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Re:Problems of Traditional Math Notation (2004) by Grustaf on Monday November 06, 2017 @09:01AM (#15635436)
I think it's safe to say that the alternative to ambiguity would be a lot more symbols, I'm not sure that would help.

I find that it's very seldom that I struggle to understand an expression because of limits in the notation system, I think this is more a case of someone coming from computer science, where notation by necessity is completely unambiguous, and being dissatisfied with math notation on a philosophical level.

Math notation is a bit like writing down spoken languages, the intention is to provide just enough information so that a native speaker can understand which word is being referenced. It's definitely not to provide an encoding of the sounds that can be decoded by anyone with a simple table of correspondences.

Sometimes I find myself looking at an expression and understanding what is meant, but not really knowing _how_ I can understand it. Like when you intuitively can pronounce a word you've never seen before, but you can't consciously determine what rules you applied to arrive at that pronunciation. I think that is beautiful!

Re:Problems of Traditional Math Notation (2004) by jstewartmobile on Monday November 06, 2017 @09:22AM (#15635595)
If I remember correctly, von Neumann was reviewing someone's dissertation (might have been Minsky's), and someone asked "Is this mathematics?", to which von Neumann replied "If it isn't now, it will be soon."

Doing the CS guys a kindness will probably pay the field back several times over. The latex-fussing and symbol collision in mathematics is not pretty.

Re:Problems of Traditional Math Notation (2004) by Grustaf on Monday November 06, 2017 @10:30AM (#15636131)
I don't actually think it is desirable to make mathematical notation unambiguous, if that is even well defined. To again use natural language as an analogy, there are only some 26 letters in most Latin based alphabets, but there are many more sounds. The same "letter", or historical sound, is pronounced differently in different contexts, but since it's almost always predictable based on context or knowledge, the system works.

In the same way, you could say that in one sense (though possibly not the mathematical sense) there are lots of different uses for "=". Most of the time this obviously hasn't been an issue, if it had been, people would have introduced new symbols. For some cases they have done just that, it can sometimes be useful to explicitly distinguish definitions with ":=" or a triangle above the =. In the same way people sometimes use a triple line = for "is identical with". But seeing that everyone knows these symbols, but still make do with just = in most cases, even they are only half useful.

Re:Problems of Traditional Math Notation (2004) by jstewartmobile on Monday November 06, 2017 @10:48AM (#15636261)
If we use ordinary language as an analogy, we're usually all speaking the same one, and ambiguity is manageable.

Whereas in the professions, we are so deep into sub-specialties and sub-languages that even without ambiguity we are approaching a Babel where mathematician does not understand mathematician and lawyer does not understand lawyer.