lambert wrote:If by old you also mean 'more renowned' this might work in your favor for future positions in academia.
But, all else being equal, I'd rather live in Pasadena, California than New Haven. Can't beat California weather.
Is it really true that Yale professors are more renowned than Caltech's?
Didn't mean to imply that, I just don't see why age is an important factor. (unless a professor is going senile and can't advise well anymore...)
I guess what's more important is a professor's reputation in their field and how active they are in it. Anyway both Yale and Caltech are good unis but, like another poster said, their math departments are very small (like 6-8 people incoming class?) and you wanna make sure there are people working in your areas of interest. But since you've figured that part out and research interests change over time, I don't think that's much of an issue. Both unis should have people with good connections for post-phd positions in academia.
Edit: yeah as EGA said, visiting will give you information straight from the horse's mouth. Surely that's much better than strangers' opinions in a forum