"Negative" versus "Minus"

I am fully comfortable with "minus $x$," and indeed like it better than "negative $x$," and have seldom used the latter in lectures.

There is no problem with the binary operator and the unary operator having the same name. Speaking and writing mathematics would be more awkward if we did not allow useful abus de langage.

From page 271 of Halmos's I want to be a mathematician:

Here is a bit of innocent fun that is not much of a challenge, but most calculus students seem to enjoy it. Partly as integration drill and partly to make a point about the use of "dummy variables", I'd call on several students, one after another, and demand that they tell me what is $\displaystyle\int\dfrac{dx}{x}$, $\displaystyle\int\dfrac{du}{u}$, $\displaystyle\int\dfrac{dz}{z}$, $\displaystyle\int\dfrac{da}{a}$, and then, as the clincher, I'd ask about $\displaystyle\int\dfrac{d(\text{cabin})}{\text{cabin}}$. Some of them would grin amiably and shout out "log cabin", and they were surprised when I told them that I didn't agree. The right answer (as I learned when I was learning calculus) is "house-boat", "log cabin plus sea".

At the same time, by the way, I'd take advantage of the occasion and tell my students that the exponential that $2$ is the logarithm of is not $10^2$ but $e^2$; that's how mathematicians use the language. The use of $\ln$ is a textbook vulgarization. Did you ever hear a mathematician speak of the Riemann surface of $\ln z$? And speaking of vulgarizations, did you ever hear a mathematician pronounce "$-3$" as "negative three"?

I would encourage (maybe insist is too strong) to use "negative". It's not the worst idiosyncrasy, though. I prefer this distinction so that the unary "-" and binary "-" are two different things.

It irritates me a little more when students say "times-ing it by 5", or "matricee".