> The burden is on those who claim it can be better to come up with something better.
We need to agree to disagree: in my mind, it's on those who say it's the best it can be to show that it indeed, cannot be better. Because otherwise their insistence on not even looking for ways to make it better looks drastically different. If you can show me that math notation is as closely aligned with how cognition works as possible without sacrificing its usability - that's great, you're right, I concede. OTOH, if the only thing you say is that it worked for a long time, worked for you, and therefore you're not interested in doing anything for it to work better - that strikes me as simply elitist.
The other problem is that nobody who is not deeply involved with math cares enough to take a closer look. How many linguists, psychologists, cognitive scientists invested their time into researching ways of making math notation better? I bet even fewer than the ones who tried researching programming. On the other hand, mathematicians are simply not equipped with knowledge and skills required to objectively assess the notation they use (neither are programmers, BTW.)
> In my mind, it's on those who say it's the best it can be to show that it indeed, cannot be better.
Indeed. The issue is that neither I nor most people are claiming it to be the best. I explicitly pointed this out in another comment.
> OTOH, if the only thing you say is that it worked for a long time, worked for you, and therefore you're not interested in doing anything for it to work better - that strikes me as simply elitist.
How is that elitist? If it works for me, why should I spend time making it better for? What do I gain from it?
And this comment doesn't even make sense. Mathematicians invent notations for their own convenience all the time. There's no committee that says "Yes, this is the official accepted notation." A mathematician uses whatever notation works for him, and if others find it useful, they adopt it.
> The other problem is that nobody who is not deeply involved with math cares enough to take a closer look. How many linguists, psychologists, cognitive scientists invested their time into researching ways of making math notation better? I bet even fewer than the ones who tried researching programming. On the other hand, mathematicians are simply not equipped with knowledge and skills required to objectively assess the notation they use (neither are programmers, BTW.)
You're not wrong, but you're also not helping. This is basically saying "Look, someone should do this!" If you think it's worthwhile, go for it. The category of professionals you have mentioned (linguists, etc) - most of them do not see it to be worthwhile. Put yourself in their shoes. Are they really going to invest a lot of effort to unseat a notation that has evolved over so many centuries, and then fight a battle to convince people to use it? That may well be a career killer.
And where the two of us will have to disagree on: Any improvement, although may be great for newcomers and amateurs, will barely have any impact on the productivity of a professional mathematician. As people have repeatedly pointed out: Notation is amongst the least challenging part of math. Sure, it is a barrier to entry, but at best you're simply lowering the barrier to entry - it won't benefit people who are already good at mathematics. A better notation will not enable them to suddenly grasp concepts they couldn't. That's why mathematicians don't bother.
To be frank (and I say it in all seriousness), the English language has more problems than the mathematical one, and if we could fix those, it would have a much larger impact.
We need to agree to disagree: in my mind, it's on those who say it's the best it can be to show that it indeed, cannot be better. Because otherwise their insistence on not even looking for ways to make it better looks drastically different. If you can show me that math notation is as closely aligned with how cognition works as possible without sacrificing its usability - that's great, you're right, I concede. OTOH, if the only thing you say is that it worked for a long time, worked for you, and therefore you're not interested in doing anything for it to work better - that strikes me as simply elitist.
The other problem is that nobody who is not deeply involved with math cares enough to take a closer look. How many linguists, psychologists, cognitive scientists invested their time into researching ways of making math notation better? I bet even fewer than the ones who tried researching programming. On the other hand, mathematicians are simply not equipped with knowledge and skills required to objectively assess the notation they use (neither are programmers, BTW.)