I come from a country which had a strong Soviet influence, and in school basically we were taught that behind every hard formula lies an intuitive explanation. As otherwise, there’s no way to come up with the formula in the first place.
This statement is not true, there are counter examples I encountered in my university studies but I would say that intuition will get you very far. Einstein was able to come up with special theory of relativity by just manipulating mental models after all. Only when he tried to generalize it, that’s when he hit the limit of the claim I learned in school.
That being said after abandoning intuition, relying on pure mathematical reasoning drives you to a desired place and from there you usually can reason about the theorem in an intuitive way again.
Math in this paper is not that hard to learn, you just need someone to present you the key idea.
> behind every hard formula lies an intuitive explanation
Probably a good thing to teach people when starting out. Especially since I think one thing people have is converting the symbols to the abstract ideas they communicate.
I agree you're definitely right that a lot of math (if not most) is really unintuitive. But I think I still like the sentiment behind that idea. Maybe it changes with translation, but I feel like that equations make a lot more sense when I break them down and think about what the symbols are doing and looking at their relationships with one another compared to when just looking at them as symbols to manipulate. Like seeing the form F=ma as more than mass and acceleration and but how in structure it is similar to F=-kx. Getting there isn't easy but once you do it is much more intuitive than it was before.
gregorygoc|6 months ago
This statement is not true, there are counter examples I encountered in my university studies but I would say that intuition will get you very far. Einstein was able to come up with special theory of relativity by just manipulating mental models after all. Only when he tried to generalize it, that’s when he hit the limit of the claim I learned in school.
That being said after abandoning intuition, relying on pure mathematical reasoning drives you to a desired place and from there you usually can reason about the theorem in an intuitive way again.
Math in this paper is not that hard to learn, you just need someone to present you the key idea.
aeonik|6 months ago
I hope anyone who is unsure will read your comment and at least try to follow it for a while.
godelski|6 months ago
I agree you're definitely right that a lot of math (if not most) is really unintuitive. But I think I still like the sentiment behind that idea. Maybe it changes with translation, but I feel like that equations make a lot more sense when I break them down and think about what the symbols are doing and looking at their relationships with one another compared to when just looking at them as symbols to manipulate. Like seeing the form F=ma as more than mass and acceleration and but how in structure it is similar to F=-kx. Getting there isn't easy but once you do it is much more intuitive than it was before.