>>What if they all overlook some crucial aspect because of the way they were trained, or their entrenched / ingrained assumptions? >This happens surprisingly r

>>What if they all overlook some crucial aspect because of the way they were trained, or their entrenched / ingrained assumptions? >This happens surprisingly rarely. It helps that we are trained to constantly question our entrenched assumptions. It also helps that finding a counterexample to a widely accepted proof tends to enhance one's career and reputation.