How important is the Ph.D. Thesis?
How important is the Ph.D. Thesis?


It depends on what you have in mind for "importance".  The intellectual content of the thesis is vitally important, since it stands for what you have accomplished in graduate school.  You should make sure it contains your best work, since early in your career you'll be judged partly on this basis.

In the long run, there is little direct value to the dissertation as a document.  (Aside from any sentimental value, laying out the historical record, and satisfying bureaucratic requirements.)  Any valuable content should be published, and the resulting publications will be the definitive source that the community will rely on in the future.  If people are still reading your thesis five years after your graduate, then that's a sign that you have not done an adequate job of publishing your work.

Opinions differ on how seriously to take the dissertation as a specialized form of academic writing.  For example, how much additional background, commentary, or literature review should it contain?  Should it be written in a different style from published papers?  This can vary between countries, fields, universities, departments, and even individual advisors.  There's no universal answer, and you'll have to investigate what fits your particular circumstances.

In particular, one fundamental question is whether your dissertation is nothing more than an account of research that has been or will be published, or whether it's an important academic exercise in which you demonstrate your perspective and thoroughness in a way that would not fit in a conventional paper.

I see the former as the default answer for mathematics in the U.S., but the latter is not completely unknown.  (There are advisors who insist that their students write far more detailed proofs in the dissertation than one would ever actually publish, to demonstrate that the student can in fact do this.)