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The mathematical notation has developed over centuries to think about and solve problems on paper. Besides it being taught in schools and hence familiar, I

The mathematical notation has developed over centuries to __think about and solve problems on paper__. Besides it being taught in schools and hence familiar, I think it’s not at all a good tool to use in the significantly different digital medium. Another reason is that the notation is mostly a tool for __oneself__ to think in, but is fairly bad at communicating (think about the level of expertise required to read a math paper vs reading someone’s code). Here’s a concrete difference to support these claims. Using math notation we often write large expressions which include many meaningful subexpressions and complex operations. In code we prefer to use lots of names (variables) and simple expressions.

Grustaf 7y ago
Reading math is hard because math is hard. The notation is incredibly powerful, intuitive and flexible. In all my years hanging around mathematicians I’ve never heard anyone complain about notation. After all, you are always free to use your own notation if you want, and if others like it they will follow.
- munificent 7y ago
  > In all my years hanging around mathematicians I’ve never heard anyone complain about notation. There's likely to be some survivorship bias at play here.
  - Grustaf 7y ago
    No, since anyone is free to invent and use whatever notation they prefer. That’s how mathematical notation has evolved so far. People come up with new notation all the time.
    - eru 7y ago
      Though when you are writing a paper, it's useful to pick standard notation. But yeah, when working something mathematical out for the first time, picking / making up the right notation is crucial.
    - ivanbakel 7y ago
      "Free" here is a bit abstract. In what way is an undergraduate mathematician free to use their own notation, as opposed to the notation of their lecturer, textbooks, and examination papers? You can think in your own terms, but mathematics has to be taught and communicated with some kind of consensus - and unless you're lucky enough to be the first in the field, that consensus has preceeded you.
      - Grustaf 7y ago
        Mathematics is completely meritocratic. If you invent a notation that is better than some existing notation, people WILL use it, without asking for your credentials.
        ivanbakel 7y ago
        I think that's a naive statement, and it's also not really relevant to the original point being made, which is that existing mathematical notation can be difficult to grok. Inventing new notation does not help with existing material - and that material is what makes mathematicians. People who can put up with old notation, especially if it is bad, are much more likely to become mathematicians: that gives a survivorship bias. Besides which, you are welcome to invent your own notation, but good luck trying to get anyone to adopt it, particularly if the mathematical field involved is studied enough. Inertia is very strong, even in very abstract disciplines - aren't physicists still treating current as flowing the wrong direction?
    - julienreszka 7y ago
      Inertia
    - michaelbrave 7y ago
      sure unless you quit because you struggled to learn what was in place.
  - wtallis 7y ago
    The most likely place to be hanging around mathematicians is at a school, and that's also where you would expect to hear students complaining about notation as an impediment to learning.
    - Someone 7y ago
      I don’t think it is a given that students are good judges about what impedes them from learning. Having said that, I personally have never had issues with notation in mathematics nor did I have the impression others I helped had. IMO, abstraction is the main stumbling block, not notation.
      - Grustaf 7y ago
        I’m talking about the math institutions at the two universities I attended, I took a lot of phd classes. But same with students, the complaint has never been about notation. In fact the only people that seem to complain about notation is computer programmers who find it too loose, but that is precisely its power.
- Ar-Curunir 7y ago
  Are you kidding? Bad notation abounds in mathematics and theoretical computer science
  - Grustaf 7y ago
    Do you have any examples?
- invalidOrTaken 7y ago
  Ken Iverson complained so much about notation he came up with his own and won the Turing award.
- 317070 7y ago
  Well, here you have one! Computer science notation is vastly superior to the common mathematical one. It's a different league of clarity. But my papers need to follow the consensus, as I'm already trying to get a hard idea across to my reader who decides to spend 15 minutes to try and understand me, maybe. So yes, then I need to introduce 15 symbols, half of them greek, and a number of operations between them using whatever line/subscript/superscript/brace is fashionable. The biggest difference is in slides. In slides I try and can usually avoid the math notation. Because I am there talking it through, which makes notation less important and gives me an opportunity to switch to long variable names and everything a function, more akin to the software notation.
  - Grustaf 7y ago
    The only people I’ve ever heard having problems with math notation (as opposed to math concepts, which are often extremely abstract) are computer scientist and computer people in general. I think what irritates them is the fluidity and flexibility of most math notation. It’s not really machine readable since it really assumes you know what you’re doing. The same string of symbols can mean vastly different things in different contexts, which is precisely the power of math notation. Brevity is actually a goal in itself, it makes it possible to keep even larger constructions in your mind at the same time. Consider einteinian notation, with implicit summation. Very terse, and very powerful when you know what you’re doing. I’m sure CS notation is great for CS but trust me, math notation is pretty damn near optimal for math. Second only to theoretical physicists, mathematicians are probably the smartest of scientists.

