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For what it's worth, I am a mathematician, and I'll say that there is definitely a lot of awkward notation out there in math, and some of it I would agree is ev
by nicf 3y ago
For what it's worth, I am a mathematician, and I'll say that there is definitely a lot of awkward notation out there in math, and some of it I would agree is even fair to describe as just bad. But I'm pretty confident in saying that basically no one is malevolently inventing notation just to make other people's lives harder! This just isn't how mathematicians think, and anyway if you intentionally invented terrible notation for your own field, you'd be hurting yourself much more than anyone else.
There are plenty of other reasons mathematical notation might be hard for beginners:
* The notation in question might have originally been invented for a narrower purpose than it's being used for now, and has been stretched beyond the domain where it fits well.
* Someone made a weird decision a hundred years ago, but now everyone's used to writing things that way, and if you want to be understood it's easier to use the same notation as everyone else.
* The notation might actually be better than you're giving it credit for, but this is only obvious once you've spent a while working in the field.
Overall, I've noticed that people coming to math from CS tend to put more weight on the question of notation than mathematicians do. I will say, from my perspective, I think it's very easy to make a bigger deal out of notation than necessary. A lot of math is just authentically pretty tricky and takes effort to learn no matter what notation you use, and I think it's pretty rare for the notation to actually be the lowest-hanging fruit here. This isn't to say that there's no mathematical notation that could use improvement (quite the opposite!) but I don't think making those changes would have quite the impact you might be imagining.
- jcranmer 3y agoThere are two other big issues with math notation that I see: * The tendency of math to have many different notations to express the same thing. My calculus textbook started by apologizing for the like seven different notations for "take the derivative of this function". Would it kill mathematicians to just pick one notation and standardize on it? * The number of times the same notation can mean two different things. I've always been particularly bothered by stuff like implicit adjacency is multiplication, except when it's not. Is "a(b + c)" supposed to mean "add b to c and use the result as the argument for a" or is it supposed to mean "add b to c and multiply it with a"? You'd think it should be obvious, but functions are a ring, with multiplication corresponding to composition...
- nicf 3y agoSure, but I think we're just talking about two slightly different things here: I was trying to describe the "sociological" reasons why math notation might end up in a state that you don't like rather than trying to list the particular things you might not like about it. I do agree with you that calculus textbooks often go overboard with notations for the derivative, and in fact I remember being taught some (like a capital D with a subscript x) that I then never saw again for the rest of my life. But as to the question of why "mathematicians" would do this, I don't think the answer is all that mysterious: "mathematicians" is a category that includes a lot of different people in different places and there's no central committee that enforces notation standards! It's like that one XKCD comic everyone posts about inventing new standards.