Mysteries are the Doctor’s stock in trade, his bread and butter, his reason for being. Seeking them out and solving them keeps his brilliant mind occupied and entertained, because for someone who’s lived as long as he has, boredom is the greatest enemy.
The universe is vast, and having a time machine makes the possibilities almost endless. No matter how many mysteries he solves, there are always more to investigate. He dreads the coming of a day when no more mysteries remain, because then there would surely be nothing left to give him purpose, and that doesn’t bear thinking about.