TITLE: Retracted Mathematics Papers
QUESTION [13 upvotes]: Can anyone cite an example of a mathematics paper that has been retracted?
It is said that on the order of 100,000 new theorems enter the mathematics literature every year. For a number of reasons including hyper-specialization and demands on referee resources it is, in my view, unlikely that all their proofs are correct.  Yet it seems no explicit effort is made to clean the literature.  False theorms float downstream along with the true ones, available for citation and use in constructing yet further theorems.
Thanks for any insight.
Cheers, Scott

REPLY [18 votes]: You have to notice that many of those theorems are dead-ends. They'll either not be used at all, or be superseded by a better one. Corrections sometimes happen, but it looks like pure changes of focus is also a big factor.
How many proofs have there been that given a point and a line, there is a single line parallel to the line going through the point, before non-euclidean geometry settled the matter?
Consider the vast litterature on proving that such and such type of polynomial can be solved by radicals. Galois theory made (almost) all of these obsolete -- be they right or wrong.
The notions of limits, continuity, derivability, etc... had no serious definition for very long, before people started to realize there were problems (like sequence of continuous functions converging to a non-continuous limit) and the $(\varepsilon,\delta)$ definitions were given, and people started to prove more solid results through this framework.
The italian school of algebraic geometry is another example coming to mind, where things were cleaned by a quite radical change in the paradigms of the field.
In fact, one could say that most of mathematics is about trying to get correct theorems out, and clean what is already there through obsolescence, be it gentle(correction) or cataclysmic(not interesting anymore).
As a final remark, I think it is reasonable to expect the recent works in automatic proof-checkers/proof-builders will sparkle a new revolutionary era.

REPLY [15 votes]: Here are some recent (not famous) examples of papers that have been retracted at the request of the Editor-in-Chief or the Publisher:
http://www.sciencedirect.com/science/article/pii/S089396591000265X
http://www.sciencedirect.com/science/article/pii/S0393044011002233
http://www.sciencedirect.com/science/article/pii/S0022247X12001254
http://www.sciencedirect.com/science/article/pii/S0166218X1100309X
http://www.sciencedirect.com/science/article/pii/S0898122112003008
I found them via the blog Retraction Watch, which also contains ample discussion about reasons and policies about retracting papers and many more examples, including background information.