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I believe most mathematicians are well aware of constructive mathematics. What makes you think that they aren't? > Basically, proof by contradiction is not a g

I believe most mathematicians are well aware of constructive mathematics. What makes you think that they aren't? > Basically, proof by contradiction is not a good idea. Based on what?

adamnemecek 8y ago
That most math books I read don’t discuss it.
- AnimalMuppet 8y ago
  Maybe you should read more widely. And maybe you should not make generalizations based on your reading list. In particular, your reading list could be selective, thereby making generalizations worthless. Or you could misread your reading list, where they do not explicitly state that they believe in and/or depend on proof by contradiction.
  - llamaz 8y ago
    Do you even study mathematics? You sound like a programmer with a passing interest in mathematics, because 99% of math books don't worry about issues like the axiom of choice or constructive math. The only ones that do are logic books.
    - AnimalMuppet 8y ago
      I quit after a bachelor's in math, so yes, I have studied mathematics, but no, I don't. Still, I'm not just a programmer with a passing interest in math. Returning to the discussion: adamnemecek said that most mathematicians needed to know about constructive mathematics. When asked why he thought they didn't, he said that most math books he read didn't discuss it (presumably, "it" = "constructivist mathematics"). So I said that adamnemecek couldn't draw that conclusion on that evidence, though I should perhaps have been clearer that, as you said, "99% of math books don't worry about issues like the axiom of choice or constructive math". You're actually agreeing with what I was trying to say - you can't look at an average math book and decide whether the author knows about constructivist math or not, because it's outside the topic of the book. Even if the book does lots of proof by contradiction, that only proves that the author is not writing a constructivist book, not that the author is unaware of constructivism. I think adamnemecek wants every math book to be explicitly constructivist. That, I think, is a complete misreading on his part of how important constructivist math is.
      - llamaz 8y ago
        Ah okay :) I misread you
- frankmcsherry 8y ago
  To paraphrase: "if it were a good idea, my books would have discussed it." Are we done here?

I believe most mathematicians are well aware of constructive mathematics. What makes you think that they aren't? > Basically, proof by contradiction is not a good idea. Based on what?

adamnemecek 8y ago

That most math books I read don’t discuss it.

AnimalMuppet 8y ago
Maybe you should read more widely. And maybe you should not make generalizations based on your reading list. In particular, your reading list could be selective, thereby making generalizations worthless. Or you could misread your reading list, where they do not explicitly state that they believe in and/or depend on proof by contradiction.
- llamaz 8y ago
  Do you even study mathematics? You sound like a programmer with a passing interest in mathematics, because 99% of math books don't worry about issues like the axiom of choice or constructive math. The only ones that do are logic books.
  - AnimalMuppet 8y ago
    I quit after a bachelor's in math, so yes, I have studied mathematics, but no, I don't. Still, I'm not just a programmer with a passing interest in math. Returning to the discussion: adamnemecek said that most mathematicians needed to know about constructive mathematics. When asked why he thought they didn't, he said that most math books he read didn't discuss it (presumably, "it" = "constructivist mathematics"). So I said that adamnemecek couldn't draw that conclusion on that evidence, though I should perhaps have been clearer that, as you said, "99% of math books don't worry about issues like the axiom of choice or constructive math". You're actually agreeing with what I was trying to say - you can't look at an average math book and decide whether the author knows about constructivist math or not, because it's outside the topic of the book. Even if the book does lots of proof by contradiction, that only proves that the author is not writing a constructivist book, not that the author is unaware of constructivism. I think adamnemecek wants every math book to be explicitly constructivist. That, I think, is a complete misreading on his part of how important constructivist math is.
    - llamaz 8y ago
      Ah okay :) I misread you
frankmcsherry 8y ago
To paraphrase: "if it were a good idea, my books would have discussed it." Are we done here?