David Lindley, The End of Physics. The Myth of a Unified Theory, 1993.
The other way is to find mathematical laws whose beuty and simplicity have particular appeal, and then attempt to fit the world to them. The latter method, which seems rather rarefied to us nowadays, is what Pythagoras intended, millenia ago, by his idea of “the harmony of numbers”. He and his followers believed that the world ought to be based on mathematical concept – prime number, circles and spheres, right angles and parallel lines – and their method of doing science was to strain to understand the phenomena they observed around them in terms of these presupposed concerpts. It was for many centuries a central believe that the whole world, from the motion of falling bodies to the existence of God, could be ultimately be understood be pure thought alone.
At the same time, it is apperant that the greatest successes of twentieth-century physics have been theories that make use of novel and enticing mathematical structures imported from the realm of pure thought. Aesthetic judgement are taking on greater importance in theoretical physics not as the result of some conscious change in the methods of science but by default.
Some of the blame, unfortunately, for this shift back toward the old Pythagorean ideal must go to Albert Einstein. His general theory of relativity is the prime example of an idea that convinces by its mathematical structure and power, and for which experimental verification is something of an afterthought.