A case I know of first-hand: A doctoral student in engineering developed some powerful pattern matching theorems based on various transformations including one that was introduced in a major conference paper. At the student's defense one of the examiners pointed out an example showing that the transformation doesn't have one of the key claimed properties. The student sat silent for a minute and then simply said that his thesis is wrong. The examiners were shocked and assured him that the situation couldn't be that bad. It turned out that it was that bad and the student did not complete his doctorate. Fortunately his advisor helped him land a good job in which he has established a successful career.
Computational Complexity
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