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> I dislike maths notation as I find it lacks rigour. I see this a lot from programmers, but in essence, you seem to be complaining that maths notation isn't w

> I dislike maths notation as I find it lacks rigour. I see this a lot from programmers, but in essence, you seem to be complaining that maths notation isn't what you want it to be, but is instead something else that mathematicians (and physicists and engineers) find useful.

Hermitian909 5y ago
As someone who's studied math and CS extensively, it's not that mathematicians don't need that rigor it's only certain sub-fields have a culture of this kind of notational rigor. You absolutely see little bubbles of research, 2-4 professors, get sealed off from the rest of the research community because their notational practices are so sloppy that no one wants to bother whereas others make it easy to understand their work. CS as a field just seems to have a higher base standard for explaining their notation and ideas. It helps in cross-collaboration by making it significantly easier to self study. Related to this, I'd say math books have a significantly worse pedagogical culture in regards to both notation and defining pre-requisites. It's very common for a math book to say "we expect readers to have taken a discrete math course" and not defining notation despite knowing the topics covered in discrete math vary greatly from school to school and may not overlap. Math professors frequently have to paper over these problems at Uni as they realize the class does not understand some notation. CS are just better about this, and I can only explain it as a part of the culture and tradition.
- mistrial9 5y ago
  I read some graph theory papers from mid-20th Century and yes, this is true
- Jensson 5y ago
  > CS are just better about this, and I can only explain it as a part of the culture and tradition. CS professors writes just as incomprehensible math as everyone else, as you can see many here brings up examples of CS professors writing incomprehensible math in their papers.
  - kazinator 5y ago
    Moreover, you might think that Lisp notation would improve it, but CS papers using S-expressions are just as incomprehensible, even to a seasoned Lisp programmer. Math notations are two-dimensional and don't suffer very badly from structural ambiguities, so that actually fixes almost nothing. The problem in unfamiliar math notations is rarely the chunking of which clump is a child of which clump. E.g say that some paper uses, say, angle brackets, with some deep meaning that you can learn about if you recurse three levels down in the list of references. I'm not confused that in <Ap>, the Ap thing is a child of the angle brackets; and calling it (frob (A p)) doesn't help much in this regard. However, at least you can search literature for the word frob more easily than for angle brackets.
    - cabalamat 5y ago
      >I'm not confused that in <Ap>, the Ap thing is a child of the angle brackets; and calling it (frob (A p)) doesn't help much in this regard. However, at least you can search literature for the word frob more easily than for angle brackets. Also it's perhaps more likely to occur to the person using the frob notation that maybe they should define frob somwewhere.
  - Hermitian909 5y ago
    I think you can easily pick examples from any field of terribly written papers but I'm attempting to describe my experience of interacting with both disciplines over many years; reading many books and papers from both.
wirrbel 5y ago
I graduated in physics so I am no stranger to math notation quirks and I think I also do understand their usefulness at times (conciseness in notation, etc). And it can be dangerous, too. As soon as the notation lures you into doing transformations that are invalid. Doesn't help that then notation is often poorly defined, and sometimes a weird mix of notations is presented. Overall the situation is also not pleasant for math people changing topics, or physicists reading papers from physical chemistry professors who 'grew up' in mathematical chemistry.
milesvp 5y ago
You may not realize that in a given field, the same variable that represents the same basic thing may be negated depending on the part of the world the paper is published from. This can be fine, if it’s your subfield, you happen to know to be careful with said variable. I don’t personally dig into a lot of disperate maths in different papers very often, but this is the single biggest complaint my polyglot friend talks about. The second biggest is when he has to read and parse the math from a dozen unrelated papers in a field to find out what some random undefined variable means in the actual paper he cares about.
JuliusBranson 5y ago
