Circumflex, perhaps?

It's not part of the traditional typographical world. It's part of the ASCII character set which goes back to Teletype days. Generally, it's only used in the context of computer code (programming, scripting, command line, etc.). Same goes for asciitilde.

On my American keyboard, it's the shifted 6, and I believe is used among other things to indicate exponents: x^2 means x squared. The keyboard was done by mathematicians, not typographers, which is bad because writing prose is the main use of the keyboards, not doing math or code. Eg. the cent sign disappeared from the standard basic keyboard, which could have also a true multiplication sign, the degree sign, etc.

for questions about basic characters, i usually turn to Microsoft's Character Design Standards first. If i'm not mistaken, our fellow 'phile Vincent Connare was the one to compile this list of standards. (correct me if i'm wrong!)

asciicircum falls under the Math Symbols descriptions.

I believe it's a nose:

:^)

Jason C

I've always called it the caret. Used in math and pointing at previous comments ie: ^ jasonc is funny!

Still, as a math symbol, it's used in the context of computer programming languages and such. I don't think I've ever seen it used in a math text book.* It's a stand in for the lack of superscripted characters in ASCII just as the asterisk and forward slash are used for multiply and divide symbols.

* Although, I went to school before personal computers were common, so maybe that's changed?

Well, the ^ would be used in a math textbook if it were giving instructions on how to key an exponential number into a computer, part of a larger section on using computers for complex calculations and such.

Thanks for the help everyone! That's a great link Paul!