MIT vs Williams for math: which is better for an undergraduate math major?

The biggest practical tradeoff is depth and scale versus intimacy and individual attention. MIT gives you a much larger math ecosystem, with more advanced course options, more graduate-level classes, and closer proximity to research activity across math, physics, computer science, and engineering. Williams offers a much smaller department, but it is unusually strong for undergraduate math, with very accessible professors, small classes, and a campus culture where undergraduates are the clear priority.

For pure math specifically, MIT has the edge in breadth. If you already know you may want to move quickly into abstract algebra, topology, number theory, geometry, or graduate-style coursework, MIT makes that easier. You are surrounded by many highly mathematical peers, and the pace can be exhilarating if that is what you want.

Williams is excellent in a different way. Its math department has a long-standing reputation for serious undergraduate teaching, and students often get more direct mentoring from faculty than they would at a large research university. Because there are no graduate students competing for attention, advanced undergrads can build close academic relationships with professors, write substantial thesis work, and be very visible in the department.

In terms of teaching, Williams is more likely to feel discussion-based, personal, and carefully centered on undergraduates. MIT can absolutely have strong teaching too, but the academic environment is more intense and self-directed, and the math culture is broader than just the department itself. That can be a major advantage if you like intellectual density and cross-pollination with adjacent fields.

For a student who really loves pure math and wants the strongest undergraduate mathematical environment overall, I would lean MIT if you want maximum depth, speed, and access to very high-level material early. I would lean Williams only if your top priority is close mentorship and a small-college setting, because among liberal arts colleges it is one of the very best places to study math.