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This question was closed but is nevertheless gathering many upvotes. I agree that the question as posed is borderline contentious, not to mention the fact that it's a statement and not a question; however I believe that there is a good question in there somewhere.
First, it should not be a question about physicists. There are mathematical results by established mathematicians (Euler, Hodge and Yamabe come immediately to mind, but there are probably many others) which have stood the test of time and have eventually been proved rigourously, but whose original "proofs" had gaps or used questionable manipulations not unlike the ones you might find in the Physics literature and to which the original question alludes.
The question could be about results which were "proved" but then turned out to be false, regardless the discipline (Physics, Maths,...) at the origin of the "proof". I seem to recall another question along these lines, though -- but I cannot find it. (Search in MO could be improved, I think.)
I notice the question has been reopened.
I reopened it because I hope to use the information in my ongoing fight against physicists.
Another plus is that it contains the words "Physicists" and "wrong".
Well, it is a safe bet that at least some of them, apart from being physicists, have a sense of humour, so it is also not a terribly ungreat idea!
It was deleted? Is it not the same answer that's there with the 3 downvotes?
I really think it is quite off-topic, in a question quite explicitely about physicists!
I certainly think that there is merit in some version of this question -- wasn't there a good question a while back which asked for specific examples, recounted without crowing or sneering, of where the old Italian school of algebraic geometry were led to erroneous statements/predictions by being sloppy about "general position" arguments?
WM: You have just made a rather broad claim about mathematicians in your comment, and it doesn't seem to be backed by much in the way of evidence. If you look around MathOverflow, you will find a lot of mistakes made by active mathematicians (myself included). The wording of your first sentence suggests a disconnect with the reality of the mathematical community.
I deleted your answer because its relation to the question is quite tenuous, and because it was flagged as offensive by another user. You never mentioned anything involving physical heuristics in any of your examples, and you wrote the answer in an inflammatory tone. My guess is that you were voted down because you were lowering the signal-to-noise ratio, not because you were challenging the orthodoxy.
The answer reappeared after deletion because I made the mistake of leaving it unlocked when I deleted it. This is due to my own unfamiliarity with the moderator interface.
WM: The question was not about bad physical theories cooked up by mathematicians (of which there are plenty), but cases where physical heuristic reasoning about mathematics yielded wrong mathematical answers. Your responses have not fit the question at all. If you can find a documented example of Cantor applying physical heuristic reasoning to conclude a false mathematical statement, you are welcome to point it out.
The fact that you are citing Cantor's private communications in your answers leads me to suspect your motivations. People do not make claims in private letters with the same confidence that they do in their published papers, and letters are traditionally a place where people can exchange speculative, incomplete thoughts. For that reason, when you claim that someone was wrong in a letter, it does not carry the sort of judgmental weight that you seem to be seeking. Of course, such false claims could be of historical interest, since we often like to know what was going on in someone's head when a correct theory later came out of something wrong. Such a discussion might be on-topic at MathOverflow, but only if prompted by a concrete question, e.g., about the historical development of a particular theory.
WM: If you can prove that transfinite set theory leads to contradictions, then there is a very straightforward way to convince all set theorists: write a complete proof in formal language. Start with the axioms of Zermelo-Frankel set theory (or your favorite variant), and derive a contradiction, justifying each step with rules of inference. Nowadays, the validity of such proofs can be checked by computer (look up Coq, for example), so if you write your proof in the correct format, you don't even have to worry about imposing on someone else's time. If you do this, we will welcome your arguments with open arms. In the absence of such a proof, we have no reason to pay attention to your claims.
@Steve, or just browse the sci.math archives in googlegroups to see the terabytes already spent in trying to explaining to WM, hmm well, something.
@Scott, @Pete: I admire your patience and civility in dealing with WM. I am not as nice as you guys, so I will stay out of the discussion. Enough said.
Robin, the best practice when dealing with spam/offensive posts is to flag the post as spam/offensive. When a post gets enough spam/offensive flags, it's locked and deleted by the community user and the owner is penalized 100 reputation. See this meta.stackoverflow post.
May I take this opportunity to apologise for starting this thread? It has degenerated into something very different than what I had intended.
@figueroa: No. If the thread degenerated, that is not your fault for starting it. You have nothing to apologize for, so don't.
Steve, Robin, perhaps you should email Anton or one of the mods if you haven't done so already?
Also, to be fair, I think that on at least one of the accounts he signs his comments/posts with "regards, WM", so this is not sock-puppetry per se (just against the norms of MO).