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There are many university ranking consultancies trying to compare one leading maths department with another and to conclude which one is better. Although this doesn't seem to be a very reasonable thing to do (since you cannot compare apples and oranges), many high school students still see such ranking as an important factor when deciding where to go. An example of ranking can be found here.

My question is: why, for example, is MIT placed above Oxford (and many other examples) in most rankings? Although different organisations give vastly different rankings, MIT seems to be always above Oxford. Is there any real difference between their undergraduate education or is it just that the criteria of rankings are unfair? (NB DO NOT focus too much on MIT and Oxford; they are just examples.)

I'd like to limit the discussion to undergraduate education only: does such ranking really help when choosing which college to go to? Also, be aware that I am NOT talking about the overall ranking of universities; I am just talking about the ranking of math departments.

I believe this question is not very opinion-based - it can be answered objectively by a detailed examination of the course contents and teaching methods, and how those are related to rankings.

I am aware that those rankings are not solely about undergraduate teaching, but chances are that high school students care about the rankings more than anyone else.

To summarise, are rankings helpful in assessing the relative merits of undergraduate education at the maths department of different institutions?

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    $\begingroup$ The rankings you linked to can not be interpreted solely as ranking in their undergraduate math programs, but rather, the rankings of entire university math departments, including doctoral programs and professors' research, etc.. Each such ranking you come across will usually include "indicators" used in that particular ranking. In the ranking you link to, there is another tab that reveals the "indicators" used to judge quality of the university's ranking in mathematics. $\endgroup$ – Namaste Oct 2 at 13:22
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    $\begingroup$ As the importance of these rankings and indicators has grown in the minds of high school students, en.wikipedia.org/wiki/Goodhart%27s_law becomes more and more important to understand. $\endgroup$ – Chris Cunningham♦ Oct 2 at 13:59
  • $\begingroup$ under-graduate (4-year) programs in math in the US gives another take, focused on undergraduate math programs. Be selective in your search terms to search for rankings (e.g., rankings, undergraduate programs in applied math (or in pure math)). $\endgroup$ – Namaste Oct 2 at 15:00
  • $\begingroup$ In my opinion, a uni provides three things: a graduation document, which you can mention in your resume; a possibility for finding future business partners; a hands-on experience in your future field of work, be it airplane manufacturing or cutting human flesh. Oh, and dorm life, of course. Hence, choosing a uni is very important if you want to become a physician or a startup leader, but much less important if you are going to do math alone while your mates are having beer parties. Good books FTW. $\endgroup$ – Rusty Core Oct 2 at 17:04
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Rankings are imprecise (e.g. may differ by source). In addition, gradation of number 2 versus number 4 (or the like) is rather a nuance, when you consider the restriction of range. More meaningful is top 5 verus top 50 or 500 or the like. Also, any ranking of schools from one country to another is problematic.

In addition, prestige of a school seems to correlate to selectivity more than quality of the instruction. So, yes, you can collect a nice brand (with value, agreed), but don't kid yourself that it is much more than that.

Finally rankings are not the most important thing in the world. Lots of people go to state schools and do fine in life.

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