The book which I'd like to nominate is entitled Deciphering the Cosmic Number: the Strange Friendship of Wolfgang Pauli and Carl Jung (2009). Although it's author, Arthur I. Miller has a Ph.D. in physics from the Massachusetts institute of technology, the book, itself isn't so much a scientific treatise, as it is an enquiry into a certain esoteric, animal known as the fine-structure-constant (approximately equal to 1/37). Unlike most other "physical constants", however this particular number is dimensionless. This makes it, in a very real sense fundamental to the fabric-of-reality (Being "dimensionless", "the constant" doesn't rely on measurements; rather, it's derived "conceptually, In other words, the universe wouldn't be the same without it).
The fine-structure-constant is also inextricably linked to the halcyon days of quantum mechanics. At the time, it was tacitly assumed that "quantum reality" is a homeomorphism of our "Newtonian world", an assumption which Pauli eventually helped to repudiate. The question which made the fine-structure-constant pertinent was how many coordinates are needed to uniquely locate an electron, in it's atomic orbit. The obvious answer was "3": three Cartesian coordinates should've sufficed, just as they do when specifying the locations of macroscopic objects. And, although a fourth coordinate did keep impinging on the debate, the impossibility of visualizing what that meant precluded it's easy acceptance.
Among other anecdotes, Miller refers back to a running feud between Johannes Kepler, and one Robert Mudd. The question, at that time was basically which numbers should bear the "divine imprimatur". Even at the dawn of the Enlightenment, certain "numbers" still retained a kind of Pythagorion panache: was the number "3" the archetype of God's aesthetics; or, was it "4"? Pauli studied the relevant correspondence between the two men, trying to glean some insights into his own numerical debacle. Although Initially, Pauli sided with Kepler, he nevertheless found himself beguiled by the arguments of the less scientifically-inclined Fludd. As he felt his own sanity slipping away, in despair, Pauli sought out Carl Jung as his therapist. Pauli was simply going mad, trying to understand why quantum space was so bizarre.
A good deal of the book is devoted to the various machinations, which a heretofore, dogmatic empiricist resorted to, in order to make his intuitive leap explaining just how weird quantum reality actually is. I see the book, Deciphering the Cosmic Code as an empiricist manual which nevertheless acknowledges the inexplicable roots of the presumably explicable. Although the "intuitive leaps" which scientists make cannot be reduced to an algorithm, they do draw on a rich history of esoteric literature, and art. Jung opened Pauli's eyes to that "history", thereby enriching a new field of scientific study. For anyone who scoffs at opening the door, of science to such spookery, the book'll no doubt seem provocative. On the other hand, it's not a license to raid the i-ching for inspiration, either. A balanced, and thoughtful reading of Miller's book should afford a newfound appreciation for the role which "gifted hunches" play in making scientific advances possible. That's why I'm recommending it.