I'm doing a maths degree, which means I am being trained to write out "mathscript", by hand, from memory.* This is suboptimal.
My job consists in a kind of applied maths, but my engagement with maths will not be through mathscript or LaTeX (or even Gallina scripts), but rather imperative computer languages which do things to data. So the degree is not optimised for my or almost anyone's life. (Aside from helping us with annoying, pissing-contest whiteboard job interviews).
By this stage, I understand Python much more easily than modern mathematical notation (despite having about 15 more years of contact with Mathscript). The magnificent folks of SymPy have made this task less than a fudge.
So: definitions and procedures from my uni curriculum, implemented as if they were running on a student, and not a machine. This might have value to you if you are a maths student already into Python, or if you want to see what SymPy can do or whatnot.
I plan to build a class hierarchy to express generalisations, and to build my way up to this tree.
Eventually I might try and use sets, or the category category, or homotopical groupoids as superclass of everything else.
In order to not drift away from mathscript entirely, I plan two versions: one using the conventional uninformative Greek letters and one actually using readable variable naming (naming as if paper were not a scarce luxury).
I suppose this project is a little misguided. The value of a maths degree used to be "gives you access to the greatest machineries of truth", but anyone with any access to the internet whatsoever has that now. Now, the degree gives you the ability to read papers and evidence of your manual abilities with those creative machines. (And this plodding internalism is at least correlated with real understanding.)
But I think writing things in SymPy gives that hard, slow value too. And there are still the exams, where I'll prove that processing once occurred in my meatbrain, and so gain the economic signal.
- Where "mathscript" is modern mathematical notation. This notation doesn't seem to have a name, but if it did it'd be "infix Arabian-Eulerian-Peanoan mathscript".