Science now has no hard evidence on the following questions and probably, because of the inherent limits of science, will probably never explain (beyond operational descriptions), in a fundamental way (without just raising deeper questions), the following;

1)  The origin of the laws of physics.  Physics of the early Universe is at the boundary of astronomy and philosophy.

2)  The source of the initial conditions of the universe.  (Why was there just the right amount of order for life?  Why so much?  Where did the initial order come from?)

3)  How does consciousness interact with matter if it does not generate a physical field of some sort?  How do centrioles have enough intelligence to control meiosis?   Centrioles     How does consciousness arise?        CURIOUS ORGANELLE

4)  Why is mathematics so effective in describing the universe?  Why is there a numerical language/model which fits reality and our minds?       Mathematics and the Language of Nature

5)  Why the speed of light speed limit is the value it is?  (Other values of the constants of the laws of physics are more likely to be explainable.  Life, the cosmos and everything.

6)  Why there is Order rather than chaos?

7) What is the vacuum and why does it have the energy it does?

8) What, if anything, exists beyond this universe?

9) What is time or at least, why does time have a direction on the large scale when it does not in the same way on the nuclear scale of individual reaction equations?  Where Does the Time Go? Forward, Physics Shows.  (Only a partial explanation of why time is as it is.  Note, they talk about particles going backward in time as seen in experiments.)

10) Why and how do we experience time?  How is time tied to consciousness?  

11)  Is there existence/consciousness after death?

12)  Whether or not miracles occur.   (One time events are not amenable to science.)