This assertion belongs to the sociology of science, so it's controversial. :)
Quite.
For instance, Greg Chaitin seems to disagree with the assertion about mathematics. He brings up FLT; wasn't that a topic of controversy?
I don't think he does. He's mostly talking about the beginnings of the establishment of the modern, controversy-free era of mathematics -- the solution of all the old controversies. Notice that he says that Gödel discovered incompleteness, Turing discovered uncomputability, he discovered (an information-theoretic concept of) randomness. All these things remain discovered. Proofs of theorems absolutely settled the matter. There was no controversy about Wiles' proof of FLT, just people examining it very closely, finding (as far as I know) one fault, which Wiles fixed. Ordinary business of the day. Deolalikar still claims on his web page to have a proof of P != NP, but no-one else believes it.
In contrast, has anyone ever claimed to have discovered something in sociology that remained uncontroversially discovered?
has anyone ever claimed to have discovered something in sociology that remained uncontroversially discovered?
Yes.
I'm adding to that below, in rot13, but let me first ask another question: have you looked for such claims, or is this strictly a rhetorical question?
From about 5 minutes of looking: Zregba; frys-shysvyyvat cebcurpvrf; a discovery from sociology that's widely appealed to here on LW, in such contexts as the study of decision theories.
Half-closing my eyes and looking at the recent topic of morality from a distance, I am struck by the following trend.
In mathematics, there are no substantial controversies. (I am speaking of the present era in mathematics, since around the early 20th century. There were some before then, before it had been clearly worked out what was a proof and what was not.) There are few in physics, chemistry, molecular biology, astronomy. There are some but they are not the bulk of any of these subjects. Look at biology more generally, history, psychology, sociology, and controversy is a larger and larger part of the practice, in proportion to the distance of the subject from the possibility of reasonably conclusive experiments. Finally, politics and morality consist of nothing but controversy and always have done.
Curiously, participants in discussions of all of these subjects seem equally confident, regardless of the field's distance from experimental acquisition of reliable knowledge. What correlates with distance from objective knowledge is not uncertainty, but controversy. Across these fields (not necessarily within them), opinions are firmly held, independently of how well they can be supported. They are firmly defended and attacked in inverse proportion to that support. The less information there is about actual facts, the more scope there is for continuing the fight instead of changing one's mind. (So much for the Aumann agreement of Bayesian rationalists.)
Perhaps mathematicians and hard scientists are not more rational than others, but work in fields where it is easier to be rational. When they turn into crackpots outside their discipline, they were actually that irrational already, but have wandered into an area without safety rails.