Proofs are usually peer reviewed extensively, though not always. The incentive there is to write papers on top of existing papers and thus gain sci-points impor

Proofs are usually peer reviewed extensively, though not always. The incentive there is to write papers on top of existing papers and thus gain sci-points important for an academic career (promotions, grants, project participation...). Tests in programming are more akin to double entry book-keeping in accounting: you specify the same program twice (not really, you usually have manually precalculated a few cases, but that's roughly the point). As such, mathematical claims (theorems, lemmas or anything, really) requiring proofs are "integration tested" in applying them elsewhere (basically, they give reasonable results). This implicitely tests their proofs too. For sure, there are probably a lot of fringe theorems based on invalid proofs.