"The most incomprehensible thing about the world is that it is comprehensible." This is one of the most famous quotes from Albert Einstein. "The fact that it is comprehensible is a miracle." Similarly, Eugene Wigner said that the unreasonable efficiency of mathematics is "a wonderful gift which we neither understand nor deserve." Thus we have a problem that may seem too metaphysical to be addressed in a meaningful way: Why do we live in a comprehensible universe with certain rules, which can be efficiently used for predicting our future?
Let us consider several other questions of a similar type. Why is our universe so large? Why parallel lines do not intersect? Why different parts of the universe look so similar? For a long time such questions looked too metaphysical to be considered seriously. Now we know that inflationary cosmology provides a possible answer to all of these questions. Let us see whether it might help us again.
To understand the issue, consider some examples of an incomprehensible universe where mathematics would be inefficient. Here is the first one: Suppose the universe is in a state with the Planck density r ~ 1094 g/cm3. Quantum fluctuations of space-time in this regime are so large that all rulers are rapidly bending and shrinking in an unpredictable way. This happens faster than one could measure distance. All clocks are destroyed faster than one could measure time. All records about the previous events become erased, so one cannot remember anything and predict the future. The universe is incomprehensible for anybody living there, and the laws of mathematics cannot be efficiently used.
If the huge density example looks a bit extreme, rest assured that it is not. There are three basic types of universes: closed, open and flat. A typical closed universe created in the hot Big Bang would collapse in about 10-43 seconds, in a state with the Planck density. A typical open universe would grow so fast that formation of galaxies would be impossible, and our body would be instantly torn apart. Nobody would be able to live and comprehend the universe in either of these two cases. We can enjoy life in a flat or nearly flat universe, but this requires fine-tuning of initial conditions at the moment of the Big Bang with an incredible accuracy of about 10-60.