="450"> </p>

http://mathoverflow.net/questions/2437/is-there-an-image-for-you-that-epitomizes-mathematics/30840#30840 Jose Brox 2010-07-07T00:43:42Z 2010-07-22T13:06:17Z

<p>For category theory, from <em>Abstract and Concrete Categories: The joy of cats</em>, by Adámek, Herrlich and Strecker, page 12:</p> <p>(http://katmat.math.uni-bremen.de/acc/acc.pdf) </p> <p><img src="http://img638.imageshack.us/img638/6223/joyofcats.jpg" height="450"> </p> <blockquote> <p>Categorists have developed a symbolism that allows one quickly to visualize quite complicated facts by means of diagrams.</p> </blockquote> <p>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.</p>

http://mathoverflow.net/questions/2437/is-there-an-image-for-you-that-epitomizes-mathematics/32451#32451 ardentMirage 2010-07-19T06:53:44Z 2010-07-19T06:53:44Z

<p>Voronoi diagrams and their respective Delaunay triangulations.</p>

http://mathoverflow.net/questions/2437/is-there-an-image-for-you-that-epitomizes-mathematics/32953#32953 babubba 2010-07-22T13:42:28Z 2010-07-22T13:42:28Z

<p><img src="http://abstrusegoose.com/strips/this_is_what_my_room_looks_like_when_i_draw.PNG"> </p>