If ever there was a time when physicists could stand aloof from the messy everyday world, that era came to an end when the first atomic bomb was detonated. It may have been an illusion that we mathematicians were able to remain pure for a few decades longer, but illusion or not, we can no longer maintain such an attitude.
This is one of the reasons I'm on the applied rather than theoretical side; applied mathematicians are explicit in considering the consequences of their work. Which doesn't mean we won't mess things up, but at least we have our eyes open.
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