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?

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
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    +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
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    A matter of timing, I suspect. The crowd is just not in the mood. – Tom Goodwillie May 11 '11 at 21:05
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    -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

44 Answers 44

Loops (aka quasigroups with identity):

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.

(taken from Historical notes on loop theory, by Hala Orlik Pflugfelder)

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    Ah! Now this is a piece of knowledge I've been (not very actively...) looking for years :) – Mariano Suárez-Álvarez May 11 '11 at 15:56

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.

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    also called "la distance SNCF" – Abdelmalek Abdesselam May 11 '11 at 15:14
  • also called the "Washington DC metric" – Gerald Edgar May 11 '11 at 15:48
  • and the "British Rail metric" – Chris Eagle May 11 '11 at 16:35
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    Why is this the Washington DC metric? (Washington is not nearly as central in the US as London is in the UK or Paris is in France...) – Michael Lugo May 11 '11 at 22:26
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    @Michael Probably because of the layout of the DC Metro--to move between two outer locations (say Shady Grove and Vienna/Fairfax), one often has to travel to the center of the District along the way. – Justin Lanier May 12 '11 at 5:50

The Hawaiian earring:

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

The space H is homeomorphic to the one-point compactification of the union of a countably infinite family of open intervals.

Topos (sorry!)

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

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
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    Yes, the horrors. Children, cover your ears. – Todd Trimble May 12 '11 at 10:27
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    I agree with Todd, especially if the children also stay away from the television. – Andreas Blass May 12 '11 at 13:57

Manhattan distance

Chinese restaurant process

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    Is the Chinese restaurant process named after the place "China", or the place "Chinese restaurant"? – Michael Lugo May 11 '11 at 22:11
  • It's named after the custom of table-sharing in Chinese restaurants, which in turn are named after the place. – Michael Hardy May 12 '11 at 3:51
  • Yes, interestingly there is also a variation called the 'Indian buffet process' – Or Zuk May 12 '11 at 12:59
  • I don't really like Indian food, so I never understood why the Indian buffet process is so-called. – Michael Lugo May 12 '11 at 16:11
  • The CRP is named after a particular restaurant in Berkeley. – Ben Wieland Jun 8 '11 at 14:55

The Chinese remainder theorem.

The Mexican hat wavelet.

Arabic (or Roman) numerals.

"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

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

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    And there is the Syracusan Square which is a special case of Graeco-Latin square ... – ogerard Feb 8 '13 at 20:29

(Non-Serious) Well, depending on how far you wish to stretch the term "place"

Midpoint Method

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    More non-serious (read: "wrong") answers: Hessian matrix (Stone-)Czech compactification, Wiener process. – Goldstern May 11 '11 at 23:04
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    Another non-serious answer: I was born in an Australian town called Singleton; the population of Singleton is larger than $1$, so it is a rather misleading name. – Philip Brooker May 12 '11 at 0:54

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

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).

  • There's also a "Russian notation" for Ferrers diagrams, although I can't remember what it is. – Michael Lugo May 12 '11 at 4:21

Las Vegas algorithms.

  • Also: Monte Carlo algorithms and Atlantic City algorithms. – Michael Lugo May 11 '11 at 22:10

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.

  • Dear Rob, I'm glad you mentioned this; it was the first example that came to my mind! And yes, he introduced it in a fantastic lecture in Montreal. Best wishes, Matt – Emerton May 13 '11 at 3:20

Two more are:

Egyptian fractions

Canadian Traveler Problem

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

Perhaps a stretch, but in mathematical finance it is traditional to name option styles after places. American and European are the most common, but http://en.wikipedia.org/wiki/Option_style also lists Bermudan, Canary, Asian, Russian, Israeli, and Parisian.

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

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

Dubrovnik polynomial

  • Care to explain? – darij grinberg May 11 '11 at 15:01
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    A knot polynomial defined by Kaufman using skein relations while at a conference in Dubrovnik (or so I understand). – Bruce Westbury May 11 '11 at 16:10
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    What if the conference had been in Split? – Tom Goodwillie May 12 '11 at 0:16

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

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

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

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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