Mathematical ideas named after places - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-19T21:22:48Z http://mathoverflow.net/feeds/question/64617 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places Mathematical ideas named after places Oliver 2011-05-11T14:40:13Z 2011-05-12T18:33:39Z <p>This question is quite unimportant, so feel free to close if you think it is inappropriate.</p> <p>I've been thinking about how mathematicians come up with names for the ideas/objects they study, and how that differs from the practices of people in other fields.</p> <p>It seems that almost always we do one of two things: 1) we pick a name that describes some feature of the object (sometimes not very well, e.g. flat modules, sets of second category), or 2) we name it after a person (who may or may not have studied that object).</p> <p>Very rarely we name something after a place. (This is much more common in other fields.) I can think of only 3 examples:</p> <p>*Japanese rings</p> <p>*Polish spaces</p> <p>*Tropical geometry</p> <p>Does anyone know of any other examples in mathematics?</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64618#64618 Answer by Or Zuk for Mathematical ideas named after places Or Zuk 2011-05-11T14:46:17Z 2011-05-11T14:46:17Z <p>Manhattan distance</p> <p>Chinese restaurant process</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64621#64621 Answer by Nate Eldredge for Mathematical ideas named after places Nate Eldredge 2011-05-11T14:51:27Z 2011-05-11T14:51:27Z <p><a href="http://en.wikipedia.org/wiki/Toronto_space" rel="nofollow">Toronto space</a>.</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64622#64622 Answer by Michael Renardy for Mathematical ideas named after places Michael Renardy 2011-05-11T14:55:02Z 2011-05-11T15:23:57Z <p>The Chinese remainder theorem.</p> <p>The Mexican hat wavelet.</p> <p>Arabic (or Roman) numerals.</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64624#64624 Answer by Bruce Westbury for Mathematical ideas named after places Bruce Westbury 2011-05-11T14:59:18Z 2011-05-11T14:59:18Z <p>Dubrovnik polynomial</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64625#64625 Answer by Harun Šiljak for Mathematical ideas named after places Harun Šiljak 2011-05-11T14:59:37Z 2011-05-11T14:59:37Z <p><a href="http://en.wikipedia.org/wiki/Japanese_theorem_for_cyclic_polygons" rel="nofollow">Japanese theorem for cyclic polygons</a></p> <p><a href="http://en.wikipedia.org/wiki/Monte_Carlo_method" rel="nofollow">Monte Carlo method</a></p> <p><a href="http://en.wikipedia.org/wiki/Hungarian_algorithm" rel="nofollow">Hungarian Algorithm</a></p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64626#64626 Answer by Bruce Westbury for Mathematical ideas named after places Bruce Westbury 2011-05-11T14:59:59Z 2011-05-11T14:59:59Z <p>Nottingham group</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64627#64627 Answer by Abdelmalek Abdesselam for Mathematical ideas named after places Abdelmalek Abdesselam 2011-05-11T15:04:00Z 2011-05-11T15:04:00Z <p>The Aarhus integral of rational homology 3-spheres <a href="http://arxiv.org/abs/q-alg/9706004" rel="nofollow">http://arxiv.org/abs/q-alg/9706004</a></p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64630#64630 Answer by darij grinberg for Mathematical ideas named after places darij grinberg 2011-05-11T15:05:43Z 2011-05-11T15:05:43Z <p>Aarhus integral, Polish notation, English/French notation (or something like that - it refers to different ways to draw Ferrers diagrams - or was it English/Italian?), Tower of Hanoi, Russian constructivism (Russian school of intuitionism).</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64631#64631 Answer by Pieter Naaijkens for Mathematical ideas named after places Pieter Naaijkens 2011-05-11T15:06:55Z 2011-05-11T15:06:55Z <p>The French Railroad metric: if $(X,d)$ is a metric space, and $p \in X$, define $d_R(x,y) = 0$ if $x = y$ and $d_R(x,y) = d(x,p) + d(y,p)$ otherwise. Apparently named so because almost every train in France goes trough Paris.</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64633#64633 Answer by Nate Eldredge for Mathematical ideas named after places Nate Eldredge 2011-05-11T15:13:09Z 2011-05-11T15:13:09Z <p>Perhaps a stretch, but in mathematical finance it is traditional to name option styles after places. American and European are the most common, but <a href="http://en.wikipedia.org/wiki/Option_style" rel="nofollow">http://en.wikipedia.org/wiki/Option_style</a> also lists Bermudan, Canary, Asian, Russian, Israeli, and Parisian.