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Mathematics sits in a very different place w.r.t. other sciences. First of all, it's very meta. Yes, it can describe any phenomenon on our planet. On the other
by bayindirh 4d ago
Mathematics sits in a very different place w.r.t. other sciences. First of all, it's very meta. Yes, it can describe any phenomenon on our planet. On the other hand, advanced mathematics is a high mountain which is very hard to climb, and changes the climber in various and irreversible ways once the journey begins.
That's said, I'm a non-mathematician, but a computer scientist. Mathematics was always my weak part, because solving problems which doesn't mean anything doesn't motivate me, and when I'm not motivated, I fail.
Without digressing so much, I want to say that, some of the things in mathematics and mathematics adjacent sciences baffle me. Many mathematicians don't understand the proofs of others, yet they accept it since it checks out within the rules of mathematics. Moreover, many engineers don't understand the formulae they work with. I have developed a very performant Boundary Element Method evaluator, yet I don't know the reason of taking Gaussian Integrals over the surface. The only answer I got is "because the method works that way".
So, if computers can make the proofs now, and we have no curious students pecking their professors to understand how these works, the whole mathematics as a science could wither and die. Because besides it being a sport, it's the very language which can model and explain anything, but it's very hard to master and understand due to that nature.
Our professors warned us against using too much Mathematica, to make us learn things the hard way and make the knowledge permanent. Now, if we offload science to a matmul engine, it's possible that we lose the connection and never able to close the gap in some cases.
Again, it boils down to "This machine has no brain, use yours (or lose it)".