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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 o

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.

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.