Indeed, confused people say things that don't make sense.

Not at all. Over and over I find really intimidating math notation actually represents pretty simple concepts. Sigma notation is a good example of this. Hmm, giant sigma or sum()?

You think changing sigma to sum() would make it easier to understand the 5 paper, 1000 page proof of the geometric Langlands conjecture?

Imagine how much unnecessary time would be added to a course about series if the lecturer had to write sum() instead of ∑ every time. If you find it hard to remember that ∑ means sum, math might not be for you, and that’s fine.

it's not so much remembering what ∑ means insomuch as that it's completely impossible to google the first time you run across it. It'll be in some PDF that doesn't allow you to copy-paste the symbol and you won't know what it's called. Rinse and repeat for any of the million symbols mathematicians use, never mind that loads of symbols are context dependent even if you could google them.

I hope mathematicians have a better reason than "it's tradition" for making the entire field completely opaque to anyone who hasn't studied math extensively.

Basic notation like sums is covered in every undergraduate math course. Any non-standard notation will be introduced by the author using it. Nobody is trying to obscure anything from you.

Yes, mathematical notation is not very discoverable at all.

Wait until you learn about integration. Measures, limits and the quirks of uncountable spaces don't become simpler once you call the operation integrate().

It's like saying that learning Arabic is the easy part of writing a great Saudi novel. True, but you have to understand that being literate is the price of admission. Clearly you consider yourself very facile with mathematical notation but you might have some empathy for the inumerate. Not everyone had the good fortune of great math teachers or even the luxury of attending a good school. I believe there is valid frustration borne out of poor mathematical education.

Well yeah, but this empathy and frustration is simply misplaced. I have empathy for people who didn't get good education, and they should be frustrated towards their bad schooling. Math notation is simply the wrong target.

If they can't see that, it's hard to think they have much chance with the actual math. "A mathematician is a person who knows how to separate the relevant from the irrelevant", a saying I was told in school.

That's funny that you would bring up something you learned in school.

> What they are missing is that the notation is the easy part.

This is so wrong it can only come from a place of inexperience and ignorance.

Mathematics is flush with inconsistent, abbreviated, and overloaded notation.

Show a child a matrix numerically and they can understand it, show them Ax+s=b, and watch the confusion.

The fact that there is a precise analogy between how Ax + s = b works when A is a matrix and the other quantities are vectors, and how this works when everything is scalars or what have you, is a fundamental insight which is useful to notationally encode. It's good to be able to readily reason that in either case, x = A^(-1) (b - s) if A is invertible, and so on.

It's good to be able to think and talk in terms of abstractions that do not force viewing analogous situations in very different terms. This is much of what math is about.

Well, obviously they will be confused because you jumped from a square of numbers to a bunch of operations. They’d be equally confused if you presented those operations numerically. I am not sure what it is you want to prove with that example. I am also not sure that a child can actually understand what a matrix is if you just show them some numbers (i.e., will they actually understand that a matrix is a linear transformer of vectors and the properties it has just by showing them some numbers?)

> a bunch of operations.

Sorry, the notation is bit confusing. The 'A' here is a matrix.

I know it is a matrix, the notation is not confusing at all. I am saying that the concept of a matrix as a set of numbers arranged in a rectangles and the concept of operations on a matrix are very different things, the confusion will not come from notation.

You must be correct, because this interaction is completely devoid of any confusion between the two people attempting to communicate clearly.

I do not have any confusion with the notation, I am confused about what the argument you’re trying to convey with English words.

Ceci n'est pas une pipe.

This is funny. “Mathematics notation is confusing to me because I refuse to learn it. I refuse to learn it because mathematics notation is confusing to me.” Okay sure, be happy with yourself.

> This is so wrong it can only come from a place of inexperience and ignorance.

Thanks for the laughs :D

> Show a child a matrix numerically and they can understand it, show them Ax+s=b, and watch the confusion.

Show a HN misunderstood genius Riemann Zeta function as a Zeta() and they think they can figure out it's zeros. Show it as a Greek letter and they'll lament how impossible it is to understand.