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?
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.
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.
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.
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.
Generally, a Ph.D. thesis must include original research which contributes to the field.
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.
Your dissertation is supposed to be a solid contribution to your field. Period.
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.
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.
"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.
