[canjobear]

Opaque names have the advantage that they don't trigger any potentially misleading associations and they emphasize the abstract nature of what is being discussed. A variable named x could be anything, even something that the mathematician/programmer didn't anticipate.

[wtallis]

I agree with this. Additionally, I think a lot of detractors of single-letter variable names don't realize that it is often the case that the structure of the equation/expression is what's interesting, not what any individual variable represents. That structure is most visible and apparent when the variables don't take up any more space than the operators.

Being able to recognize things like "oh, that's a polynomial!" is extremely useful, especially in the context of learning new math rather than a more applied context. And I think it would be extremely hard to spot an opportunity to do integration by parts when working with Java-style verbose variable names.