Question

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 1

universal example?

Answer 2

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 3

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 4

Königsberg bridge problem

Answer 5

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 6

Toronto space.

Answer 7

Japanese theorem for cyclic polygons

Monte Carlo method

Hungarian Algorithm

Answer 8

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 9

Manhattan distance

Chinese restaurant process

Answer 10

Topos (sorry!)

Answer 11

The Chinese remainder theorem.

The Mexican hat wavelet.

Arabic (or Roman) numerals.

Answer 12

The Erlangen program.

Answer 13

"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 14

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

Answer 15

Nottingham group

Answer 16

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

Midpoint Method

Answer 17

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 18

Las Vegas algorithms.

Answer 19

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 20

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

Answer 21

Two more are:

Egyptian fractions

Canadian Traveler Problem

Answer 22

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

Answer 23

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 24

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 25

The Delian problem.

Answer 26

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

Answer 27

Dubrovnik polynomial

Answer 28

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

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

Answer 29

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

Answer 30

The Warsaw circle is a motivating example in shape theory.