Would you be interested in heading something like this up?
I can come up with a few questions (or more appropriately answers).
Also, what are you thoughts on doing something that combines a little bit of both -- ie history, problem solving, etc... Being able to choose categories like in jeopary...
The reason why I am against using problem solving or any problem which requires thinking is because in real Jeopardy! questions are answered within 5 seconds. Rather concetrate on questions (answers) which can be answered quickly. I had a few ideas what categories we can make it.
History: Stuff about mathematicians lives, and the time period where they lived. Also possibly the history behind some theorem or theory.
Theorems: Post a theorem. And the contestants need to state the name of the theorem. Like for example for $200 you can ask something like

and the question would be, "What is the fundamental theorem of Calculus.
Name the author: Given a name of a famous book in math. The answer would be the name of the author who wrote the book.
Mathematicians: Random things about mathematicians themselves. For example, for $1000, "He can be described as an Italian by birth, German by adoption, and French by choice". (The question would be "Who is Lagrange?").
I am sure you can post other categories also. It just happens to be difficult making it only math. Maybe a little bit of science it okay too. But please! Nothing about movies, celebrities, music, and TV.