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Yeah well - next time I read a proof by a mathematician that skips several steps that to mathematicians are unimportant or "obvious" yet fundamentally blocked m

Yeah well - next time I read a proof by a mathematician that skips several steps that to mathematicians are unimportant or "obvious" yet fundamentally blocked my understanding of the proof overall - I'll think on this reaction and smile... Or maybe even just write some mathematical overviews myself that leave out stuff that drives mathematicians insane with frustration... It would be justice...

gcc_programmer 7y ago
Would you write code with syntax errors and blame the compiler for not understand how smart you are, or would you just learn the language and write correct code? Your frustration shows lack of understanding and appreciation for mathematics, when in reality maths and computer science are two sides of the same coin. If you can be good at one, you can be good at the other :)
- ajross 7y ago
  > Would you write code with syntax errors and blame the compiler for not understand how smart you are No, but you might tolerate example code with mild syntax errors (like using a "..." to skip unrelated material, or skipping import declarations and boilerplate to better clarify the point being made). You don't demand that every example in a programming tutorial be a fully buildable piece of software, why are you demanding that a simpified calculus tutorial exhibit full rigor?
  - bordercases 7y ago
    > why are you demanding that a simpified calculus tutorial exhibit full rigor? Aren't they just suggesting a marginal amount of rigor to communicate that the "definition" is in fact based on justifications which render it non-arbitrary?
Tainnor 7y ago
I sympathise with your point of view and I agree that sometimes mathematicians are not keeping their audience in mind enough. You don't always need completely rigorous proofs for non-mathematicians. But I think that it's a false dichotomy to only consider "extremely rigorous" or "simplified to the point of being wrong" as the only teaching philosophies. There is a middle ground where you can be somewhat hand-wavy and inexact without getting the conceptual broad strokes wrong.

gcc_programmer 7y ago

Would you write code with syntax errors and blame the compiler for not understand how smart you are, or would you just learn the language and write correct code? Your frustration shows lack of understanding and appreciation for mathematics, when in reality maths and computer science are two sides of the same coin. If you can be good at one, you can be good at the other :)

ajross 7y ago
> Would you write code with syntax errors and blame the compiler for not understand how smart you are No, but you might tolerate example code with mild syntax errors (like using a "..." to skip unrelated material, or skipping import declarations and boilerplate to better clarify the point being made). You don't demand that every example in a programming tutorial be a fully buildable piece of software, why are you demanding that a simpified calculus tutorial exhibit full rigor?
- bordercases 7y ago
  > why are you demanding that a simpified calculus tutorial exhibit full rigor? Aren't they just suggesting a marginal amount of rigor to communicate that the "definition" is in fact based on justifications which render it non-arbitrary?

Tainnor 7y ago

I sympathise with your point of view and I agree that sometimes mathematicians are not keeping their audience in mind enough. You don't always need completely rigorous proofs for non-mathematicians. But I think that it's a false dichotomy to only consider "extremely rigorous" or "simplified to the point of being wrong" as the only teaching philosophies. There is a middle ground where you can be somewhat hand-wavy and inexact without getting the conceptual broad strokes wrong.