TITLE: Is there fundamental goal of mathematics?
QUESTION [13 upvotes]: I did not ask this question before scaring of down-voting but could not stop the curiosity and cannot find the answer by searching the web. In physics we are looking for say smallest mass or particle, many many years ago it was electron may be, sometime ago it became quarks and we are still looking for it.Is there anything equivalent in mathematics? I know there are many unsolved mathematical, we can search in the web and find many, but that does not answer the question: are we looking for something fundamental? Are we looking for something fundamental finding which will solve many present problems? 
Sorry if the question was not clear, but the answer provided by @jack and edited by@celtschk, gave me whatever I was looking for. As jack said the concept I was asking is not an active research now and that exactly I was looking for.

REPLY [3 votes]: I don't think your characterization of "the" fundamental goals of physics is accurate. At any given time, there are unsolved problems in physics, and there are unsolved problems in mathematics, and these problems maybe catch the interest of a lot of people, or maybe a smaller number of people, or maybe just a few people.
I think physics and mathematics are actually quite similar: we explore, we try to discover new true things, we try to demonstrate their truth rigorously using appropriate methods (experimental method in physics; logical proof in mathematics).
If there is a difference in this regard between mathematics and physics, it is that the number of interesting and tractable problems in physics is rather more tightly constrained than in mathematics, because a physics problem must comport with physical reality. Mathematicians are much freer in that regard, although they still must comport with logical reality.