<p>Both schools have fantastic math programs. That said, if you got into Williams, you clearly had some great options, but vied for a more secluded and upper-size LAC. Your experience at Mudd–especially socially–would be very, very different from that at Williams. I have twin friends, one at Williams and one at Mudd, and their experiences have differed completely. So if you liked Williams in the first place, you may want to stick with that. Especially if you want to ensure yourself an adequate GPA for grad school.</p>