[fingerlocks]

Math has a different problem. Because of the wide breadth of the field, and highly specialized nature of problems, it can take a very long time for anyone to actually verify a result with confidence. If ever. Unless you’re doing something famous like P!=NP, there might not be many people capable of checking your work in a reasonable amount of time.

The story of Fermat’s Last is a great example, what would have happened if that wasn’t a famous problem?

[read_if_gay_]

I agree, even proofs are wrong more often than you’d think, but I’m not sure whether math is actually so uniquely broad that other fields don’t suffer from this problem.

[gspr]

Maybe it's not its breadth, but its depth. That isn't to say that other fields aren't deep, don't get me wrong. But the more tightly coupled with the high-level physical world a field is (think for example medicine or biology), the more it is prone to having technologoical advances from the outside make new sub-fields crop up and old ones die. Think of for example the multitude of research areas made possible by gene editing, or high-resolution NMR imaging.

Of course this happens to some extent in math too, but a lot of subfields aren't killed or born due to outside technological changes. Number theory remains number theory, and still builds directly on centuries of work, even if computer verification has helped in some cases (disclaimer: I'm not a number theorist).

For most subfields of mathematics, you have a lot of depth to cover before you get to the forefront of research. That isn't to say that it's by any means easy to get to the forefront of more high-level physical sciences, but there are certainly subfields in biology or medicine that didn't exist a mere 40 years ago (also true in math, but in general far more rare there).

[andi999]

Also math can hinge on small technicalities. Like Andrew Wiles got a pre review for the proof of fermat conjecture and all was well. I depth review later found a serious gap/flaw which fortunately with hard work and luck he could plug. In contrast if you invent the electron microskop and you get images, you still made the invention (even if small or even big details might be wrong, and the result could be better). In other science often the gist is not effected.