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DanArmak comments on Academic Cliques - Less Wrong
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I'm not a mathematician, but my impression impression is that this has gotten less true, as the typical proof published in mathematics journals has gotten more convoluted and harder to check. Mathematicians are now often forced to rely on trusting their colleagues to know whether a proof is correct or not. See here.
Not that this makes mathematics any worse off than other fields. I'm pretty sure all fields these days require people to trust their colleagues.
Interesting. What about machine proof checking? Why don't mathematicians publish all results in a formal notation (in addition to the human-oriented one) that allows all proofs to be checked, and entered into an Internet repository available to automated proof assistants?
For the same reason not all software is written in Coq/Agda/other proof systems: it would be incredibly expensive, slow, and demand very rare skills.
Because it takes a lot of extra time and work to formalize a proof to the level where it can be automatically checked.