Dear Ahmida,

Of course there are some though unsolved problems in Mathematics but unlike in Physics they are solicitations of proofs of expected-to-be-true solutions of well formulated problems. Dark Energy and Dark Matter are much more deeper problems than that they are enigmas a hole in our physical understanding all that exists is speculations and attempts to formulate the problem based on what we observe and measure. So no there is nothing in mathematics that could be compared to Dark Energy and Dark Matter.

Beyond the remaining unsolved Millennium problems, there also exist clearly formulated problems that are proven to be inherently unsolvable. Some other existing problems could be inherently unanswerable but this has not been proven either way yet (indeed, some of the remaining Millennium fall within this category.) 

In computer science, there is P and NP, etc.

There is also the controversial issue of what Cantor's antinomy, where mathematics breaks down, means. Staying within the realm of infinity and looking at its meanings in reality, there is the possibly unanswerable issue of whether there exists instances of mathematical objects of strength strictly higher than aleph-2 - we can enumerate classes of objects with metrics of aleph-0, aleph-1, and aleph-2, but no such classes are known as of yet for aleph-3 and higher.

According to an article by Rith K & Schäfer A in Scientific American of July 1999, "The Mystery of Nucleon Spin", page 60, no one has been able to formulate the equations of QCD with sufficient precision to correctly describe a nucleon. So this seems to be a practical example of an established theory that has not yet been mathematically justified. A challenge still to be addressed.

Plenty of problems, the three body problem, the Galaxy problem, etc.

if one considers that gödel Theorem is not true, there are not so many unsolvable Problems.