# Mathematical ideas named after places [closed]

This question is quite unimportant, so feel free to close if you think it is inappropriate.

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.

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).

Very rarely we name something after a place. (This is much more common in other fields.) I can think of only 3 examples:

*Japanese rings

*Polish spaces

*Tropical geometry

Does anyone know of any other examples in mathematics?

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## closed as no longer relevant by Daniel Litt, Oliver, Dan Petersen, Franz Lemmermeyer, Ben Webster♦May 12 '11 at 18:30

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Yet another empty question... – SNd May 11 '11 at 15:01
+1, I think this is at least a little amusing. I must admit, I don't understand why this question has been received poorly (as indicated by the number of votes on SNd's comment, and the number of upvotes on the question itself) when other "empty questions," such as the one about jokes, get over 30 positive votes. What am I missing? – Eric Naslund May 11 '11 at 19:54
A matter of timing, I suspect. The crowd is just not in the mood. – Tom Goodwillie May 11 '11 at 21:05
-1. I voted this down because I don't see the value in the question being open (just go to Emmanuel's blog post if you're interested in this). The question is just taking up valuable real estate on the front page as it gets continually bumped by what are generally low quality answers. (and even the OP claims the question is unimportant!) – Peter McNamara May 12 '11 at 5:01

The Woods Hole formula, as that is where there was a race to prove this Riemann-Roch-Lefschetz formula.

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What if named after a person who derives his name from a place?

e.g. Hamburger expansion

How about moonshine? If moon is allowed, why not Stone (as in Stone-Weierstrass)? And then Stein manifold, Einstein metric, Eisenstein criterion?

There are also buildings and chambers and apartments of Jacques Tits. (BTW, is the last word of previous sentence a place?)

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Why focus on Stone? Surely Weierstrass got his name from the Weierstrasse, on which one of his ancestors happened to live. But I am afraid this new twist opens up a potential avalanche of responses, and I would rather discourage pursuing it. – Michael Renardy May 12 '11 at 17:24

Nowhere differentiable: named for Ainsworth, Nebraska, I believe.

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Two more are:

Egyptian fractions

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The Arctic Circle Theorem (http://arxiv.org/abs/math/9801068)

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The Scottish Book, named as you know for the Scottish Cafe in Lwow where Banach and his friends would meet and discuss mathematics.

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Black Cow Factor in Optimal Cloning of Pure States by R.F. Werner (arXiv:quant-ph/9804001). He writes,

"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."

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The semi-symmetric Ljubljana graph, from algebraic graph theory.

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Italian Algebraic Algebraic Geometry

One that is not but I used to think so: Catalan number :)

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The Warsaw circle is a motivating example in shape theory.

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Topos (sorry!)

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Don't apologize: this is an excellent answer! – Georges Elencwajg May 12 '11 at 7:31

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.

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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 Hilbert modular forms and Iwasawa theory, p. 62). The theorem states that the Tate parameter of an elliptic curve $E_{/\overline{\mathbf{Q}}}$ with split, multiplicative reduction is transcendental (over $\mathbf{Q}$).

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Two amusing examples from distributed computing are:

The Bysentian generals problem. 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".

Paxos algorithms. 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 here, the novel exposition of the paper led to a very delayed publication of what has since been recognized as an important result (and is reportedly used in Google, Microsoft and IBM products).

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While visiting the city in question, Nesetril defined an ultrafilter he called a Riga P-point.

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In computer science, the Vienna Definition Language, or the related Vienna Development Method. (A tool for definining program semantics).

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Italian squares which include Latin squares, Tuscan squares, Roman squares, Florentine squares and Vatican squares as special cases.

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"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."

http://en.wikipedia.org/wiki/Roman_surface

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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)

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This mixes a Greek prefix with a Latin word, and is therefore an abomination (like "television" and "automobile"). – Michael Hardy May 12 '11 at 3:56
Yes, the horrors. Children, cover your ears. – Todd Trimble May 12 '11 at 10:27
I agree with Todd, especially if the children also stay away from the television. – Andreas Blass May 12 '11 at 13:57
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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).

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For the sake of completeness, the four Russians were V.L. Arlazarov, E.A. Dinic, M.A. Kronrod and I.A. Faradjev, authors of the paper On economical finding of transitive closure of a graph. Dokl. Akad. Nauk SSSR 194 (1970). – Harun Šiljak May 11 '11 at 20:07
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universal example?

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Swiss cheese (one type in complex analysis, another in cosmology)

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Don't forget the Swiss cheese operad. – Todd Trimble May 12 '11 at 1:20
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Königsberg bridge problem

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The Cracovian algebra- of matrices with some non-associative multiplication

http://en.wikipedia.org/wiki/Cracovian

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