Mathematical ideas named after places - MathOverflow [closed]

Mathematical ideas named after places

2011-05-11T14:40:13Z

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?

Answer by Or Zuk for Mathematical ideas named after places

2011-05-11T14:46:17Z

Manhattan distance

Chinese restaurant process

Answer by Nate Eldredge for Mathematical ideas named after places

2011-05-11T14:51:27Z

Toronto space.

Answer by Michael Renardy for Mathematical ideas named after places

2011-05-11T14:55:02Z

The Chinese remainder theorem.

The Mexican hat wavelet.

Arabic (or Roman) numerals.

Answer by Bruce Westbury for Mathematical ideas named after places

2011-05-11T14:59:18Z

Dubrovnik polynomial

Answer by Harun Šiljak for Mathematical ideas named after places

2011-05-11T14:59:37Z

Japanese theorem for cyclic polygons

Monte Carlo method

Hungarian Algorithm

Answer by Bruce Westbury for Mathematical ideas named after places

2011-05-11T14:59:59Z

Nottingham group

Answer by Abdelmalek Abdesselam for Mathematical ideas named after places

2011-05-11T15:04:00Z

The Aarhus integral of rational homology 3-spheres http://arxiv.org/abs/q-alg/9706004

Answer by darij grinberg for Mathematical ideas named after places

2011-05-11T15:05:43Z

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).

Answer by Pieter Naaijkens for Mathematical ideas named after places

2011-05-11T15:06:55Z

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.

Answer by Nate Eldredge for Mathematical ideas named after places

2011-05-11T15:13:09Z

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.

Answer by Tom Church for Mathematical ideas named after places

2011-05-11T15:15:49Z

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)

Answer by Gerald Edgar for Mathematical ideas named after places

2011-05-11T15:17:31Z

Königsberg bridge problem

Answer by Michael Kissner for Mathematical ideas named after places

2011-05-11T15:21:52Z

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

Midpoint Method

Answer by Pietro Majer for Mathematical ideas named after places

2011-05-11T15:25:00Z

The Erlangen program.

Answer by Margaret Friedland for Mathematical ideas named after places

2011-05-11T15:44:32Z

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.

Answer by Margaret Friedland for Mathematical ideas named after places

2011-05-11T15:51:28Z

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

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

Answer by Peter Shor for Mathematical ideas named after places

2011-05-11T15:54:46Z

Las Vegas algorithms.

Answer by Robert Israel for Mathematical ideas named after places

2011-05-11T16:41:20Z

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

Answer by Tom Goodwillie for Mathematical ideas named after places

2011-05-11T17:45:45Z

universal example?

Answer by Matt Ollis for Mathematical ideas named after places

2011-05-11T18:42:53Z

The Oberwolfach Problem and the Hamilton-Waterloo Problem

Answer by none for Mathematical ideas named after places

2011-05-11T18:53:10Z

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).

Answer by none for Mathematical ideas named after places

2011-05-11T19:34:43Z

Look at http://blogs.ethz.ch/kowalski/2010/08/19/what-countries-are-mathematical-objects/

Answer by Andreas Blass for Mathematical ideas named after places

2011-05-11T19:50:20Z

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)

Answer by Andreas Blass for Mathematical ideas named after places

2011-05-11T19:59:18Z

The Conway-Paterson-Moscow theorem

Answer by Michael Hardy for Mathematical ideas named after places

2011-05-11T20:05:17Z

"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

Answer by Matt Ollis for Mathematical ideas named after places

2011-05-11T20:15:52Z

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

Answer by Goldstern for Mathematical ideas named after places

2011-05-11T21:38:39Z

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

Answer by Juris Steprans for Mathematical ideas named after places

2011-05-11T21:48:40Z

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

Answer by Mark Lewko for Mathematical ideas named after places

2011-05-11T22:52:30Z

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).

Answer by Rob Harron for Mathematical ideas named after places

2011-05-12T00:54:12Z

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 $\mathbf{Q}$).

Answer by Rob Harron for Mathematical ideas named after places

2011-05-12T01:04:14Z

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.

Answer by Allen Knutson for Mathematical ideas named after places

2011-05-12T02:07:56Z

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

Answer by David Roberts for Mathematical ideas named after places

2011-05-12T03:06:44Z

Topos (sorry!)

Answer by Jeremy Brazas for Mathematical ideas named after places

2011-05-12T03:37:03Z

The Warsaw circle is a motivating example in shape theory.

Answer by Jesus Martinez Garcia for Mathematical ideas named after places

2011-05-12T04:05:45Z

Italian Algebraic Algebraic Geometry

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

Answer by Matt G for Mathematical ideas named after places

2011-05-12T04:53:30Z

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

Answer by Martin Schwarz for Mathematical ideas named after places

2011-05-12T05:50:43Z

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."

Answer by Justin Lanier for Mathematical ideas named after places

2011-05-12T05:58:26Z

The Delian problem.

Answer by Gerald Edgar for Mathematical ideas named after places

2011-05-12T13:15:36Z

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

Answer by Andreas Blass for Mathematical ideas named after places

2011-05-12T14:01:08Z

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

Answer by Or Zuk for Mathematical ideas named after places

2011-05-12T15:53:43Z

Two more are:

Egyptian fractions

Canadian Traveler Problem

Answer by Marty for Mathematical ideas named after places

2011-05-12T16:19:34Z

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

Answer by pradip Keskar for Mathematical ideas named after places

2011-05-12T17:18:36Z

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?)

Answer by joker for Mathematical ideas named after places

2011-05-12T18:14:44Z

outer space