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.

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.
