In The Big Questions, Steven Landsburg ventures far beyond his usual domain to take on questions in metaphysics, epistemology and ethics. Beginning with Plato, mathematicians have argued for the reality of mathematical forms. Rene Thom, for example, once said "mathematicians should have the courage of their most profound convictions and thus affirm that mathematical forms indeed have an existence that is independent of the mind considering them." Roger Penrose put it more simply, mathematical abstractions are "like Mount Everest," they are, he said, "just there."
All this must make Steven Landsburg history's most courageous mathematician because for Landsburg mathematical abstractions are not like Mount Everest, rather Mount Everest is a mathematical abstraction. Indeed, for Landsburg, it's math all the way down – math is what exists and what exists is math, A=A.
Read the book for more on this view, which is as good as any metaphysics that has ever been and a far sight better than most. Moreover, Landsburg's view is not empty, it does have real implications. Since there is no uncertainty in math, for example, Landsburg's view supports a hidden variables or multiple-worlds view of quantum physics.
Speaking of quantum physics, The Big Questions, has the clearest explanation of the Heisenberg uncertainty principle that I have ever read. In fact, this is a necessary consequence of Landsburg's metaphysical views; since it's all math all the way down, the explanation of the uncertainty principle is the explanation of the math and any true uncertainty or mystery is simply a fault of our own misunderstanding.
Turning to epistemology, the theory of beliefs and knowledge, two chapters stand out for me. I learned a lot from Landsburg remarkable clear explanation of Aumann's agreement theorem–and I say that despite the fact that in the office next to mine is Robin Hanson, one of the world's experts on the theorem (see Robin's papers on disagreement and also his paper with Tyler, but read Landsburg first!).
Landsburg's skills of explanation are also brought to bear in a wonderful little chapter explaining the theory of instrumental variables and of structural econometric modeling – and this from an avowedly armchair economist!