</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64634#64634 Answer by Tom Church for Mathematical ideas named after places Tom Church 2011-05-11T15:15:49Z 2011-05-11T15:15:49Z <p><a href="http://en.wikipedia.org/wiki/Quasigroup#Loop" rel="nofollow">Loops</a> (aka quasigroups with identity):</p> <blockquote> <p>It was at this point that the terminology of quasigroup theory underwent a historic change. It became apparent that it was necessary to distinguish between two classes of quasigroups: those with and those without an identity element. A new name was needed to designate the system with identity. This occurred around 1942, among people of Albert’s circle in Chicago, who coined the word “loop” after the Chicago Loop. For Chicago locals, the term “Loop” designated the main business area and the elevated train that literally made a loop around this part of the city.</p> </blockquote> <p>(taken from <a href="http://www.emis.de/journals/CMUC/pdf/cmuc0002/pflug.pdf" rel="nofollow">Historical notes on loop theory</a>, by Hala Orlik Pflugfelder)</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64635#64635 Answer by Gerald Edgar for Mathematical ideas named after places Gerald Edgar 2011-05-11T15:17:31Z 2011-05-11T15:53:17Z <p>Königsberg bridge problem</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64636#64636 Answer by Michael Kissner for Mathematical ideas named after places Michael Kissner 2011-05-11T15:21:52Z 2011-05-11T15:21:52Z <p>(Non-Serious) Well, depending on how far you wish to stretch the term "place"</p> <p><a href="http://en.wikipedia.org/wiki/Midpoint_method" rel="nofollow">Midpoint Method</a></p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64639#64639 Answer by Pietro Majer for Mathematical ideas named after places Pietro Majer 2011-05-11T15:25:00Z 2011-05-11T15:25:00Z <p>The <a href="http://en.wikipedia.org/wiki/Erlangen_program" rel="nofollow">Erlangen program</a>.</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64642#64642 Answer by Margaret Friedland for Mathematical ideas named after places Margaret Friedland 2011-05-11T15:44:32Z 2011-05-11T15:44:32Z <p>The Hawaiian earring:</p> <p><a href="http://en.wikipedia.org/wiki/Hawaiian_earring" rel="nofollow">http://en.wikipedia.org/wiki/Hawaiian_earring</a></p> <p>The space H is homeomorphic to the one-point compactification of the union of a countably infinite family of open intervals. </p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64645#64645 Answer by Margaret Friedland for Mathematical ideas named after places Margaret Friedland 2011-05-11T15:51:28Z 2011-05-11T15:51:28Z <p>The Cracovian algebra- of matrices with some non-associative multiplication</p> <p><a href="http://en.wikipedia.org/wiki/Cracovian" rel="nofollow">http://en.wikipedia.org/wiki/Cracovian</a></p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64647#64647 Answer by Peter Shor for Mathematical ideas named after places Peter Shor 2011-05-11T15:54:46Z 2011-05-11T16:02:19Z <p><a href="http://en.wikipedia.org/wiki/Las_Vegas_algorithm" rel="nofollow">Las Vegas algorithms</a>. </p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64655#64655 Answer by Robert Israel for Mathematical ideas named after places Robert Israel 2011-05-11T16:41:20Z 2011-05-11T16:41:20Z <p>Swiss cheese (one type in complex analysis, another in cosmology)</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64667#64667 Answer by Tom Goodwillie for Mathematical ideas named after places Tom Goodwillie 2011-05-11T17:45:45Z 2011-05-11T17:45:45Z <p>universal example?</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64671#64671 Answer by Matt Ollis for Mathematical ideas named after places Matt Ollis 2011-05-11T18:42:53Z 2011-05-11T18:42:53Z <p><a href="http://www.spsu.edu/math/holliday/Oberwolfachs.html" rel="nofollow">The Oberwolfach Problem and the Hamilton-Waterloo Problem</a></p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64674#64674 Answer by none for Mathematical ideas named after places none 2011-05-11T18:53:10Z 2011-05-11T18:53:10Z <p>There's a Four Russians algorithm in computer science. I don't remember what the algorithm did or who the four Russians were, but the description "named after the cardinality and nationality of its inventors" stuck in my mind. I think that description is from the first edition of Principles of Compiler Design (aka the Green Dragon Book) by Aho and Ullman. (Googling finds some descriptions of the algorithm).