[pjc50]

Why not one step further, and let the original formula be the code? Directly compilable Latex:

    \vec r = \frac {n_{1}}{n_{2}} \cdot (\vec v - dot(\vec v, \vec n) \cdot \vec N) - \sqrt{1 - \frac {n_{1}^2}{n_{2}^2} \cdot (1 - dot(\vec v, \vec n))} \cdot \vec N

(This is partly a joke and partly a serious suggestion, there are definitely people out there who would find that easier to write, especially if the IDE rendered it properly. I stole it by searching for ni_over_nt and finding http://viclw17.github.io/2018/08/05/raytracing-dielectric-ma... )

[ddragon]

Julia (a language focused on science/math) does it partially. For example in the editor or REPL you can just type \sqrt [tab] \alpha [tab] and it will generate √α which is valid code. Most math symbols in unicode are supported and overloadable. And you can also write matrix like a table, such as

[1 2 3

4 5 6

7 8 9].

And you can transform Julia expressions to LaTeX:

https://github.com/korsbo/Latexify.jl

But even they didn't go as far as being able to parse full LaTeX expressions (though you technically could with reader macros plus editor support).

[OoooooooO]

You could probably do it that way in Julia.