The logo of the IHES http://www.ihes.fr/jsp/site/Portal.jsp (upper left) is lovely, but what exactly does represent mathematically?
(There's a slightly larger version at http://www.ihes.fr/~abbes/Ogus/IHES.jpg.)
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3$\begingroup$ Great question! I've wondered this myself several times over the years. $\endgroup$– KConradCommented Jan 28, 2016 at 22:41
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1$\begingroup$ Oh I've always thought it was some sort of (unreadable) monogram of the letters "IHES", I'm delighted it has some actual mathematical meaning :) $\endgroup$– QfwfqCommented Jan 28, 2016 at 23:04
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$\begingroup$ Why the question was not asked to Alexander Grothendieck ? That is, unfortunately, too late now ! $\endgroup$– Al-AmraniCommented Feb 13, 2016 at 16:32
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2 Answers
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the artist who recreated this knot in bronze has much information on his web site, and sells a replica here (proceeds to IHES)
answered Jan 28, 2016 at 21:27
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4$\begingroup$ The artist (Alex Feingold) writes "In Spring 2014 I made a bronze sculpture based on the logo of the Institut Hautes des Etudes Scientifique...". If I interpret this correctly, the logo came first (by many years, I think), and is not the work of Feingold. $\endgroup$ Commented Jan 28, 2016 at 21:50
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3$\begingroup$ The logo goes back pretty far: here it is on the cover of a book published in 1961. $\endgroup$ Commented Jan 28, 2016 at 22:00
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1$\begingroup$ I saw this webpage, but I couldn't discern specific content. There are several knots shown on this page: at the top, there are the Mobius figure 8 knot as well as a tubular (3,5) torus knot. These are different knots, and it is not claimed that the IHES knot is either of these. Can you help to clarify why this website answers my question? JV $\endgroup$ Commented Jan 29, 2016 at 0:54
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(I think the thing is essentially an "open" trefoil.) The more-or-less flattened images of such knots or braidings/pleatings have appeared in Islamic decorative art from ~1000 years ago, and Celtic art from ~2000. I do not have images handy, and the ones I could find easily might be in copyrighted physical sources, etc. I recall reading somewhere that, although there was no prohibition of images in Celtic art (unlike Islamic), there was a fascination with (rather cursive) geometric patterns, knots, etc.
answered Jan 28, 2016 at 23:41
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$\begingroup$ How do you see this? Does it matter how you connect the ends (at oo)? JV $\endgroup$ Commented Jan 29, 2016 at 0:55
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$\begingroup$ @JohnVoight, yes, I think some correct choices have to be made "at infinity" to make this be a literal trefoil. Due to some personal interests long ago, somehow it appears "immediate" to me that this thing is "in that ballpark". Perhaps the question is why an asymmetry was apparently deliberately chosen, in contrast to the potential/natural symmetrical version almost always chosen in those old art-situations. Sure, a repeating pattern needs more symmetry... and a one-off might seem to want asymmetry. $\endgroup$ Commented Jan 29, 2016 at 0:59
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$\begingroup$ ... and, just for context, I think that in those years the ideas of "catastrophe theory" and "classification of singularities" were newish, had great cachet, and we know what that might lead to, PR-wise. :) $\endgroup$ Commented Jan 29, 2016 at 1:01