[analog31]

I think it certainly has an effect. My rationale is comparing the earliest writings on algebra and calculus to the present-day notation. Al-Khwrizmi used no symbols or numerals in his text. I can't guess at Newton because the text is in Latin, but the notation looks pretty difficult to me. At the time, you practically had to be a philosopher to understand that writing, much less do anything with it. Likewise I think Clerk-Maxwell's electromagnetic theory was impenetrable until Heaviside created a new notation for it. And we just had a HN thread talking about Mary Somerville's translation of Laplace.

Today we teach algebra and calculus to schoolchildren. I believe as bad as the notation probably still is, the improvement from the original texts is nothing short of qualifying as its own revolution in mathematics. So it's interesting to imagine it being even better.

But I also believe that we only teach one side of math in school, basically manipulation of expressions. We barely touch on other ways that people do math, through the exploration of data, computation, and theory (proofs). So we're painting a distorted picture of what math even is, making it all the harder to justify why it's important beyond just being a gatekeeper.