I think "useful" is doing a lot of work here. A lot of math notation exists clearly to gate keep. It's often nonsensical. It's a shame because it really makes mathematicians look bad (re:annoying) to those who can see through it. It's not hard to see through it or anything, but it is obnoxious. All you need is an english explanation of the notation, and then you're good, but often all of the sources on the topic are written in the same obnoxious babble language. Take sequential Monte Carlo / sequential importance sampling for instance. This powerpoint on it is clownishly bad: http://people.eecs.berkeley.edu/~jordan/courses/260-spring10/readings/samsi_lec2.pdf http://people.eecs.berkeley.edu/~jordan/courses/260-spring10... This is supposed to be an algorithm implemented in code. It's essentially illegible without code examples, which it doesn't feature. Code examples tell you what the cipher signifies; at no point does the cipher provide any value to the learner. Fanciful bayes-theoretical statements and so on basically reduce to "iteratively build enlarging valid states." Given the fact that this simple statement is missing, I question if the professor has some sort of communication disorder or if they're just a troll. Similar to pomo philosophers, it's probably a mix.
- Jensson 5y ago
  Lecture powerpoints are bad everywhere since you are meant to listen to the lecturer speaking about them, they aren't meant to be read independently like this. Try to understand programming based on a programming lecture powerpoint, it is usually impossible. Edit: Also you can't write code for what he is talking about in that lecture. Code cannot deal with infinities or continuous values. You'd get approximations which isn't the same thing, then you'd need to prove that those approximations are good enough which would have to be done without code anyway.
klibertp 5y ago
Yes. What's wrong with changing math notation? Why wouldn't you do it if you know that it would make it easier for others to approach? What's the rationale behind doing exactly nothing to make the notation more approachable for the masses?
- ColinWright 5y ago
  Math notation has evolved to be what it is because it is useful for the actual doing of math, and the communication of math to those who have sufficient background. It's not deliberately designed to keep people out, and there are literally hundreds of thousands of books that introduce people to the notations used, to help on-board them. Haskell is unreadable to one who has not trained in it or similar languages ... why don't they make the syntax more readable? Or C++ with its modern templating ... why don't they change the syntax to make it more readable? You might be tired of wandering into someone else's area of expertise and telling them: You must change! You must make it more accessible! Believe me, mathematicians are tired of non-mathematicians wandering up and saying: Look! Computer programs are easy and intuitive and everyone can understand them, even without training! Make math like that! Do you really believe that math notation is deliberately designed to make it hard for people untrained in math to learn how to use it? Do you really believe that no one has tried to make it more accessible? Do you really believe you know more about why math notation is what it is than mathematicians and trained mathematics educators do?
  - klibertp 5y ago
    > It's not deliberately designed to keep people out, It looks that way, to many people, even in this thread. > why don't they change the syntax to make it more readable? They do, actually. Quite often at that. It's called releasing new version. > Look! Computer programs are easy and intuitive and everyone can understand them, even without training! Make math like that! No. Computer code is as far from intuitive as it can be. Nobody says otherwise. So you don't need to do anything to get there, the notation's good on that front (meaning: completely non-intuitive). That's where the IDEs come in. And debuggers. And other tools. Lots of tools. They really help. You could use them, because the IDEs-for-math already exist. In college I had exactly one semester to familiarize myself with one of them, and it was never mentioned again until graduation. > Do you really believe that math notation is deliberately designed to make it hard for people untrained in math to learn how to use it? Why, do you believe it's not possible for it to be that way? See: https://en.wikipedia.org/wiki/Pythagoras#Prohibitions_and_regulations https://en.wikipedia.org/wiki/Pythagoras#Prohibitions_and_re... > Do you really believe that no one has tried to make it more accessible? Why did they fail? (If they didn't - where's the exponential growth of first years' mathematicians in training) > Do you really believe you know more about why math notation is what it is than mathematicians and trained mathematics educators do? I'm 100% not interested in why it is like this, it's not my problem, so I really wouldn't know. Would you be interested in how at some point you had to write `class X(object):` and that it later changed to simply `class X:`? Would you go hunt on the mailing list to see who exactly came up with the idea? Or why they thought it would be better that way? Would you be interested in that if you just had to write a 10-lines of Python, to scrape some web site?
JohnHaugeland 5y ago
No. Leave math notation whatever it is Just do a better job of documenting it

