In his latest book, Our Mathematical Universe: My Quest for the Ultimate Nature of Reality, Max Tegmark tries to answer what is maybe the most fundamental question in science and philosophy: what is the nature of reality?

Our understanding of reality has certainly undergone deep change in the last few centuries. From Galileo and Newton, to Maxwell, Einstein, Bohr and Heisenberg, Physics has evolved by leaps and bounds, as well as our understanding of the place of humans in the Universe. And yet, in some respects, we know little more than the ancient Greeks. Is the visible Universe all that exists? Could other universes, with different laws of physics, exist? Does the universe split into several universes every time a quantum observation takes place? Why is mathematics such a good model for physics (an old question) and could there exist other universes which obey different mathematical structures? These questions are not arbitrary ones, as their answers take us into the four levels of the multiverse proposed by Tegmark.

As you dive into it, the book takes us into an ever-expanding model of reality. Tegmark defines four level of multiverses: the first one consisting of all the (possibly infinite) spacetime of which we see only a ball with a radius of 14 billion light-years, since the rest is too far for light to have reached us; the second one which possibly holds other parts of spacetime which obey different laws of physics; a third one, implied by the many-worlds interpretation of quantum physics; and a fourth one, where other mathematical structures, different from the spacetime we know and love, define the rules of the game.

It is certainly a lot to take in, in a book that has less than 400 pages, and the reader may feel dizzy at times. But, in the process, Tegmark does his best at explaining what inflation is and why it plays such an important role in cosmology, how the laws of quantum physics can be viewed simply as an equation (the Schrödinger equation) describing the evolution of a point in Hilbert space, doing away with all the difficult-to-explain consequences of the Copenhagen interpretation, the difficulties caused by the measure problem, why is the space so flat, and many, many other fascinating topics in modern physics.

Since the main point of the book is to help is understand our place in this not only enormous Universe but unthinkably enormous multiverse, he brings us back to Earth (literally) with a few disturbing questions, such as:

- What is the role of intelligence and consciousness in this humongous multiverse?
- Why is this Universe we see amenable to life, in some places, and why have we been so lucky to be born exactly here?
- Shall one view oneself as a random sample of an intelligent being existing in the universe (the SSA, or Self-Sampling Assumption proposed by Bostrom in his book Anthropic Bias)
- If the SSA is valid, does it imply the Doomsday Argument, that it is very unlikely that humans will last for a long time because such a fact that would make it highly unlikely that I would have been born so soon?

All in all, a fascinating read, if at times is reads more like sci-fi than science!