Sean Carroll had a great podcast recently with Max Tegmark. Tegmark believes that we are truly a mathematical structure, and he makes some interesting arguments to support his reasoning. For example, we have discovered many equations which seem to model our observations to a great precision. Kepler's law of planetary motion, Newton's laws, Planck's constant, the Dirac equation, and so on all seem to do such a good job at explaining how things work. We have found patterns and organized elements on a spiffy periodic table, and have discovered subatomic particles such as the electron and various quarks.
What I found interesting in the talk was how in the end (as far as we know) we have these subatomic particles which have properties that we assign numbers for. For example, the spin of an electron, the charge of a top quark, or the frequency of a photon. Properties that seem to not simply be a number (like the color red) is at some level just related to a number (wavelength of the photon is say 650 nanometers.
Why is it so hard to make the leap that all that exists are numbers and equations? In a sense, this isn't too far off from Carroll's view of the Many Worlds interpretation, which posits that all that exists is the wavefunction (as defined by the Schrodinger equation). What problems arise from Tegmark's mathematical universe? For one, we could presume that this leads us to believe that we are lines of code, similar to the Matrix movie. Is there some computer running our universe? If you open your mind to that idea, it only leads to whether that universe is really the foundation or if is like an infinite set of Russian nesting dolls.
Here is a link to the podcast if interested
 Mindscape Podcast