Math was written on paper long before there were computers. As a result, the use of infix notation was an act of necessity not a calculated decision. Now that we have computers and keyboards we should use prefix notation.
> I find in only a glance I can tell what everything is binding to.
It must be nice to live in a world with only 4 infix operators and expressions that have only 3 infix operators.
For example, lots of folks think that sqrt should be a prefix operator, not yet another function. I suppose you're going to assume that the top bar will serve as parentheses.
BTW "-b + sqrt(bb-4ac) / 2a" is the interesting expression. Is it "(-b + sqrt(bb-4ac)) / (2a)" or "-b + (sqrt(bb-4ac)) / 2a)" And, are you certain what "bb-4ac" means? (There's at least one major language where it doesn't mean "(bb)-(4ac)".)
We aren't talking about programming languages. We are talking about teaching math in school. In most of school mathematics, there are only 4 infix operators (well, and also the comparison operators).
> We are talking about teaching math in school. In most of school mathematics, there are only 4 infix operators (well, and also the comparison operators).
And that's how the exceptions swallow the rule. And, it's also how we get infix programming languages where that's definitely not true, and so on. Where should we make the switch?
Why exactly is it a necessity to use infix on paper? And what exactly is the argument for using prefix just because we have computers? I'd argue quite the opposite, computers give use even more convenience to use whatever we like. I think it is a rather arbitrary choice, but it may relate to the prevalence of subject-verb-object in (spoken) languages; i.e., operators act like a verbs.
