I often say that "hard sciences" have often progressed much more than social/human sciences.
[1] https://en.wikipedia.org/wiki/Replication_crisis#In_medicine
With the above, I think we've empirically proven that we can't trust mathmeticians more than any other humans We should still rigorously verify their work with diverse, logical, and empirical methods. Also, build ground up on solid ideas that are highly vetted. (Which linear algebra actually does.)
The other approach people are taking are foundational, machine-checked, proof assistants. These use a vetted logic whose assistant produces a series of steps that can be checked by a tiny, highly-verified checker. They'll also oftne use a reliable formalism to check other formalisms. The people doing this have been making everything from proof checkers to compilers to assembly languages to code extraction in those tools so they are highly trustworthy.
But, we still need people to look at the specs of all that to see if there are spec errors. There's fewer people who can vet the specs than can check the original English and code combos. So, are they more trustworthy? (Who knows except when tested empirically on many programs or proofs, like CompCert was.)
This had been assigned many times previously. When my friend disproved the lemma, he asked the professor what he had done wrong. Turns out the lemma was in fact false, despite dozens of grad students having turned in "proofs" of the lemma already. The paper itself still stood, as a weaker form of the lemma was sufficient for its findings, but still very interesting.
Yet, I believe there hasn't been much progress as compared with STEM. But it is just a belief at the end of the day. There might be some study about this out there.