Williams has a stronger reputation in math than Amherst does. One indication that is perhaps more powerful that comparing course titles (especially since Amherst students can take courses at four other colleges with relative ease): According to the NCES statistics from the class of 2014, Williams, whose student body is about 22% larger than Amherst's, had more than double the number of primary math majors, and roughly double if you adjust for the size difference: 26 (4.7% of the class) vs. 11 (2.4%). The Williams Mathematics and Statistics Department webpage lists 222 students in the classes of 2016 and 2017 who are declared math or statistics majors (including, of course, second majors, who would not be in the NCES statistics). Amherst doesn't have an equivalent list that's public, but the group photograph of majors on its departmental website is very much less crowded than Williams'. Both colleges list selected postgraduate activities of alumni math majors, and while there are lots of similarities in the lists, it's noticeable that Williams lists three students pursuing PhDs in core mathematics fields, and Amherst lists none. I think all this indicates that the math community at Williams is broader, deeper, and more vibrant than the math community at Amherst.
@Data10 : I guess you're right, or at least more right than I was. The one-time snapshot of athletes is probably a little low for indicating the number of people who are on team rosters at some point in their college careers, since there is certain to be some churn due to injuries and changing priorities. About half the kids I know who played varsity sports in college did not play all four years. But I don't see anything to indicate that's a huge factor at Amherst, at least.
@ucbalumnus : What this running sidebar has been about is the fact that elite LACs are much more limited than Division I colleges in the number of kids they "recruit," but many of them have strong athletic cultures that depend on large numbers of students who are skilled -- high school varsity or strong club starters -- but not "recruits". While officially the admissions departments are not lowering any standards to admit the non-recruits, it's hard for me to believe that they aren't paying attention to admitting enough football or hockey players that, when the dust clears, there will be enough potential walk-ons to staff all the varsity teams. Contrary to @cobrat 's statements about Oberlin, I don't think it's common at all at competitive Division III schools for newbies to walk on to varsity teams. Club teams, yes; varsity teams, no. It certainly didn't happen at my kids' D-III school. In fact, a BFF of one of my kids, a statewide independent school champion at the relevant sport, was an athletic recruit at Oberlin. That Oberlin team had high skill levels and required a great deal of year-round commitment; no one was walking on casually because they needed warm bodies. The way it worked with that student, by the way, was that the coach offered (and gave, at least so it seemed) significant support, but conditioned on an ED application that assured the student would not use the Oberlin acceptance and aid package as a bargaining chip with other colleges.