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> There are places where math is hard, needs work, and most people have come to a point where they feel that the effort won't be worth it The problem with math

by Aaargh20318 7y ago

> There are places where math is hard, needs work, and most people have come to a point where they feel that the effort won't be worth it The problem with math is that it's seems much harder than it actually is. Every time I have to look into some specific math I haven't worked with before I spend a lot of time decoding what they actually mean. Usually what is happening is not that difficult at all, mathematicians just insist on writing it down in the most convoluted and incomprehensible way imaginable. It's like they took every bad coding practice and applied it all to math. Why have descriptive variable names if you can just use random greek letters ? Why give a function or operation a name at all if you could make up some weird symbol instead ? And of course you want those symbols to have different meanings depending on context. Imagine if programmers worked like that and wrote everything as obfuscated C++ code, because fuck you.

bonoboTP 7y ago
True. Many times the notation gets in the way, but math is very conservative in this regard. Often I'd just prefer seeing a formula in SymPy (symbolic math library for Python) code.
ColinWright 7y ago
> Why have descriptive variable names if you can just use random greek letters? This is a common complaint I see from programmers all the time. However, I've seen people trying to do real maths with descriptive names, and it fails very, very quickly. This is by no means comprehensive, but as a (probably thought) experiment, try writing reasonable complex code without variable name completion. You write the same variable name over and over and over, and after a while you realise that since this variable is only use in this screenful or two of code, it's easy enough just to use a short name and know what it is, because you're only thinking about it here, in this context. I'm not going to try to defend mathematical notation in general because there are enormous inconsistencies, many of which are historical, accidental, and indefensible. But when you're doing the maths it becomes tolerable, then usable, then actively helpful. It's like the parentheses in Lisp - all newbies complain about them, and those versed in the art know that after a while they not only don't matter, they are a genuine positive. But unless you take the time to do the math, that won't happen for you. That makes it sound like a deliberate barrier, but it's not, it really isn't.
- Aaargh20318 7y ago
  > This is by no means comprehensive, but as a (probably thought) experiment, try writing reasonable complex code without variable name completion. So why don't math tools have variable name completion ? and/or why insist on still doing things on paper in 2019 ? The other things about variable names is that they force you to think about what a variable actually contains. This in itself is very helpful not only for others reading your work, but also for yourself when trying to grasp a problem.
  - ColinWright 7y ago
    The research mathematicians I work with just stare in incomprehension at the idea of doing their work on any computer-mediated system. Yes, there are things that can be done, and yes, computer proof-assistants have made huge strides, and yes, there are always people at the cutting edge doing amazing work. But your everyday research mathematician will just stare in disbelief. I don't know your background, your profile is empty, but it sounds like you are someone who genuinely has no idea of how research in math works, and therefore feel that you really must have a better way of doing things. And maybe you have. But speaking as someone who has a PhD in pure math, and who has worked in safety critical software, I can only say that so far everything you're suggesting just really doesn't make sense. The reason that for centuries mathematicians use single letter glyphs to represent the things they're dealing with is because it is, for the purpose of doing the work, the most effective thing to use.
    - Aaargh20318 7y ago
      > The research mathematicians I work with just stare in incomprehension at the idea of doing their work on any computer-mediated system. Yes, there are things that can be done, and yes, computer proof-assistants have made huge strides, and yes, there are always people at the cutting edge doing amazing work. I'm not talking about computer assisted proofs or anything like that. Just using a readable syntax and the mathematical equivalent of a word processor would be an enormous step forward. No one is writing books in cursive with a fountain pen anymore either, which is basically analogue to what mathematicians are still doing.
chongli 7y ago
Why have descriptive variable names if you can just use random greek letters Because math is abstract. The variables and constants don’t mean anything in most cases and are only given different symbols to distinguish one from another. Descriptive variable names or even descriptive subscripts get OLD very quickly when you’re working through a page of calculations to solve a problem. The beauty of math, if you’re using it to solve some real world problem, is that you can forget about what the symbols mean and focus on solving the equations, evaluating the integral or derivative, or whatever other calculation you’re doing. Once you’ve completed all of the calculations and gotten your answer simplified as much as possible, then you can go back to the problem you were trying to solve and interpret your result in context. Since you’ve done all of your calculations purely symbolically, you can see the relationships between the quantities you’re working with. In many cases, some quantities you thought were important actually cancel out and don’t appear in your final answer at all. This tells you something fundamental about the independence of your quantities. Perhaps the most famous case of this comes from physics: the acceleration of an object in free fall is independent of its mass. You would not see this so clearly if you substituted numerical quantities as soon as possible.
- Aaargh20318 7y ago
  > The variables and constants don’t mean anything in most cases Don't they really mean anything or are mathematicians just unable to grasp what they mean ? To me this seems like a symptom of an underlying bigger problem in our understanding of math rather than those variables not having a meaning.

bonoboTP 7y ago

True. Many times the notation gets in the way, but math is very conservative in this regard. Often I'd just prefer seeing a formula in SymPy (symbolic math library for Python) code.