</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64680#64680 Answer by none for Mathematical ideas named after places none 2011-05-11T19:34:43Z 2011-05-11T19:34:43Z <p>Look at <a href="http://blogs.ethz.ch/kowalski/2010/08/19/what-countries-are-mathematical-objects/" rel="nofollow">http://blogs.ethz.ch/kowalski/2010/08/19/what-countries-are-mathematical-objects/</a></p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64681#64681 Answer by Andreas Blass for Mathematical ideas named after places Andreas Blass 2011-05-11T19:50:20Z 2011-05-11T19:50:20Z <p>anarboricity of graphs (named in honor of the city of Ann Arbor by Frank Harary, but also having something to do with non-trees (http://mathworld.wolfram.com/Anarboricity.html)</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64683#64683 Answer by Andreas Blass for Mathematical ideas named after places Andreas Blass 2011-05-11T19:59:18Z 2011-05-12T17:21:00Z <p>The <a href="http://www.tanyakhovanova.com/BlogStuff/Conway/Headache.pdf" rel="nofollow">Conway-Paterson-Moscow theorem</a></p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64685#64685 Answer by Michael Hardy for Mathematical ideas named after places Michael Hardy 2011-05-11T20:05:17Z 2011-05-11T20:05:17Z <p>"The Roman surface (so called because Jakob Steiner was in Rome when he thought of it) is a self-intersecting mapping of the real projective plane into three-dimensional space, with an unusually high degree of symmetry."</p> <p><a href="http://en.wikipedia.org/wiki/Roman_surface" rel="nofollow">http://en.wikipedia.org/wiki/Roman_surface</a></p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64689#64689 Answer by Matt Ollis for Mathematical ideas named after places Matt Ollis 2011-05-11T20:15:52Z 2011-05-11T20:15:52Z <p><a href="http://books.google.com/books?id=Ey8iXKkQpDkC&amp;pg=PA80&amp;lpg=PA80&amp;dq=%22italian+square%22+latin+tuscan&amp;source=bl&amp;ots=AzcDDPTqUk&amp;sig=v9GIP3l1wKs6Yu0oXXnLQfxbJlQ&amp;hl=en&amp;ei=7u3KTd6uNoragQeLr5HeBQ&amp;sa=X&amp;oi=book_result&amp;ct=result&amp;resnum=1&amp;ved=0CCQQ6AEwAA#v=onepage&amp;q=%22italian%20square%22%20latin%20tuscan&amp;f=false" rel="nofollow">Italian squares</a> which include Latin squares, Tuscan squares, Roman squares, Florentine squares and Vatican squares as special cases.</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64697#64697 Answer by Goldstern for Mathematical ideas named after places Goldstern 2011-05-11T21:38:39Z 2011-05-11T21:38:39Z <p>In computer science, the Vienna Definition Language, or the related Vienna Development Method. (A tool for definining program semantics).</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64699#64699 Answer by Juris Steprans for Mathematical ideas named after places Juris Steprans 2011-05-11T21:48:40Z 2011-05-11T21:48:40Z <p>While visiting the city in question, Nesetril defined an ultrafilter he called a Riga P-point.</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64705#64705 Answer by Mark Lewko for Mathematical ideas named after places Mark Lewko 2011-05-11T22:52:30Z 2011-05-11T23:02:45Z <p>Two amusing examples from distributed computing are:</p> <p>The <a href="http://en.wikipedia.org/wiki/Byzantine_fault_tolerance" rel="nofollow">Bysentian generals problem</a>. The problem asks for an algorithm that allows a large number of processors to reach a consensus on something (say a bit value) when some of the processors behave in a malicious way. The original paper motivated the problem with a fictional account of Byzantine generals trying to coordinate a joint attack. There's also a related "Chinese Generals Problem".</p> <p><a href="http://en.wikipedia.org/wiki/Paxos_%28computer_science%29" rel="nofollow">Paxos algorithms</a>. This is a family of algorithms that also allow a number of participants to reach a consensus. These were introduced by Leslie Lamport in paper written as a story about the downfall of an ancient Parliament on the (fictional) island of Paxos. The story ends when the parliament inadvertently restricts membership to dead sailors which, of course, can then not be corrected. As you can read about <a href="http://research.microsoft.com/users/lamport/pubs/pubs.html#lamport-paxos" rel="nofollow">here</a>, the novel exposition of the paper led to a very delayed publication of what has since been recognized as an important result (and is <a href="http://en.wikipedia.org/wiki/Paxos_%28computer_science%29#Production_use_of_Paxos" rel="nofollow">reportedly used</a> in Google, Microsoft and IBM products).</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64720#64720 Answer by Rob Harron for Mathematical ideas named after places Rob Harron 2011-05-12T00:54:12Z 2011-05-12T00:54:12Z <p>K. Barré-Sirieix, G. Diaz, F. Gramain and G. Philibert proved the Mahler–Manin conjecture in St-Étienne, so the result is now called the "Theorem of St-Étienne" (see Hida's book <em>Hilbert modular forms and Iwasawa theory</em>, p. 62). The theorem states that the Tate parameter of an elliptic curve $E_{/\overline{\mathbf{Q}}}$ with split, multiplicative reduction is transcendental (over $\mathbf{Q}$).