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When you write a thesis is it supposed to all be 100% independent research?

Does the thesis need to be ground-breaking? For example, the thesis from Riemann about Differential Geometry.

Does a thesis always have to be 'revolutionary' in math and physics?

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    I hardly ever seen a revolutionary thesis: no, most of the theses, whatever the level, and whatever the field, are not revolutionary or groundbreaking. Some are excellent, some are good, and some are plainly bad. – Massimo Ortolano Sep 16 '16 at 10:18
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    If every physicist and mathematician needed to pull a Riemann to get a PhD there would be very few doctors indeed. – Davidmh Sep 16 '16 at 10:27
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    If every thesis was ground-breaking and revolutionary, we would get used to it and we wouldn't call them "ground-breaking" and "revolutionary" anymore. :) – Federico Poloni Sep 16 '16 at 11:14
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    I think a PhD thesis should absolutely be ground-breaking. The patch of ground it breaks doesn't have to be particularly large, but if it doesn't break any new ground, then it's basically just a literature review. To me, "ground-breaking" and "revolutionary" are two totally different things, and you can certainly have the first without the second. – Nuclear Wang Sep 16 '16 at 12:51
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    Are you talking about a PhD thesis, a masters thesis, or that strange animal I have seen in, for example, Mexico, a Bachelor's thesis? – aparente001 Sep 16 '16 at 14:14
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This depends heavily on the level of the thesis (Masters, Ph.D) and the educational system in which the institute issueing the degree sits.

Typically, at Master's level you need to demonstrate familiarity and competence in the execution of research. Ie, you need to show that you can understand and implement methods. However, the results may be unoriginal.

For a Ph.D, you need to do original research. This means that an original result needs to be published in the thesis. However, the interpretation of original may take many forms. As you note, it's almost impossible to publish an entirely new form of knowledge.

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    To clarify, Ph.D. research must be original, but it doesn't necessarily have to be revolutionary or groundbreaking. Well, it has to be "ground-breaking" in the sense that it needs to make a novel contribution to the body of knowledge of the field, but it doesn't have to be "groundbreaking" in the sense that it opens up a brand new field of study that sends shockwaves through the community. (So think farming versus earthquakes.) There are many, many Ph.D. theses out there where the results were only used by a handful (or no) future researchers. – R.M. Sep 16 '16 at 15:33
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Is it supposed that all the thesis must be 100% independent research ?

Well, yes apart from the introduction, the chapters on background and such. Also your research usually depends on your advisor and research group, but still it had to be your work and not somebody else's.

Should the thesis be ground-breaking ? Like the thesis from Riemann about Differential geommetry?

No. First, this is impossible but second, demanding this would be bad for science. The impact of groundbreaking theses vs. incremental theses is largely overestimated. Without all these small steps made in thousands of theses there would be basically no progress at all.

Have a thesis always to be 'revolutionary' in math and physics?

No.

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A Ph.D. thesis is supposed to be "publishable". Not all published papers are revolutionary or ground-breaking. And not all theses are revolutionary or ground-breaking.

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    Is the requirement really that the thesis be "publishable"? Is it not more accurate that it should be original and make some contribution to the field. It just so happens that manuscripts describing research which is original and contribute something are more likely to be published. What you're saying seems akin to saying that what I'm looking for in a partner is that they be desirable to other people, when really what I'm looking for in a partner is a set of traits which may just so happen to be desirable to other people. – Ian_Fin Sep 16 '16 at 12:36
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    @Ian_Fin That depends on the connotation of "publishable". – JAB Sep 16 '16 at 13:58
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In addition to the fact that "revolutionary" and "groundbreaking" are not required, as noted in the other answers, it is important to understand that these properties also cannot generally even be assessed. Notions like "revolutionary" and "groundbreaking" are post-facto analyses of the impact of a work, and as such generally can only be assessed much later.

Sometimes, the implications of a work are immediately clear. Other times, however, particularly with deeply theoretical work, the consequences or even the correctness may not be understood for many years afterward. See, for example, this question on rejection of famous mathematical results.

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Generally, a Ph.D. thesis must include original research which contributes to the field.

  • It does not have to be 100% original research. In fact, the thesis should (some would say must) include an overview of the state of research in the subject and set your original research in context.
  • Especially in mathematics, it may be necessary to repeat well-known definitions and theorems to remove any ambiguity regarding notation. Those would have to be cited, even if you change the notation.
  • It may also be necessary to adapt prior results to your specific requirements.

For instance, a thesis could be a fundamentally new proof for an old theorem. The thesis could be more than a hundred pages, but only one or two are original results.

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Your dissertation is supposed to be a solid contribution to your field. Period.

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    Can you expand on this? I think I see where you're going, but it would be good to directly address the author's questions. – Ric Sep 17 '16 at 0:34
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Every PhD topic which I have seen since 1995 is incremental improvements making use of the technology recipes of the preceeding 20+ years. For example beating the high score for pulse peak power out of a semiconductor laser of recipe similar to those of Basov in the 1970's but a different shape (along with the detailed test and simulation tasks to get that). For something as really new as "try getting a few flakes of graphite transferred by van-der-waals adhesion to sticky tape from a 6B pencil mark on paper to a glass slide, and then four-point microprobe it under a microscope to measure the carrier lifetime and conductivity within a monocrystalline domain of graphite", that would never have got funding because it was too novel; those sometimes get called "Friday Afternoon Experiments" and tend to be a byproduct of having the basic research equipment doing something more ordinary for the rest of the week. If you think of a potential Friday Afternoon Experiment which is truly novel then you have to think of something more ordinary and incremental by which your supervisor can buy the relevant test equipment, and live with it that someone else might do the novel experiment.

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The requirement for a thesis is that the work is original - this can be proved. Revolutionary or ground-breaking are subjective terms which can neither be proved or disproved... what is revolutionary to one person is merely incremental to another depending on their knowledge base and perspective.

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"Revolutionary" is far too much to ask - if every thesis were revolutionary, the field would have hundreds of "revolutions" a year. "Groundbreaking", yes, in a certain sense - you should be doing something new, something that's a genuine contribution to the field, rather than reporting on something done previously. But it needn't be big.

The critical thing is that a PhD thesis is a demonstration that you are capable of contributing to the field - something a holder of a PhD is expected to be able to do. So while the thesis need not be 100% original (it's perfectly fine to review others' results as background, for example) the core of it must be, without exception.

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