Comment by jckt
2 months ago
Disregarding the competing definitions of “science”, a significant value in mathematical work is “the journey”. The truth or falsehood of individual results are rarely as important as the machinery developed to deliver it. If all the genie did was tell you something was true or false, the only learning you gain is to backtrack and develop the machinery yourself. To a certain extent this is true of the other sciences too.
This is a genie that does far more than tell you whether something is true or false though.
Maybe the genie provides full proofs of each result. So will the journey still matter? For a true mathematician it should not.
Of course it does because the joy of math is discovering something yourself. At some point you just want to stare at a blank sheet of paper, start with a premise and go on a journey. Are you a mathematician or scientist? I am and just typing "tell me the proof of this result" sounds immensely boring to me.
Have you ever played a video game with an "invincibility cheat"? Boring. But you do get to the end and "solve the game".
Don't conflate the joy of doing math with the benefits of knowing new mathematics.
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Not from a logical positivist perspective, which is why you conveniently disregarded "competing views".