Hermitian909 5y ago

As someone who's studied math and CS extensively, it's not that mathematicians don't need that rigor it's only certain sub-fields have a culture of this kind of notational rigor. You absolutely see little bubbles of research, 2-4 professors, get sealed off from the rest of the research community because their notational practices are so sloppy that no one wants to bother whereas others make it easy to understand their work. CS as a field just seems to have a higher base standard for explaining their notation and ideas. It helps in cross-collaboration by making it significantly easier to self study. Related to this, I'd say math books have a significantly worse pedagogical culture in regards to both notation and defining pre-requisites. It's very common for a math book to say "we expect readers to have taken a discrete math course" and not defining notation despite knowing the topics covered in discrete math vary greatly from school to school and may not overlap. Math professors frequently have to paper over these problems at Uni as they realize the class does not understand some notation. CS are just better about this, and I can only explain it as a part of the culture and tradition.

mistrial9 5y ago
I read some graph theory papers from mid-20th Century and yes, this is true
Jensson 5y ago
> CS are just better about this, and I can only explain it as a part of the culture and tradition. CS professors writes just as incomprehensible math as everyone else, as you can see many here brings up examples of CS professors writing incomprehensible math in their papers.
- kazinator 5y ago
  Moreover, you might think that Lisp notation would improve it, but CS papers using S-expressions are just as incomprehensible, even to a seasoned Lisp programmer. Math notations are two-dimensional and don't suffer very badly from structural ambiguities, so that actually fixes almost nothing. The problem in unfamiliar math notations is rarely the chunking of which clump is a child of which clump. E.g say that some paper uses, say, angle brackets, with some deep meaning that you can learn about if you recurse three levels down in the list of references. I'm not confused that in <Ap>, the Ap thing is a child of the angle brackets; and calling it (frob (A p)) doesn't help much in this regard. However, at least you can search literature for the word frob more easily than for angle brackets.
  - cabalamat 5y ago
    >I'm not confused that in <Ap>, the Ap thing is a child of the angle brackets; and calling it (frob (A p)) doesn't help much in this regard. However, at least you can search literature for the word frob more easily than for angle brackets. Also it's perhaps more likely to occur to the person using the frob notation that maybe they should define frob somwewhere.
- Hermitian909 5y ago
  I think you can easily pick examples from any field of terribly written papers but I'm attempting to describe my experience of interacting with both disciplines over many years; reading many books and papers from both.

wirrbel 5y ago

I graduated in physics so I am no stranger to math notation quirks and I think I also do understand their usefulness at times (conciseness in notation, etc). And it can be dangerous, too. As soon as the notation lures you into doing transformations that are invalid. Doesn't help that then notation is often poorly defined, and sometimes a weird mix of notations is presented. Overall the situation is also not pleasant for math people changing topics, or physicists reading papers from physical chemistry professors who 'grew up' in mathematical chemistry.

milesvp 5y ago

You may not realize that in a given field, the same variable that represents the same basic thing may be negated depending on the part of the world the paper is published from. This can be fine, if it’s your subfield, you happen to know to be careful with said variable. I don’t personally dig into a lot of disperate maths in different papers very often, but this is the single biggest complaint my polyglot friend talks about. The second biggest is when he has to read and parse the math from a dozen unrelated papers in a field to find out what some random undefined variable means in the actual paper he cares about.

