Question: Some colleges boast that they are "3rd in the world" or "1st in the nation" for such and such a program. How can I verify these claims, and how can I see who else is on the list?
There is no official worldwide list of the best academic programs .... or the best anything ... when it comes to college quality. Most references to school rankings stem from US News and World Report's annual "America's Best Colleges" issue. If you read US News, you can find potentially helpful statistics that compare class sizes, retention rates, average SAT scores, etc. But don't take the rankings hierarchy as gospel truth. Make your OWN assessments of which schools are right for you.
Some institutions that make boastful claims, especially the ones that trumpet their #1 status, have nothing to go on except their own high opinions of what they're offering, with the hope of roping in applicants who may be a tad less cynical than you are. (Since there's no official way to disprove what they're saying, why not say it, right?) Others may be basing their proclamations on any of the myriad lists that emerge each year. Princeton Review, for instance, publishes "Best" rosters that cover everything from "Best College Library" to "Best Campus Food" to "Great Schools for Biology Majors" (or "Accounting Majors," "Engineering Majors," "Education Majors," and so on).
If a college you're considering is touting their superiority in any area, you should feel free to write to admission officials and ask about the source of the claim. If you do it in a curious and friendly way--and not so you sound like you're putting admission officials on the defensive--you may get a helpful reply. If you receive a response that cites the origins of the ranking, you can then look to see what other colleges and universities earned similar accolades. Chances are good, however, that you won't receive any answer at all. But, if you do, you may have made a useful contact in the admission office--someone with whom you can continue to correspond as you go through the application process, as other, unrelated questions arise.