Notation an symbology comes out of a minmax optimisation. Minimizing complexity maximizing reach. As with every local critical point, it is probably not the only state we could have ended at.

For example, for your point 1: we could probably start there, but once you get familiar with the notation you dont want to keep writing a huge list of parameters, so you would probably come up with a higher level data structure parameter which is more abstract to write it as an input. And then the next generation would complain that the data structure is too abstract/takes too much effort to be comunicated to someone new to the field, because they did not live the problem that made you come with a solution first hand.

And for you point 2: where do you draw the line with your hyperlinks. If you mention the real plane, do you reference the construction of the real numbers? And dimensionl? If you reason a proof by contradiction, do you reference the axioms of logic? If you say "let {xn} be a converging sequence" do you reference convergence, natural numbers and sets? Or just convergence? Its not that simple, so we came up with a minmax solution which is what everybody does now.

Having said this, there are a lot of articles books that are not easy to understand. But that is probably more of an issue of them being written by someone who is bad at communicating, than because of the notation.

Go ahead. Write a math paper with your proposed new notation with hyperlinks and submit it to a journal somewhere.

Probably not. The conventional math notation has three major advantages over the "[n]o superscripts or subscripts or [G]reek letters and weird symbols" you're proposing:

1. It's more human-readable. The superscripts and subscripts and weird symbols permit preattentive processing of formula structures, accelerating pattern recognition.

2. It's familiar. Novel math notations face the same problem as alternative English orthographies like Shavian (https://en.wikipedia.org/wiki/Shavian_alphabet) in that, however logical they may be, the audience they'd need to appeal to consists of people who have spent 50 years restructuring their brains into specialized machines to process the conventional notation. Aim t3mpted te rait qe r3st ev q1s c0m3nt 1n mai on alterned1v i6gl1c orx2grefi http://canonical.org/~kragen/alphanumerenglish bet ai qi6k ail rez1st qe t3mpt8cen because, even though it's a much better way to spell English, nobody would understand it.

3. It's optimized for rewriting a formula many times. When you write a computer program, you only write it once, so there isn't a great burden in using a notation like (eq (deriv x (pow e y)) (mul (pow e y) (deriv x y)) 1), which takes 54 characters to say what the conventional math notation¹ says in 16 characters³. But, when you're performing algebraic transformations of a formula, you're writing the same formula over and over again in different forms, sometimes only slightly transformed; the line before that one said (eq (deriv x (pow e y)) (deriv x x) 1), for example². For this purpose, brevity is essential, and as we know from information theory, brevity is proportional to the logarithm of the number of different weird symbols you use.

We could certainly improve conventional math notation, and in fact mathematicians invent new notation all the time in order to do so, but the direction you're suggesting would not be an improvement.

People do make this suggestion all the time. I think it's prompted by this experience where they have always found math difficult, they've always found math notation difficult, and they infer that the former is because of the latter. This inference, although reasonable, is incorrect. Math is inherently difficult, as far as anybody knows (an observation famously attributed to Euclid) and the difficult notation actually makes it easier. Undergraduates routinely perform mental feats that defied Archimedes because of it.

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¹ \frac d{dx}e^y = e^y\frac{dy}{dx} = 1

² \frac d{dx}e^y = \frac d{dx}x = 1

³ See https://nbviewer.org/url/canonical.org/~kragen/sw/dev3/logar... for a cleaned-up version of the context where I wrote this equation down on paper the other day.

I'd love getting rid of all the weird symbols in favor of clear text functions or whatever. As someone who never learnt all the weird symbols its really preventing me from getting into math again... It is just not intuitive.