First Impressions of the Fortress Language

It might not make much sense from a programming perspective, but it's very natural for a mathematician. The same way that mathematicians are happy with one-letter variable names, they're happy with juxtaposition as their one operator notation. They just redefine everything whenever they start a new problem.

If you think about it, matrix multiplication is a totally different operation from multiplication in the reals. We just happen to use the same notation for it because it follows some of the same rules (associativity, distributivity) that we're in the habit of using to manipulate equations.

This can get pretty extreme. There's a branch of math called functional analysis, which identifies functions with infinite-dimensional vectors, and then does calculus on those "vectors" like they were points in any other space. In their notation,

v = Tu

is like matrix multiplication

y = Ax

except that u and v are functions, and T is some kind of integral.

I think this is one reason the Lisp crowd gets cranky about the parenthesis thing -- the infix operators we all know and love are a lot less well-defined than we think they are.