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It's absolutely possible to learn some math without understanding it beyond a symbol-manipulation level. But if you have a strong enough intuition, you will be
by laretluval 9y ago
It's absolutely possible to learn some math without understanding it beyond a symbol-manipulation level. But if you have a strong enough intuition, you will be able to translate it into math. So yes, understanding does precede mathmatical formalization.
- fwdpropaganda 9y agoTry doing actual calculations without mathematical formalization and let me know how it goes.
- laretluval 9y agoBeing able to do calculations does not imply understanding. For instance I can apply the identity e^pi*i=-1 algebraically without having any understanding of why the identity is true, how complex numbers relate to rotation, etc.
- fwdpropaganda 9y agoI didn't say that being able to do calculations implies understanding did I? Now, understanding implies being able to do calculations. And you said that you could understand without maths, which means you can do calculations without maths. So try that and let me know how it goes.
- laretluval 9y agoNo, I said that if you have a strong enough intuition you will be able to recreate the math from that intuition. But knowing the math does not suffice to give you the intuition.