ColinWright 7y ago

> Why have descriptive variable names if you can just use random greek letters? This is a common complaint I see from programmers all the time. However, I've seen people trying to do real maths with descriptive names, and it fails very, very quickly. This is by no means comprehensive, but as a (probably thought) experiment, try writing reasonable complex code without variable name completion. You write the same variable name over and over and over, and after a while you realise that since this variable is only use in this screenful or two of code, it's easy enough just to use a short name and know what it is, because you're only thinking about it here, in this context. I'm not going to try to defend mathematical notation in general because there are enormous inconsistencies, many of which are historical, accidental, and indefensible. But when you're doing the maths it becomes tolerable, then usable, then actively helpful. It's like the parentheses in Lisp - all newbies complain about them, and those versed in the art know that after a while they not only don't matter, they are a genuine positive. But unless you take the time to do the math, that won't happen for you. That makes it sound like a deliberate barrier, but it's not, it really isn't.

Aaargh20318 7y ago
> This is by no means comprehensive, but as a (probably thought) experiment, try writing reasonable complex code without variable name completion. So why don't math tools have variable name completion ? and/or why insist on still doing things on paper in 2019 ? The other things about variable names is that they force you to think about what a variable actually contains. This in itself is very helpful not only for others reading your work, but also for yourself when trying to grasp a problem.
- ColinWright 7y ago
  The research mathematicians I work with just stare in incomprehension at the idea of doing their work on any computer-mediated system. Yes, there are things that can be done, and yes, computer proof-assistants have made huge strides, and yes, there are always people at the cutting edge doing amazing work. But your everyday research mathematician will just stare in disbelief. I don't know your background, your profile is empty, but it sounds like you are someone who genuinely has no idea of how research in math works, and therefore feel that you really must have a better way of doing things. And maybe you have. But speaking as someone who has a PhD in pure math, and who has worked in safety critical software, I can only say that so far everything you're suggesting just really doesn't make sense. The reason that for centuries mathematicians use single letter glyphs to represent the things they're dealing with is because it is, for the purpose of doing the work, the most effective thing to use.
  - Aaargh20318 7y ago
    > The research mathematicians I work with just stare in incomprehension at the idea of doing their work on any computer-mediated system. Yes, there are things that can be done, and yes, computer proof-assistants have made huge strides, and yes, there are always people at the cutting edge doing amazing work. I'm not talking about computer assisted proofs or anything like that. Just using a readable syntax and the mathematical equivalent of a word processor would be an enormous step forward. No one is writing books in cursive with a fountain pen anymore either, which is basically analogue to what mathematicians are still doing.

chongli 7y ago

Why have descriptive variable names if you can just use random greek letters Because math is abstract. The variables and constants don’t mean anything in most cases and are only given different symbols to distinguish one from another. Descriptive variable names or even descriptive subscripts get OLD very quickly when you’re working through a page of calculations to solve a problem. The beauty of math, if you’re using it to solve some real world problem, is that you can forget about what the symbols mean and focus on solving the equations, evaluating the integral or derivative, or whatever other calculation you’re doing. Once you’ve completed all of the calculations and gotten your answer simplified as much as possible, then you can go back to the problem you were trying to solve and interpret your result in context. Since you’ve done all of your calculations purely symbolically, you can see the relationships between the quantities you’re working with. In many cases, some quantities you thought were important actually cancel out and don’t appear in your final answer at all. This tells you something fundamental about the independence of your quantities. Perhaps the most famous case of this comes from physics: the acceleration of an object in free fall is independent of its mass. You would not see this so clearly if you substituted numerical quantities as soon as possible.

Aaargh20318 7y ago
> The variables and constants don’t mean anything in most cases Don't they really mean anything or are mathematicians just unable to grasp what they mean ? To me this seems like a symptom of an underlying bigger problem in our understanding of math rather than those variables not having a meaning.