I think the best choice could depend on how set the boy’s career goals are. Once someone gets to college a wide world of different futures remains open. Talent in math can take a student in many directions within college and beyond. The broad public reputation of UM is much stronger than CMU’s. If the kid is open to a range of possible future careers, and if the amount of debt he would graduate with is something that can be overcome in a few years, I think he should choose UM.
My son was offered an honors scholarship amounting to about 50% of COA at UM, and a full-ride Alumni Distinguished Scholarship at MSU. But he chose to enroll at UChicago (with a small National Merit Award – and with his parents and grandparents bearing most of the costs). He didn’t know what career line he would follow, but he thought an academic career was possible. A degree from either UM or UofC would be a very good jumping off place for graduate school and an academic career. One lure of UofC was that it was located in a major league city.