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Because mathematicians are human and want to read math in a language designed for humans instead of for machines.

klibertp 11y ago
Which is stupid and counterproductive, because it makes the reader spend much more mental effort when reading math than necessary. A "machine" could verify parts of formulas, basic assertions, and also provide additional tools like syntax highlighting, inline docs and auto-completion. There is no saving maths notation now. It will die out and it will be replaced with a machine-friendly notation because benefits are too huge to ignore in the long run. Meanwhile, mathematicians will throw tantrums in defence of their notation, like all single-language users did throughout the history when their language was being replaced with something else. I wonder, how do math polyglots - the ones who know both normal maths notation and alternatives (like Mathematica and programming languages) - feel about this.
- GFK_of_xmaspast 11y ago
  Polyglot here--I have a phd in mathematics and my entire career since then has involved programming computers in exchange for money (generally using c++ and python)--and I think that idea is absurd.
- zodiac 11y ago
  Hey, I'm doing a pure math/CS double major so I can probably answer your question. I honestly prefer notation to be as terse as possible when reading/writing proofs. Oh either case reading notation is a tiny part of the effort needed to do math - if you force me to read papers using explicit, verbose notation I wouldn't complain too much. I have no idea why I would throw a tantrum. IME verbose notation makes it easier to "type check" an equation or expression, but checking a proof is much more involved than that.
  - klibertp 11y ago
    Thanks, I hear about the terseness often and I agree it's convenient, what I want is a more formal and unambiguous way of making things terse. A bit more consistency doesn't have to come at the expense of terseness and expressiveness. And while you're obviously right that syntactic issues constitute just a minor part of work (at least after you're fluent in a language), the time you spend on them does add up in the long run. Not to mention such issues increase the barrier to entry for the new users unnecessarily...
    - zodiac 11y ago
      > A bit more consistency doesn't have to come at the expense of terseness and expressiveness. Yeah, mathematicians are often ambiguous out of laziness, because they have no incentive to make it terse+unambiguous, and making it terse+unambiguous takes more effort than making it terse. Also sometimes you cannot get maximal terseness and unambiguity at the same time. For example if f is a function of 2 real variables, you fix the first to be x_0 and take the derivative with respect to the second, I would write this as f'(x_0, y), but I'm sure you agree that this is ambiguous to some people.

Which is stupid and counterproductive, because it makes the reader spend much more mental effort when reading math than necessary. A "machine" could verify parts of formulas, basic assertions, and also provide additional tools like syntax highlighting, inline docs and auto-completion. There is no saving maths notation now. It will die out and it will be replaced with a machine-friendly notation because benefits are too huge to ignore in the long run. Meanwhile, mathematicians will throw tantrums in defence of their notation, like all single-language users did throughout the history when their language was being replaced with something else. I wonder, how do math polyglots - the ones who know both normal maths notation and alternatives (like Mathematica and programming languages) - feel about this.

GFK_of_xmaspast 11y ago
Polyglot here--I have a phd in mathematics and my entire career since then has involved programming computers in exchange for money (generally using c++ and python)--and I think that idea is absurd.
zodiac 11y ago
Hey, I'm doing a pure math/CS double major so I can probably answer your question. I honestly prefer notation to be as terse as possible when reading/writing proofs. Oh either case reading notation is a tiny part of the effort needed to do math - if you force me to read papers using explicit, verbose notation I wouldn't complain too much. I have no idea why I would throw a tantrum. IME verbose notation makes it easier to "type check" an equation or expression, but checking a proof is much more involved than that.
- klibertp 11y ago
  Thanks, I hear about the terseness often and I agree it's convenient, what I want is a more formal and unambiguous way of making things terse. A bit more consistency doesn't have to come at the expense of terseness and expressiveness. And while you're obviously right that syntactic issues constitute just a minor part of work (at least after you're fluent in a language), the time you spend on them does add up in the long run. Not to mention such issues increase the barrier to entry for the new users unnecessarily...
  - zodiac 11y ago
    > A bit more consistency doesn't have to come at the expense of terseness and expressiveness. Yeah, mathematicians are often ambiguous out of laziness, because they have no incentive to make it terse+unambiguous, and making it terse+unambiguous takes more effort than making it terse. Also sometimes you cannot get maximal terseness and unambiguity at the same time. For example if f is a function of 2 real variables, you fix the first to be x_0 and take the derivative with respect to the second, I would write this as f'(x_0, y), but I'm sure you agree that this is ambiguous to some people.