For the sake of an argument, let's assume you are right, and the language of math sucks.
Then, we have had centuries of mathematicians inventing ever changing notations and ending up with a notation that sucks.
If so, those mathematicians must be extremely stupid. Surely persons of average intelligence must be able to come up with better notations, and find proofs for stuff that is out of reach of those morons?
I do not rule out that notation can be improved. After all, it took millennia to move from Greek and Roman arithmetic systems to Arabic notation. There is no reason to assume we have reached a global optimum. However, I also find it unlikely that mathematical notations truly are stupid.
Your argument is like someone complaining about the difficulty of discriminating between "37" and "73" because it is way easier to see the difference between 37 and 73 scratches in a piece of wood.
> If so, those mathematicians must be extremely stupid.
Not necessarily. Before modern times mathematicians worked alone and didn't need a notation that others would understand. Newton, for example -- his calculus notation wasn't very good, and over time Liebniz' notation ended up being used instead (completely apart from the issue of who invented the calculus).
> Surely persons of average intelligence must be able to come up with better notations, and find proofs for stuff that is out of reach of those morons?
This doesn't support the thesis that mathematicians are stupid. Most mathematicians only care that they understand their own notation, and give less weight to its comprehensibility to others. And some mathematicians in the distant past deliberately used obscure notation to conceal their work from others.
I would look to educators to come up with a more comprehensible system of notation, not necessarily those at the frontiers of mathematics.
Apart from the fact that you mean the "royal society", yes, both true. They also came into conflict about priority with respect to the calculus. And surprisingly enough, that debate rages on.
This is hardly true. Mathematical notation changes all the time-in fact, inconsistency is a significant problem, because Mathematicians love to experiment with notation, definitions, etc.
Seriously, just look at a Mathematical logic book from 50 years ago vs. one today. You won't even recognize half the words, let alone the symbols.
I agree, it's a fun exercise to try and come up with a "better" form of notation that works in the general case. I think that most people will find that modern mathematics notation is really good stuff.
Then, we have had centuries of mathematicians inventing ever changing notations and ending up with a notation that sucks.
If so, those mathematicians must be extremely stupid. Surely persons of average intelligence must be able to come up with better notations, and find proofs for stuff that is out of reach of those morons?
I do not rule out that notation can be improved. After all, it took millennia to move from Greek and Roman arithmetic systems to Arabic notation. There is no reason to assume we have reached a global optimum. However, I also find it unlikely that mathematical notations truly are stupid.
Your argument is like someone complaining about the difficulty of discriminating between "37" and "73" because it is way easier to see the difference between 37 and 73 scratches in a piece of wood.