If you’re a working mathematician, it’s the only way you think.

If you are the X then you must do/be Y is called gatekeeping.

And of course this is not true.

I know mathematicians who work almost exclusively on a computer, and others who have an old dusty computer from 20 years ago in the corner of their office that they barely touch. Most are somewhere in between.

Mathematics is one of the oldest disciplines in the world. Grumbling about the legacy of its ancient history as ‘gatekeeping’ is puerile.

This started worth talking about notation. Notation of mathematics has changed significantly over time - Newton's Principae is not readable without accounting for changes. In the history of maths, that is a fairly recent work.

I actually agree with your premise: mathematics and it’s notations (plural) are ancient. The current notations are those that were found to be most convenient by centuries of practice by expert practitioners.

This is of course very true but doesn’t take into account invention of computer that is relatively recent.

Since it in principle never makes mistakes (in practice there are of course bugs, but they are usually different in nature than human errors) it changes what is possible and most convenient. You no longer have to optimise for simplicity as heavily for example. On the other hand computers basically can’t deal with ambiguity, so the rules and statements have to be stated very simply and clearly.

I believe computers can change the landscape of what’s best notation. This is an interesting, interdisciplinary topic to explore.

I think APL was originally created as a fix to this problem. A completely revamped math notation to make it more fit to computers as a medium, instead of pen and paper.

If it was created thus then it could hardly be considered successful. To all but the dedicated and obsessive cognoscenti APL is nothing but gobbledygook.

> If you are the X then you must do/be Y is called gatekeeping.

Let's be precise here: the parent hasn't used "must" here, just stated their observation. It's possible that many if not most mathematicians work this way, but it's not definitely the only one, and it doesn't mean it can't be changed. Actually, there is a lot of work being done on theorem provers, for example.

If you are a python programmer you must program in python.

Yes. I'm sorry but how is this not obvious? Do you enjoy hand-writing code on paper?

The natural medium for math is on whiteboards and paper. A computer algebra system like Mathematica is useful, but it augments what is traditionally a paper-and-pencil activity. It makes sense that the standard notation for math is something that is amenable to physical tools.

And it makes sense that the computer tools to assist mathematicians should more closely match this standard notation.

In many cases yes. Especially non-programmers really like that the equation they type into their software looks exactly the the equation in the paper they are copying it from.

Who said it was my highest priority? Obviously having a solver is the highest priority, but it turns out that if you purport to have made a mathematica competitor, that was the baseline. If you don't have that, you have nothing. So the question is never "can it do what it needs to", it's always "can it do the things which keep me using Mathematica, instead of Sage, like letting me compose notebooks that contain, and show, actual maths?"

And yes, I enjoy writing in math notation because it's an immediately understandable notation compared to 500 character programming statement.