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Go to definition (for symbols or notation) would certainly be helpful in reading a mathematical paper, but how is that related to choosing good notation? Do yo
by shasta 11y ago
Go to definition (for symbols or notation) would certainly be helpful in reading a mathematical paper, but how is that related to choosing good notation? Do you have an example of mathematical notation that "fails in practice"? In my experience, mathematical notation becomes established because it works well enough in practice.
- skybrian 11y agoI don't have any specific example, but I've read that many (most?) math papers are incomprehensible to outsiders, even mathematicians in other fields. I also seem to remember an article about a proof that's gone unchecked for years. So, from the outside, it seems like there are big problems with communication in the mathematics community, and it's simply accepted that it has to be that way because math is hard.
- kaitai 11y agoGood notation certainly aids understanding, but math is a vast endeavor where the details matter. In switching from one programming language to another, often a rough understanding of corresponding concepts is enough: how to print has different details in different languages but it's not that different, and the details are easy to look up. On the other hand, just switching from topology to symplectic geometry involves asking entirely different questions -- having different values and pursuing different goals. Maybe it's more like switching from web dev to scientific computing as well as switching languages. Yes, a lot of mathematical papers are incomprehensible to others in the field. But it's not just because of notation. You wouldn't ask a content marketer who is great at A/B testing to deal with tweaking something in the linux kernel because it's all "computers".
- shasta 11y agoThis is like saying that the Windows codebase is incomprehensible and thus C / C++ must need better syntax.