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There pretty much is one true notation. There could be some slight variations, like bolding vectors, putting an arrow over them or not distinguishing them at al

There pretty much is one true notation. There could be some slight variations, like bolding vectors, putting an arrow over them or not distinguishing them at all from scalars. But 95% of the time everyone uses the same notation.

ColinWright 5y ago
I don't know your background, but I wonder how broad it is in terms of mathematical topics. The notations used in Algebraic Topology vs Category Theory vs Algebraic Number Theory vs Analytical Combinatorics vs Complex Analysis. This isn't a criticism, it's just that notations vary wildly in those areas, and there's lots of cross-over of notations, not all of which agree with each other. I'm not an expert, but I've had some exposure to the problem(s).
- Grustaf 5y ago
  I studied diff geo at phd level and met stat at undergrad level, plus a sprinkling of category theory, some discrete mathematics and some physics, so I’ve been exposed to most of these. I presumed we were talking about basic mathematics here since new notation is the least of your worries when your thinking about fibre bundles and cohomologies, but I can’t really think of any significant overlap in notation that would be different between the fields I’ve come across. Could you give some examples?
  - ColinWright 5y ago
    I'm trying to be more general than specific questions at the mid-undergrad level, because looking in from the outside, people seem to thing that if only the notation weren't so mysterious then they could understand everything. But this comment -- https://news.ycombinator.com/item?id=29344238 https://news.ycombinator.com/item?id=29344238 -- gives a flavour, talking about coming across "π" in different contexts and having to give different interpretations. But I remember sketching an algorithm to someone and just inventing notations on the fly as I did so, knowing that they would simply be ways to remember the underlying ideas. Even so, at 1st year undergrad the notations used in Mathematical Physics vary from those used in Introductory Graph Theory, and again from Real Analysis. But once the reader knows the underlying semantics, the actual notation is mostly a non-issue (as you know).
    - Grustaf 5y ago
      Alright, but are there really any overlapping concepts between graph theory and analysis? There can’t be many! The comment you linked to is pretty strange, given the limited number of symbols in the Greek and Latin alphabets, there’s obviously going to be a lot of reuse, but I can’t see how that could really cause any confusion though, unless you’re just grabbing books from the shelf and opening them at random. And even then, it should almost always be clear from context if pi is a number or a plane, and if it’s a function that will be visually distinguished. I’ve seen non-mathematicians use words as names of variables and functions, it always makes me shudder. I unsuccessfully tried to introduce Hebrew letters as an alternative,when I discovered how to use the in Latex, but it never caught on… I actually find math notation incredibly intuitive and effective, I think it’s close to optimal. In fact it’s only after getting into programming that it even occurred to me how elegant and magical it is. I understand what things mean and can write things myself, without being able to exactly explain how, or to translate it into a fully specified system that a computer would understand.

ColinWright 5y ago

I don't know your background, but I wonder how broad it is in terms of mathematical topics. The notations used in Algebraic Topology vs Category Theory vs Algebraic Number Theory vs Analytical Combinatorics vs Complex Analysis. This isn't a criticism, it's just that notations vary wildly in those areas, and there's lots of cross-over of notations, not all of which agree with each other. I'm not an expert, but I've had some exposure to the problem(s).

Grustaf 5y ago
I studied diff geo at phd level and met stat at undergrad level, plus a sprinkling of category theory, some discrete mathematics and some physics, so I’ve been exposed to most of these. I presumed we were talking about basic mathematics here since new notation is the least of your worries when your thinking about fibre bundles and cohomologies, but I can’t really think of any significant overlap in notation that would be different between the fields I’ve come across. Could you give some examples?
- ColinWright 5y ago
  I'm trying to be more general than specific questions at the mid-undergrad level, because looking in from the outside, people seem to thing that if only the notation weren't so mysterious then they could understand everything. But this comment -- https://news.ycombinator.com/item?id=29344238 https://news.ycombinator.com/item?id=29344238 -- gives a flavour, talking about coming across "π" in different contexts and having to give different interpretations. But I remember sketching an algorithm to someone and just inventing notations on the fly as I did so, knowing that they would simply be ways to remember the underlying ideas. Even so, at 1st year undergrad the notations used in Mathematical Physics vary from those used in Introductory Graph Theory, and again from Real Analysis. But once the reader knows the underlying semantics, the actual notation is mostly a non-issue (as you know).
  - Grustaf 5y ago
    Alright, but are there really any overlapping concepts between graph theory and analysis? There can’t be many! The comment you linked to is pretty strange, given the limited number of symbols in the Greek and Latin alphabets, there’s obviously going to be a lot of reuse, but I can’t see how that could really cause any confusion though, unless you’re just grabbing books from the shelf and opening them at random. And even then, it should almost always be clear from context if pi is a number or a plane, and if it’s a function that will be visually distinguished. I’ve seen non-mathematicians use words as names of variables and functions, it always makes me shudder. I unsuccessfully tried to introduce Hebrew letters as an alternative,when I discovered how to use the in Latex, but it never caught on… I actually find math notation incredibly intuitive and effective, I think it’s close to optimal. In fact it’s only after getting into programming that it even occurred to me how elegant and magical it is. I understand what things mean and can write things myself, without being able to exactly explain how, or to translate it into a fully specified system that a computer would understand.