4 ms·

Yes, with the assumption that the reader is familiar with any symbol or notation not explained in said paragraph. I find it very irritating and a barrier to sha

Yes, with the assumption that the reader is familiar with any symbol or notation not explained in said paragraph. I find it very irritating and a barrier to sharing knowledge when I'm unable to understand a paper because some notation is just assumed to be known - especially because there's no sensible way of looking up math/symbols online.

xyzzyz 5y ago
If you don’t know the notation, you almost surely don’t know the concepts themselves, and so the barrier to your understanding is lack of your background knowledge, not just notation issues. Math is just genuinely complex and hard, and people who have experience with basic mathematics in school or university simply should not expect the advanced stuff to be within easy grasp, as they sometimes do. Consider this classic, very well written paper: https://math.berkeley.edu/~nadler/atiyah.classification.pdf https://math.berkeley.edu/~nadler/atiyah.classification.pdf The “Generalities” section has only one page and hardly any equations, author simply defines notation he uses. And yet, it requires something like 2+ years of prior education in advanced mathematics (either in strong undergrad program, or in a graduate program) to really grasp it. Author even defines his notation: “E [is] the sheaf of germs of regular sections of E, and \Gamma(E) [is] the vector space of global regular sections of E, thus \Gamma(E) = H^0(X, E).”. Sure, he doesn’t define what H^0(X,E) is, but if I told you that it’s the degree zero sheaf cohomology group of E, would that make any difference to you?
- 127 5y ago
  Yet so many papers I read are just another Gaussian wearing another pants.
- sundarurfriend 5y ago
  > If you don’t know the notation, you almost surely don’t know the concepts themselves The difference is that it is much easier to websearch a concept by name than by notation. "degree zero sheaf cohomology group" is a big handle to search, discover, and learn things with, whereas "H^0(X,E)" is a deadend.
  - xyzzyz 5y ago
    Or, you can just pick a relevant textbook, which will be better than anything you can possibly google.
- wizzwizz4 5y ago
  > If you don’t know the notation, you almost surely don’t know the concepts themselves, I find that this isn't true. I spent quite a few years working on number theory problems on my own, just out of interest. I developed several techniques that I just couldn't understand when other people used them, because they had really weird notations, like |x-Σbⁿdₙ|<ϵ, with no definitions for any of the letters. (Feel free to guess what that means. Hint: nothing to do with set membership.) Sure, you can work it out if you can compare several different papers, so it's only a barrier for a few days… but it's still a barrier.
jacamera 5y ago
I've found this book to be very helpful: Mathematical Notation: A Guide for Engineers and Scientists [0]. It's compact, very well organized, and has several indexes to make symbol lookups easier and good summaries of what they mean. [0] https://www.amazon.com/gp/product/1466230525 https://www.amazon.com/gp/product/1466230525

xyzzyz 5y ago

If you don’t know the notation, you almost surely don’t know the concepts themselves, and so the barrier to your understanding is lack of your background knowledge, not just notation issues. Math is just genuinely complex and hard, and people who have experience with basic mathematics in school or university simply should not expect the advanced stuff to be within easy grasp, as they sometimes do. Consider this classic, very well written paper: https://math.berkeley.edu/~nadler/atiyah.classification.pdf https://math.berkeley.edu/~nadler/atiyah.classification.pdf The “Generalities” section has only one page and hardly any equations, author simply defines notation he uses. And yet, it requires something like 2+ years of prior education in advanced mathematics (either in strong undergrad program, or in a graduate program) to really grasp it. Author even defines his notation: “E [is] the sheaf of germs of regular sections of E, and \Gamma(E) [is] the vector space of global regular sections of E, thus \Gamma(E) = H^0(X, E).”. Sure, he doesn’t define what H^0(X,E) is, but if I told you that it’s the degree zero sheaf cohomology group of E, would that make any difference to you?

127 5y ago
Yet so many papers I read are just another Gaussian wearing another pants.
sundarurfriend 5y ago
> If you don’t know the notation, you almost surely don’t know the concepts themselves The difference is that it is much easier to websearch a concept by name than by notation. "degree zero sheaf cohomology group" is a big handle to search, discover, and learn things with, whereas "H^0(X,E)" is a deadend.
- xyzzyz 5y ago
  Or, you can just pick a relevant textbook, which will be better than anything you can possibly google.
wizzwizz4 5y ago
> If you don’t know the notation, you almost surely don’t know the concepts themselves, I find that this isn't true. I spent quite a few years working on number theory problems on my own, just out of interest. I developed several techniques that I just couldn't understand when other people used them, because they had really weird notations, like |x-Σbⁿdₙ|<ϵ, with no definitions for any of the letters. (Feel free to guess what that means. Hint: nothing to do with set membership.) Sure, you can work it out if you can compare several different papers, so it's only a barrier for a few days… but it's still a barrier.

jacamera 5y ago

I've found this book to be very helpful: Mathematical Notation: A Guide for Engineers and Scientists [0]. It's compact, very well organized, and has several indexes to make symbol lookups easier and good summaries of what they mean. [0] https://www.amazon.com/gp/product/1466230525 https://www.amazon.com/gp/product/1466230525