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Did you mean MIT for Cambridge? Both Harvard and MIT are in Cambridge and so are a number of other universities.

Off the top of my head for math Princeton, UC Berkley, Stanford, Columbia. Again I'm not sure I'd put Harvard at the top of the list. Another good school for Computer Science is U. of Illinois Champagne/Urbana. What I think of Harvard as being the best for is subjects like Politics.

Edited to add.. Just looked up a list for math. OK Harvard & MIT are both near the top. And I forgot Carnegie Mellon, Yale, UCLA and Cal Tech.