For literature, the Mesopotamians had Gilgamesh, which is a significant contribution because it is one of the earliest written epics that we have today.
For philosophy, a major contribution would have been the development of an influence on Greek and Hellenistic philosophy.
Mesopotamians introduced a lot into the world of medicine. They did a lot with prognosis, diagnosis, physical examination, and prescriptions. Their work with medicine was very logic-based so they would compile lists of symptoms and observations and treat patients accordingly. Although they still tried to excorcise curses.
The Mesopotamians were the creators of the 24 hour day, 360 degree circle, and 60 minutes. In astronomy, they could predict the cycle changes by the stars. However, these were all based on 60 (we are based on 10s, thus decimals, etc). This means that though they made contributions to modern day mathematics, their contributions are not as resilient.
As you can see, the Mesopotamians made strong contributions in all of the options above, however due to the base 60, the math and astronomy contributions may not have been as great.