To be concise: to permit the sale of weapons of mass slaughter such as was used in Buffalo a couple of days ago, the burden of proof should be on the seller to ensure that the purchaser does not want to kill people with it. The idea that the burden of proof goes the other way, that unless there is evidence that the purchaser will kill with the gun the seller bears no moral or legal responsibility is dangerously stupid.
Mathematics as a discipline teaches accountability. Every claim, whether it be a computation result or a statement (theorem) about how things work is accountable. We teach this accountability developmentally, with lower expectations at the beginning, and sometimes folk who study mathematics casually don't understand this. In my multivariable calculus classes, which I teach most frequently, I usually phrase my expectations as "give me a reason to believe your answer", citing my time working at an investment bank where my recommendations had financial repercussions and my supervisor never took my word for anything. In higher-level mathematics classes such as Abstract Algebra or Analysis I can be more explicit: these are the things we all agree to assume, these are the proof techniques which we understand; can you make an argument that convinces the community who have accepted those axioms and rules of inference that what you claim is true? We work hard to remove the ego fro...
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