There is a story I read about tiling the plane with convex pentagons.
You can read about it in this article on pages 1 and 2.
Summary of the story: A guy showed in his doctorate work all classes of tiling the plane with convex pentagons, and proved that they are indeed all possible cases. Later, riddle was published in popular science magazine to find all these classes. One of the readers found a tiling that did not belong to any of the classes, and so the claim and the proof turned out to be wrong.
Reading this made me think about some questions.
Is it rare when a theorem was proved and the proof was published, and later it turned out that the theorem is wrong?
Can we somehow guess how many theorems out there that we think are right, but actually are wrong? I bet that if in our case, the theorem was about tiling in $R^3$ nobody would ever notice.
What can be the effect of such theorems on mathematics in general? Can it be a serious issue for mathematics even if the wrong theorems were not very important, but still, some stuff was based on them?