JuliusBranson 5y ago

I think "useful" is doing a lot of work here. A lot of math notation exists clearly to gate keep. It's often nonsensical. It's a shame because it really makes mathematicians look bad (re:annoying) to those who can see through it. It's not hard to see through it or anything, but it is obnoxious. All you need is an english explanation of the notation, and then you're good, but often all of the sources on the topic are written in the same obnoxious babble language. Take sequential Monte Carlo / sequential importance sampling for instance. This powerpoint on it is clownishly bad: http://people.eecs.berkeley.edu/~jordan/courses/260-spring10/readings/samsi_lec2.pdf http://people.eecs.berkeley.edu/~jordan/courses/260-spring10... This is supposed to be an algorithm implemented in code. It's essentially illegible without code examples, which it doesn't feature. Code examples tell you what the cipher signifies; at no point does the cipher provide any value to the learner. Fanciful bayes-theoretical statements and so on basically reduce to "iteratively build enlarging valid states." Given the fact that this simple statement is missing, I question if the professor has some sort of communication disorder or if they're just a troll. Similar to pomo philosophers, it's probably a mix.

Jensson 5y ago
Lecture powerpoints are bad everywhere since you are meant to listen to the lecturer speaking about them, they aren't meant to be read independently like this. Try to understand programming based on a programming lecture powerpoint, it is usually impossible. Edit: Also you can't write code for what he is talking about in that lecture. Code cannot deal with infinities or continuous values. You'd get approximations which isn't the same thing, then you'd need to prove that those approximations are good enough which would have to be done without code anyway.

klibertp 5y ago

Yes. What's wrong with changing math notation? Why wouldn't you do it if you know that it would make it easier for others to approach? What's the rationale behind doing exactly nothing to make the notation more approachable for the masses?

ColinWright 5y ago
Math notation has evolved to be what it is because it is useful for the actual doing of math, and the communication of math to those who have sufficient background. It's not deliberately designed to keep people out, and there are literally hundreds of thousands of books that introduce people to the notations used, to help on-board them. Haskell is unreadable to one who has not trained in it or similar languages ... why don't they make the syntax more readable? Or C++ with its modern templating ... why don't they change the syntax to make it more readable? You might be tired of wandering into someone else's area of expertise and telling them: You must change! You must make it more accessible! Believe me, mathematicians are tired of non-mathematicians wandering up and saying: Look! Computer programs are easy and intuitive and everyone can understand them, even without training! Make math like that! Do you really believe that math notation is deliberately designed to make it hard for people untrained in math to learn how to use it? Do you really believe that no one has tried to make it more accessible? Do you really believe you know more about why math notation is what it is than mathematicians and trained mathematics educators do?
- klibertp 5y ago
  > It's not deliberately designed to keep people out, It looks that way, to many people, even in this thread. > why don't they change the syntax to make it more readable? They do, actually. Quite often at that. It's called releasing new version. > Look! Computer programs are easy and intuitive and everyone can understand them, even without training! Make math like that! No. Computer code is as far from intuitive as it can be. Nobody says otherwise. So you don't need to do anything to get there, the notation's good on that front (meaning: completely non-intuitive). That's where the IDEs come in. And debuggers. And other tools. Lots of tools. They really help. You could use them, because the IDEs-for-math already exist. In college I had exactly one semester to familiarize myself with one of them, and it was never mentioned again until graduation. > Do you really believe that math notation is deliberately designed to make it hard for people untrained in math to learn how to use it? Why, do you believe it's not possible for it to be that way? See: https://en.wikipedia.org/wiki/Pythagoras#Prohibitions_and_regulations https://en.wikipedia.org/wiki/Pythagoras#Prohibitions_and_re... > Do you really believe that no one has tried to make it more accessible? Why did they fail? (If they didn't - where's the exponential growth of first years' mathematicians in training) > Do you really believe you know more about why math notation is what it is than mathematicians and trained mathematics educators do? I'm 100% not interested in why it is like this, it's not my problem, so I really wouldn't know. Would you be interested in how at some point you had to write `class X(object):` and that it later changed to simply `class X:`? Would you go hunt on the mailing list to see who exactly came up with the idea? Or why they thought it would be better that way? Would you be interested in that if you just had to write a 10-lines of Python, to scrape some web site?

JohnHaugeland 5y ago

No. Leave math notation whatever it is Just do a better job of documenting it