</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64721#64721 Answer by Rob Harron for Mathematical ideas named after places Rob Harron 2011-05-12T01:04:14Z 2011-05-12T01:04:14Z <p>There is Colmez's "Montréal functor" which is part of the $p$-adic local Langlands business. The story is he introduced it in a lecture in Montréal.</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64729#64729 Answer by Allen Knutson for Mathematical ideas named after places Allen Knutson 2011-05-12T02:07:56Z 2011-05-12T18:33:39Z <p>The <a href="http://en.wikipedia.org/wiki/Atiyah-Bott_fixed-point_theorem#History" rel="nofollow">Woods Hole</a> formula, as that is where there was a race to prove this Riemann-Roch-Lefschetz formula.</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64732#64732 Answer by David Roberts for Mathematical ideas named after places David Roberts 2011-05-12T03:06:44Z 2011-05-12T03:06:44Z <p><a href="http://en.wiktionary.org/wiki/topos" rel="nofollow">Topos</a> (sorry!)</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64735#64735 Answer by Jeremy Brazas for Mathematical ideas named after places Jeremy Brazas 2011-05-12T03:37:03Z 2011-05-12T03:37:03Z <p>The <a href="http://ncatlab.org/nlab/show/Warsaw+circle" rel="nofollow">Warsaw circle</a> is a motivating example in shape theory.</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64737#64737 Answer by Jesus Martinez Garcia for Mathematical ideas named after places Jesus Martinez Garcia 2011-05-12T04:05:45Z 2011-05-12T04:05:45Z <p>Italian Algebraic Algebraic Geometry</p> <p>One that is not but I used to think so: Catalan number :)</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64743#64743 Answer by Matt G for Mathematical ideas named after places Matt G 2011-05-12T04:53:30Z 2011-05-12T04:53:30Z <p>The semi-symmetric <a href="http://en.wikipedia.org/wiki/Ljubljana_graph" rel="nofollow">Ljubljana graph</a>, from algebraic graph theory. </p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64748#64748 Answer by Martin Schwarz for Mathematical ideas named after places Martin Schwarz 2011-05-12T05:50:43Z 2011-05-12T05:50:43Z <p>Black Cow Factor in <i>Optimal Cloning of Pure States</i> by R.F. Werner (arXiv:quant-ph/9804001). He writes,</p> <p> "The reason for this terminology is that it plays an important role in discussions of the cloning problem started by Chiara Machiavello and Artur Ekert at the Black Cow Café in Croton-on-Hudson, NY, and further clarified in collaboration with Dagmar Bruß [BEM]. I learned about this line of argument from a set of “Black Cow Notes” by Nicolas Gisin and Sandu Popescu." </p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64749#64749 Answer by Justin Lanier for Mathematical ideas named after places Justin Lanier 2011-05-12T05:58:26Z 2011-05-12T05:58:26Z <p>The <a href="http://en.wikipedia.org/wiki/Doubling_the_cube" rel="nofollow">Delian problem</a>.</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64780#64780 Answer by Gerald Edgar for Mathematical ideas named after places Gerald Edgar 2011-05-12T13:15:36Z 2011-05-12T13:25:17Z <p>The Scottish Book, named as you know for the <a href="http://en.wikipedia.org/wiki/Scottish_Caf%25C3%25A9" rel="nofollow">Scottish Cafe</a> in Lwow where Banach and his friends would meet and discuss mathematics.</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64789#64789 Answer by Andreas Blass for Mathematical ideas named after places Andreas Blass 2011-05-12T14:01:08Z 2011-05-12T14:01:08Z <p>The Arctic Circle Theorem (http://arxiv.org/abs/math/9801068)</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64803#64803 Answer by Or Zuk for Mathematical ideas named after places Or Zuk 2011-05-12T15:53:43Z 2011-05-12T15:53:43Z <p>Two more are:</p> <p>Egyptian fractions</p> <p>Canadian Traveler Problem</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64807#64807 Answer by Marty for Mathematical ideas named after places Marty 2011-05-12T16:19:34Z 2011-05-12T16:19:34Z <p>Nowhere differentiable: named for Ainsworth, Nebraska, I believe.</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64818#64818 Answer by pradip Keskar for Mathematical ideas named after places pradip Keskar 2011-05-12T17:18:36Z 2011-05-12T17:18:36Z <p>What if named after a person who derives his name from a place?</p> <p>e.g. Hamburger expansion</p> <p>How about moonshine? If moon is allowed, why not Stone (as in Stone-Weierstrass)? And then Stein manifold, Einstein metric, Eisenstein criterion? </p> <p>There are also buildings and chambers and apartments of Jacques Tits. (BTW, is the last word of previous sentence a place?)</p> http://mathoverflow.net/questions/64617/mathematical-ideas-named-after-places/64824#64824 Answer by joker for Mathematical ideas named after places joker 2011-05-12T18:14:44Z 2011-05-12T18:14:44Z <p><a href="http://en.wikipedia.org/wiki/Out%28Fn%29" rel="nofollow">outer space</a></p>