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..they have an independent right to existence.; mathematical structures are not invented, they are discovered. How far does that carry? What about algorithms?
by jonsen 17y ago
..they have an independent right to existence.; mathematical structures are not invented, they are discovered.
How far does that carry? What about algorithms? Do they also have have an independent right to existence? Can you invent an algorithm at all or do you in fact discover it?
- miloshh 17y agoWhat about when you come up with a buggy algorithm? Did you do a bad job at inventing an algorithm, or a great job at discovering a wonderful, previously unknown (though incorrect) one? :)
- lmkg 17y ago> mathematical structures are not invented, they are discovered This is a doorway to a pretty abstract philosophical discussion, not a statement of fact. I don't think that math is actually real in the strictest sense, so I'm on the fence about invent vs discover. While I think that mathematical constructions are idealizations similar to Platonic Ideals, I don't believe like Plato did that there's a perfect Plato-space where these idealizations live. When an artist arranges common-place paints (or sounds or dance moves or whatever) into a novel combination, he is said to have created rather than discovered a new work of art. Is there a good reason why this should not be true when a mathematician takes common-place axioms and makes a new arrangement of them that validates as a proof?
- jseliger 17y agoYeah -- I think this is an example of a place where the language breaks down thanks to the different connotations that "invent" and "discover" have. It seems like math has some properties of both, and the choice of word says more about the person using the word than it does about the phenomena being described.