I'd say it's because it's the field with (a) the strictest formal definition of what "correct" means, and (b) no dependence on experiment, and hence no data and no statistics.
Everything you need to determine whether or not a given proof is correct is either in the paper in front of you, in the literature, or implied by the literature. If you can't follow the implications, you ask the author of the proof to clarify it.
Compare this to research in, say, medicine, where there are always millions of variables and progress requires careful controls, a statistician, an enormous budget that supports many trials of the same thing, and hope.
My hypothesis is that this is also why so many mathematicians do great work when they're young: It's one of the few fields where you don't have to do everything N times, because the error does not depend inversely on the square root of N. Once you've figured something out in math, it stays figured out. So all you need to become a mathematician -- besides your own mind -- is a library, the ability to read, and patience. (Although, in practice, nobody becomes a great mathematician without a teacher or two to guide them through the library. Even Ramanujan only found a couple of the books on his own.)
Everything you need to determine whether or not a given proof is correct is either in the paper in front of you, in the literature, or implied by the literature. If you can't follow the implications, you ask the author of the proof to clarify it.
Compare this to research in, say, medicine, where there are always millions of variables and progress requires careful controls, a statistician, an enormous budget that supports many trials of the same thing, and hope.
My hypothesis is that this is also why so many mathematicians do great work when they're young: It's one of the few fields where you don't have to do everything N times, because the error does not depend inversely on the square root of N. Once you've figured something out in math, it stays figured out. So all you need to become a mathematician -- besides your own mind -- is a library, the ability to read, and patience. (Although, in practice, nobody becomes a great mathematician without a teacher or two to guide them through the library. Even Ramanujan only found a couple of the books on his own.)