How much room is there for original mathematics research? Should more universities and colleges offer degrees in mathematical research?
I am in the process of incorporating a non-profit college and I am considering offering a degree in mathematical research. However, it would have to be original research, e.g. a new proof or a new formula of some kind.
Is original research in mathematics something that can be done by anyone with some education and talent in mathematics, or is it something far too difficult for your average mathematician?
EDIT
The target student for this university would not be a young person wanting to learn mathematics, they should go to a traditional university. The target student is people like you guys on math.stackexchange. Anyone who already has good knowledge of math and who wants to expand this knowledge through researching something that will (1) be guaranteed to be published by a university affiliated journal, (2) get a degree, up to a Ph.D., by doing something in their own time that they both enjoy and adds to the world's knowledge-base.
 A: Firstly, a bit of an aside, which nevertheless seems relevant: many of "the people like you guys" on Math.SE are either mathematical Ph.D.s, or Ph.D. students.  Several of them are academic staff at universities or similar institutions.  
Secondly, regarding the initial question on whether more universities should offer degrees in mathematical research: this is what the Ph.D. is.   Experience shows that it is difficult to engage in successful mathematical research without a strong undergraduate background in mathematics, and without mentoring by faculty who are themselves successful mathematical researchers.  This is why the Ph.D. is a graduate degree, and why universities compete for strong researchers to make up their faculty.
I think the question "Is original research in mathematics something that can be done by anyone with some education and talent in mathematics, or is it something far too difficult for your average mathematician?" sets up a false dichotomy.  I don't think that original research is something that can easily be done by anyone with some education and talent in mathematics; a good academic environment and good advising is essential.  On the other hand, it is not far too difficult for your average mathematician: most university mathematicians are engaging in original research.  But they are not students!  They were students in a Ph.D. program, and most of them did find original research very difficult at that time --- but they developed their talent for it over their years of study, got their Ph.D., and (in most or at least many cases) continued to mature as a researcher as their career progressed.  (For example, it is pretty unusual for very recent Ph.D.'s to advise Ph.D. students, because they are too new at the research game themselves; the wherewithal to successfully advise students is something that develops as one's own ability as a researcher matures.)
In conclusion, I don't really understand what you are envisioning/asking about that is different from the traditional Ph.D. program.  
A: Well, new discoveries can always happen even with basic arithmetic I'm sure there's something out there we may not know about.
Think Isaac Newton, his knowledge of math back then wasn't better than the average high school student today. He basically knew algebra and created the calculus out of need. If one of those students is extremely curious and reaches a question to which there is no answer, this may lead him to new maths and discoveries.
