Depending on who I'm talking to, I've heard that Princeton, MIT, and Harvard are each the best in the world (for undergrads). I'm not really in a position to judge, so let it suffice to say that all three are fairly impressive.

If you defined 'many people' I'd be much obliged.

(Not challenging the assertion, just curious who.)

The sample I hear from about Harvard's undergraduate math program consists largely of participants on the Art of Problem Solving forum

http://www.artofproblemsolving.com/Forum/index.php?f=143

and those participants include many young people from various countries who have participated in the International Mathematics Olympiad.

according to the latest u.s. news ranking

http://grad-schools.usnews.rankingsandreviews.com/grad/mat/s...

Princeton is first and Harvard, MIT, Stanford and Berkeley are tied for second. Harvard is always mentioned as one of the top Math depts. more so than MIT in my experience.