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Taking a proofs based Euclidean geometry course was the single most useful class I've ever taken. It totally changes the way you think about mathematics, and ev

Taking a proofs based Euclidean geometry course was the single most useful class I've ever taken. It totally changes the way you think about mathematics, and even made me a better writer. The way it teaches you to begin with a premise and reach logical conclusions through concrete, connected steps is applicable to all fields of thought. Anyone unfamiliar with Euclid should remedy that immediately.

umanwizard 9y ago
Why is this specific to Euclidean geometry as opposed to any other mathematical writing? If you pick up a modern calculus book, one advantage over Euclid is that the proofs will actually be correct ;)
- claytonjy 9y ago
  It's probably not _specific_ to Euclidean geometry, but in the american school system it's common to see proof-based geometry in high school, while you generally don't dwell much on the proofs of calculus unless you take a real analysis class at university. So it's more about timing/exposure than the field itself.
- jacobolus 9y ago
  The US high school math curriculum relegates deductive proofs to a course in “geometry”, which typically ends up being a somewhat watered down version of Euclid, with a few extra topics tossed in at the end. Arguably there are better subjects to use for teaching deductive reasoning, and better formalizations for teaching geometry. This particular approach has a lot of historical inertia though.
thaumasiotes 9y ago
> The way it teaches you to begin with a premise and reach logical conclusions through concrete, connected steps is applicable to all fields of thought. Anyone unfamiliar with Euclid should remedy that immediately. I majored in math and work in software. I feel comfortable with my ability to reach logical conclusions, regardless of the fact that I haven't read the Elements. And no, proofs courses (I've taken a few) never changed the way I thought about mathematics.
- aidos 9y ago
  I'm reeeeeally confused with what sort of maths major contains a few proofs courses. Mathematics is proofs upon proofs. If mathematical proofs don't change the way you think about mathematics, I'm really not sure what's left....
  - theoh 9y ago
    Yes, as has been discussed here before, thinking in terms of proofs is a huge part of mathematical maturity, as required by university undergraduate mathematics. See "The Book of Proof" etc.
  - thaumasiotes 9y ago
    You're assuming without evidence that I began by not thinking of math in terms of proofs. This is not true; I took pains to give proofs of the basic properties of exponents when asked to help my sister with her algebra. > I'm reeeeeally confused with what sort of maths major contains a few proofs courses. I was referring to courses for which the goal was "we'll teach you how to do proofs", not courses which required proofs.
    - aidos 9y ago
      Fair enough, I should have read your comment more charitably — as perhaps you could have of your parent's. They were being somewhat hyperbolic but the sentiment was more along the lines of "Euclid is approachable for anyone, not just maths people" than "if you haven't read Euclid, you won't understand proofs." Like your parent, I also took a Euclidean geometry course during undergrad and still cite it as one of my favourites. There's something beautiful about striping mathematics back its foundations and building it back up with just a ruler and a compass.

umanwizard 9y ago

Why is this specific to Euclidean geometry as opposed to any other mathematical writing? If you pick up a modern calculus book, one advantage over Euclid is that the proofs will actually be correct ;)

claytonjy 9y ago
It's probably not _specific_ to Euclidean geometry, but in the american school system it's common to see proof-based geometry in high school, while you generally don't dwell much on the proofs of calculus unless you take a real analysis class at university. So it's more about timing/exposure than the field itself.
jacobolus 9y ago
The US high school math curriculum relegates deductive proofs to a course in “geometry”, which typically ends up being a somewhat watered down version of Euclid, with a few extra topics tossed in at the end. Arguably there are better subjects to use for teaching deductive reasoning, and better formalizations for teaching geometry. This particular approach has a lot of historical inertia though.

thaumasiotes 9y ago

> The way it teaches you to begin with a premise and reach logical conclusions through concrete, connected steps is applicable to all fields of thought. Anyone unfamiliar with Euclid should remedy that immediately. I majored in math and work in software. I feel comfortable with my ability to reach logical conclusions, regardless of the fact that I haven't read the Elements. And no, proofs courses (I've taken a few) never changed the way I thought about mathematics.

aidos 9y ago
I'm reeeeeally confused with what sort of maths major contains a few proofs courses. Mathematics is proofs upon proofs. If mathematical proofs don't change the way you think about mathematics, I'm really not sure what's left....
- theoh 9y ago
  Yes, as has been discussed here before, thinking in terms of proofs is a huge part of mathematical maturity, as required by university undergraduate mathematics. See "The Book of Proof" etc.
- thaumasiotes 9y ago
  You're assuming without evidence that I began by not thinking of math in terms of proofs. This is not true; I took pains to give proofs of the basic properties of exponents when asked to help my sister with her algebra. > I'm reeeeeally confused with what sort of maths major contains a few proofs courses. I was referring to courses for which the goal was "we'll teach you how to do proofs", not courses which required proofs.
  - aidos 9y ago
    Fair enough, I should have read your comment more charitably — as perhaps you could have of your parent's. They were being somewhat hyperbolic but the sentiment was more along the lines of "Euclid is approachable for anyone, not just maths people" than "if you haven't read Euclid, you won't understand proofs." Like your parent, I also took a Euclidean geometry course during undergrad and still cite it as one of my favourites. There's something beautiful about striping mathematics back its foundations and building it back up with just a ruler and a compass.