I have been intrigued by the theory expounded by the MIT physicist Max Tegmark that the universe is composed entirely of mathematical structure and logical pattern, and that all perceived and measured reality is that which has emerged quite naturally from the mathematics. That theory simplifies the question of why mathematics is such a powerful and necessary tool in the sciences. The theory is platonist in essence, reducing all of existence to pure mathematical forms that, perhaps, lie even beyond the realm of spacetime. Mathematics, in fact, may be eternal in that sense.
The Tegmarkian scheme contains some compelling arguments. One is that atomic and subatomic particles have only mathematical properties (mass, spin, wavelength, etc). Any proton, for example, is quite interchangeable with any other. And, of course, these mathematical particles are the building blocks of the universe, so it follows that the universe is composed of mathematical structures. Another is that the vastness of the universe is...