Once upon a time I was trying to explain the idea of the Trinity -- as much as anyone can, let alone an enthusiastic but frequently clueless theological amateur -- to someone who just could not get his head around the concept. Finally in frustration I exclaimed, "God is not a problem you have to solve!"
Which, in one sense is quite true. (Although sometimes I feel as if I am a problem God has to solve.)
But on the other hand...as someone in my book discussion group put it, at heart we're all Gnostics; we all want to know. Both science and religion, at their best, honor this impulse to understand the world, both physical and spiritual, around us. Cambridge physicist-turned-Anglican-priest John Polkinghorne says, "In their search for truth, science and religion are intellectual cousins under the skin...religion is our encounter with divine reality, just as science is our encounter with physical reality."
Polkinghorne discusses the Trinity, in the context of a scientific sensibility, in this lecture . I wish I'd had this when speaking to the individual who just couldn't sign on to Christianity because of this particular doctrine; I think it might have helped.
My own favorite explanation for the Trinity, short and sweet, comes from Henri Nouwen: God loves relationships so much that God is a relationship.
I think down at the university that's called a working hypothesis. Hey -- it works for me.
Trinity, medieval German