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Another way to put it: is math invented or discovered? If you ask them, mathematicians may give opinion one way or the other, but they do not actually care ver

Another way to put it: is math invented or discovered? If you ask them, mathematicians may give opinion one way or the other, but they do not actually care very much, because this question has nothing to do with their work.

Galanwe 2y ago
> If you ask them, mathematicians may give opinion one way or the other, but they do not actually care very much Indeed, this is more of a meta scientific, or epistemogic, question (edit: though it seems the French "épistemologie" is not really translatable to "epistemology" in English, at least not in its original meaning) > Another way to put it: is math invented or discovered? I think this is the question encompassed by constructivist epistemology. https://en.m.wikipedia.org/wiki/Constructivism_(philosophy_of_science) https://en.m.wikipedia.org/wiki/Constructivism_(philosophy_o...
viraptor 2y ago
Reminds me of the scientists arguing a long time ago whether the egg or the sperm is more important for creating new life. They wasted lots of time that could be dedicated to learning more.
magicalhippo 2y ago
> is math invented or discovered? Yes and yes. Or to put it another way, why does it have to be an "or" question? To me some things in math are discovered, like prime numbers, pi, Euler's number. Other things are more like an invention, like the Runge-Kutta methods[1] or the Finite Element Method[2]. [1]: https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods [2]: https://en.wikipedia.org/wiki/Finite_element_method https://en.wikipedia.org/wiki/Finite_element_method
- tim333 2y ago
  True. There are a lot of articles like this that waffle on for ages when it seems kind of obvious that both are true. I even bought Hersh's book that waffles on for ~400 pages trying to argue for invented by studiously avoiding the obvious truth that pi would have the same value in alien civilisations and so isn't just a human invention. Instead he tries to politicize it amazingly enough. Apparently invented is lefty, discovered is right wing and right wing bad so it's not discovered. Ridiculous argument really.
ianmcgowan 2y ago
I love the mental picture from Greg Egan's Diaspora of the truth mines, literally hacking the math like chunks of coal: "If ve ever wanted to be a miner in vis own right -- making and testing vis own conjectures at the coal face, like Gauss and Euler, Riemann and Levi-Civita, deRham and Cartan, Radiya and Blanca -- then Yatima knew there were no shortcuts, no alternatives to exploring the Mines firsthand. Ve couldn't hope to strike out in a fresh direction, a route no one had ever chosen before, without a new take on the old results. Only once ve'd constructed vis own map of the Mines -- idiosyncratically crumpled and stained, adorned and annotated like no one else's -- could ve begin to guess where the next rich vein of undiscovered truths lay buried."

Galanwe 2y ago

> If you ask them, mathematicians may give opinion one way or the other, but they do not actually care very much Indeed, this is more of a meta scientific, or epistemogic, question (edit: though it seems the French "épistemologie" is not really translatable to "epistemology" in English, at least not in its original meaning) > Another way to put it: is math invented or discovered? I think this is the question encompassed by constructivist epistemology. https://en.m.wikipedia.org/wiki/Constructivism_(philosophy_of_science) https://en.m.wikipedia.org/wiki/Constructivism_(philosophy_o...

viraptor 2y ago

Reminds me of the scientists arguing a long time ago whether the egg or the sperm is more important for creating new life. They wasted lots of time that could be dedicated to learning more.

magicalhippo 2y ago

> is math invented or discovered? Yes and yes. Or to put it another way, why does it have to be an "or" question? To me some things in math are discovered, like prime numbers, pi, Euler's number. Other things are more like an invention, like the Runge-Kutta methods[1] or the Finite Element Method[2]. [1]: https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods [2]: https://en.wikipedia.org/wiki/Finite_element_method https://en.wikipedia.org/wiki/Finite_element_method

tim333 2y ago
True. There are a lot of articles like this that waffle on for ages when it seems kind of obvious that both are true. I even bought Hersh's book that waffles on for ~400 pages trying to argue for invented by studiously avoiding the obvious truth that pi would have the same value in alien civilisations and so isn't just a human invention. Instead he tries to politicize it amazingly enough. Apparently invented is lefty, discovered is right wing and right wing bad so it's not discovered. Ridiculous argument really.

ianmcgowan 2y ago

I love the mental picture from Greg Egan's Diaspora of the truth mines, literally hacking the math like chunks of coal: "If ve ever wanted to be a miner in vis own right -- making and testing vis own conjectures at the coal face, like Gauss and Euler, Riemann and Levi-Civita, deRham and Cartan, Radiya and Blanca -- then Yatima knew there were no shortcuts, no alternatives to exploring the Mines firsthand. Ve couldn't hope to strike out in a fresh direction, a route no one had ever chosen before, without a new take on the old results. Only once ve'd constructed vis own map of the Mines -- idiosyncratically crumpled and stained, adorned and annotated like no one else's -- could ve begin to guess where the next rich vein of undiscovered truths lay buried."