3 ms·

I think one thing that you have to remember is, ISO standards aside, mathematical notation isn't a fixed thing but a living tradition that evolves over time.

klibertp 11y ago
Which is totally true for programming languages, yet they somehow manage to have standards, all the undefined behaviour of C be damned. How come it's not the case for mathematics? Maths notation has very many problems, most of which stem from the fact that its syntax isn't formally specified. I have no idea why would mathematicians want to continue using this informally specified, ambiguous notation when there are alternatives.
- serge2k 11y ago
  because we know how to read and don't care what a bunch of outsiders think.
  - klibertp 11y ago
    Yeah, that's exactly my suspicion! I'm just happy it's not true for Computer Science and programming. Whatever you want to say about a social side of programming, there's no denying it that outsiders and beginners are warmly welcomed in the community. We create and provide for free tutorials and guides for beginners, we design languages to be as easy for people to understand as possible (we don't exactly know what makes languages easy to understand, but we at least try!), we create tools for visualisation and summarizing code, and so on. Similar activities seem to be unpopular with mathematicians. I can't help but feel mathematicians are just a bunch of elitist pricks, who know they are on their way out and who try to build artificial barriers for entry into their field to make themselves needed for a bit longer. It's actually natural, most people will fight to retain their status (and jobs). It reminds me of "refucktoring", writing convoluted, unreadable code just to make sure nobody, else than you, can work with it. Such programmers are shunned in our community, yet they are heroes in mathematics. Oh well, as an "outsider" it's not my problem.
- GFK_of_xmaspast 11y ago
  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...

klibertp 11y ago

Which is totally true for programming languages, yet they somehow manage to have standards, all the undefined behaviour of C be damned. How come it's not the case for mathematics? Maths notation has very many problems, most of which stem from the fact that its syntax isn't formally specified. I have no idea why would mathematicians want to continue using this informally specified, ambiguous notation when there are alternatives.

serge2k 11y ago
because we know how to read and don't care what a bunch of outsiders think.
- klibertp 11y ago
  Yeah, that's exactly my suspicion! I'm just happy it's not true for Computer Science and programming. Whatever you want to say about a social side of programming, there's no denying it that outsiders and beginners are warmly welcomed in the community. We create and provide for free tutorials and guides for beginners, we design languages to be as easy for people to understand as possible (we don't exactly know what makes languages easy to understand, but we at least try!), we create tools for visualisation and summarizing code, and so on. Similar activities seem to be unpopular with mathematicians. I can't help but feel mathematicians are just a bunch of elitist pricks, who know they are on their way out and who try to build artificial barriers for entry into their field to make themselves needed for a bit longer. It's actually natural, most people will fight to retain their status (and jobs). It reminds me of "refucktoring", writing convoluted, unreadable code just to make sure nobody, else than you, can work with it. Such programmers are shunned in our community, yet they are heroes in mathematics. Oh well, as an "outsider" it's not my problem.
GFK_of_xmaspast 11y ago
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...