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I can't agree more. Math is about intuition of what the symbols are doing. In the case of functions, intuition about how the symbols are transforming the input.

I can't agree more. Math is about intuition of what the symbols are doing. In the case of functions, intuition about how the symbols are transforming the input. I've always thought I was "bad at math." It wasn't until my late 20's when I took it upon myself to get better at calculus and I used "Calculus Success in 20 Minute a Day[0]" did I finally realize why I was "bad" at it; I never understood what I was doing. That series of book really put intuition at the forefront. I began to realize that the crazy symbols and formulas were stand-in for living, breathing dynamic systems: number transformers. Each formula and symbol represented an action. Once I understood Math as a way to encode useful number transformation, it all clicked. Those rules and functions were encoded after a person came up with something they wanted to do. The formula or function is merely a compact way of describing this dynamic system to other people. The irony was I always thought math was boring. In retrospect it was because it was taught as if it had no purpose other than to provide useless mental exercise. Once I started realizing that derivatives are used all around me to do cool shit, I was inspired to learn how they worked because I wanted to use them to do cool shit too. I went through several years of math courses and none of them even attempted to tell me that math was just a way to represent cool real world things. It took a $10 used book from amazon to do that. Ain't life grand? [0]:https://www.amazon.com/Calculus-Success-20-Minutes-Day/dp/1576858898 https://www.amazon.com/Calculus-Success-20-Minutes-Day/dp/15...

andrepd 9y ago
But math isn't about intuition, much to the contrary, it's about rigorous reasoning. In math "intuition" and "common sense" are worth nothing. Only objective proof matters. It's a valuable lesson too, learning not to take anything on a hunch and only take as true what what you carefully and logically prove.
- ice109 9y ago
  you use intuition to come up with the argument. then you use a proof to convince others.
  - andrepd 9y ago
    No, you use intuition to come up with an idea the use that idea to write a proof for yourself. Intuition is invaluable as a starting point, but it's often misleading.
    - ice109 9y ago
      you're very naive. i think you're probably still an undergrad or maybe have never done serious math. https://terrytao.wordpress.com/career-advice/there%E2%80%99s-more-to-mathematics-than-rigour-and-proofs/ https://terrytao.wordpress.com/career-advice/there%E2%80%99s...
      - andrepd 9y ago
        But the article agrees with me: > The point of rigour is not to destroy all intuition; instead, it should be used to destroy bad intuition while clarifying and elevating good intuition. In mathematics, intuition is the starting point and guiding principle, but never worth anything by itself without rigour.
- alistproducer2 9y ago
  For me, before you get a level where you can understand proofs or even how to read them, you need to understand why lemmas, axioms, and other components are true. My take is more about how to learn to understand the calculatory side of math, which I think is a prerequisite for taking on the reasoning and logical side of it.

andrepd 9y ago

But math isn't about intuition, much to the contrary, it's about rigorous reasoning. In math "intuition" and "common sense" are worth nothing. Only objective proof matters. It's a valuable lesson too, learning not to take anything on a hunch and only take as true what what you carefully and logically prove.

ice109 9y ago
you use intuition to come up with the argument. then you use a proof to convince others.
- andrepd 9y ago
  No, you use intuition to come up with an idea the use that idea to write a proof for yourself. Intuition is invaluable as a starting point, but it's often misleading.
  - ice109 9y ago
    you're very naive. i think you're probably still an undergrad or maybe have never done serious math. https://terrytao.wordpress.com/career-advice/there%E2%80%99s-more-to-mathematics-than-rigour-and-proofs/ https://terrytao.wordpress.com/career-advice/there%E2%80%99s...
    - andrepd 9y ago
      But the article agrees with me: > The point of rigour is not to destroy all intuition; instead, it should be used to destroy bad intuition while clarifying and elevating good intuition. In mathematics, intuition is the starting point and guiding principle, but never worth anything by itself without rigour.
alistproducer2 9y ago
For me, before you get a level where you can understand proofs or even how to read them, you need to understand why lemmas, axioms, and other components are true. My take is more about how to learn to understand the calculatory side of math, which I think is a prerequisite for taking on the reasoning and logical side of it.