The mathematical notation has developed over centuries to __think about and solve problems on paper__. Besides it being taught in schools and hence familiar, I

Grustaf 7y ago

Reading math is hard because math is hard. The notation is incredibly powerful, intuitive and flexible. In all my years hanging around mathematicians I’ve never heard anyone complain about notation. After all, you are always free to use your own notation if you want, and if others like it they will follow.

munificent 7y ago
> In all my years hanging around mathematicians I’ve never heard anyone complain about notation. There's likely to be some survivorship bias at play here.
- Grustaf 7y ago
  No, since anyone is free to invent and use whatever notation they prefer. That’s how mathematical notation has evolved so far. People come up with new notation all the time.
  - eru 7y ago
    Though when you are writing a paper, it's useful to pick standard notation. But yeah, when working something mathematical out for the first time, picking / making up the right notation is crucial.
  - ivanbakel 7y ago
    "Free" here is a bit abstract. In what way is an undergraduate mathematician free to use their own notation, as opposed to the notation of their lecturer, textbooks, and examination papers? You can think in your own terms, but mathematics has to be taught and communicated with some kind of consensus - and unless you're lucky enough to be the first in the field, that consensus has preceeded you.
    - Grustaf 7y ago
      Mathematics is completely meritocratic. If you invent a notation that is better than some existing notation, people WILL use it, without asking for your credentials.
      - ivanbakel 7y ago
        I think that's a naive statement, and it's also not really relevant to the original point being made, which is that existing mathematical notation can be difficult to grok. Inventing new notation does not help with existing material - and that material is what makes mathematicians. People who can put up with old notation, especially if it is bad, are much more likely to become mathematicians: that gives a survivorship bias. Besides which, you are welcome to invent your own notation, but good luck trying to get anyone to adopt it, particularly if the mathematical field involved is studied enough. Inertia is very strong, even in very abstract disciplines - aren't physicists still treating current as flowing the wrong direction?
  - julienreszka 7y ago
    Inertia
  - michaelbrave 7y ago
    sure unless you quit because you struggled to learn what was in place.
- wtallis 7y ago
  The most likely place to be hanging around mathematicians is at a school, and that's also where you would expect to hear students complaining about notation as an impediment to learning.
  - Someone 7y ago
    I don’t think it is a given that students are good judges about what impedes them from learning. Having said that, I personally have never had issues with notation in mathematics nor did I have the impression others I helped had. IMO, abstraction is the main stumbling block, not notation.
    - Grustaf 7y ago
      I’m talking about the math institutions at the two universities I attended, I took a lot of phd classes. But same with students, the complaint has never been about notation. In fact the only people that seem to complain about notation is computer programmers who find it too loose, but that is precisely its power.
Ar-Curunir 7y ago
Are you kidding? Bad notation abounds in mathematics and theoretical computer science
- Grustaf 7y ago
  Do you have any examples?
invalidOrTaken 7y ago
Ken Iverson complained so much about notation he came up with his own and won the Turing award.
317070 7y ago
Well, here you have one! Computer science notation is vastly superior to the common mathematical one. It's a different league of clarity. But my papers need to follow the consensus, as I'm already trying to get a hard idea across to my reader who decides to spend 15 minutes to try and understand me, maybe. So yes, then I need to introduce 15 symbols, half of them greek, and a number of operations between them using whatever line/subscript/superscript/brace is fashionable. The biggest difference is in slides. In slides I try and can usually avoid the math notation. Because I am there talking it through, which makes notation less important and gives me an opportunity to switch to long variable names and everything a function, more akin to the software notation.
- Grustaf 7y ago
  The only people I’ve ever heard having problems with math notation (as opposed to math concepts, which are often extremely abstract) are computer scientist and computer people in general. I think what irritates them is the fluidity and flexibility of most math notation. It’s not really machine readable since it really assumes you know what you’re doing. The same string of symbols can mean vastly different things in different contexts, which is precisely the power of math notation. Brevity is actually a goal in itself, it makes it possible to keep even larger constructions in your mind at the same time. Consider einteinian notation, with implicit summation. Very terse, and very powerful when you know what you’re doing. I’m sure CS notation is great for CS but trust me, math notation is pretty damn near optimal for math. Second only to theoretical physicists, mathematicians are probably the smartest of scientists.