Physicist Lee Smolin has an interesting pre-print in the History and Philosophy of Physics section of arxiv.org : "Lessons from Einstein's 1915 discovery of general relativity". ( If one has read books at the level of Penrose's popular works, this paper should be quite comprehensible.)

Smolin argues, that contrary to the myth created by Einstein himself, it was not beautiful mathematics that led Einstein to his theory of general relativity. Historians of physics have gone through Einstein's notebooks, and what they shared with Smolin led him to this:

It was Einstein's physical insight and intuition that gave him his greatest successes, and when he had no new insights and relied on the beauty of mathematics, as in his futile quest for a unified theory, he got absolutely nowhere.

Smolin draws the lesson:

The physical principles "that Einstein invented such as the principle of equivalence and the principle of the relativity of inertial frames"..."are directly about nature."

All very good, but then Smolin goes on to propose that background independence ("...the laws of nature should be statable in a form that does not rely on the specification of a fixed geometry of spacetime") might be one such physical principle. Here, I'm lost. This seems to me to be a statement the real content of which can only be expressed in mathematics. I'm hard-pressed to think of genuinely doable experiments that test this principle.

Smolin weighs in on the holography principle: "This says that a model world with gravity can be described as if it were a world without gravity, with one fewer dimension, where that surface theory has one degree of freedom per Planck area", and says that this principle does not have the physical content of the principles of relativity and equivalence, and cannot be tested in single experiment.

So color me puzzled. But it suits my particular inclination that physics proceeds with physical insight, not with mathematics. Of course, if we're stuck with no unexplained anomalous observations or experimental results, and we have no good physical principle, then we can only pay attention to the mathematics, and hope that it leads to something. The history of the last forty years of particle physics is that this is a slender straw to cling to.

Smolin argues, that contrary to the myth created by Einstein himself, it was not beautiful mathematics that led Einstein to his theory of general relativity. Historians of physics have gone through Einstein's notebooks, and what they shared with Smolin led him to this:

I had a very happy day about fifteen years ago when I visited Jurgen Renn in Berlin and he showed me images of the notebooks in which Einstein had created general relativity. What impressed me was that Einstein was using the same techniques all physicists use to grasp the essential features of a phenomena they want to model. These are the development of approximate expressions, together with theplayful creation of simple examples and models. These are the tools every physicist is taught, which they employ throughout their career, first, to do their homework and, later, to make progress in their research.

The mathematics Einstein used may appear beautiful to some who study it, but what is going on in Einstein’s notebooks was not beautiful. It was hardheaded and pragmatic. When you dine at a fancy restaurant you may be impressed by the aesthetic presentation of a dish as it is brought to the table. But this is only the last step, just as the freshness of the ingredients as they come from the farm is only the first step. In between, hidden in the kitchen, it is all just hard, practical work. Mistakes are made, but these, ideally, never leave the kitchen. In Einstein’s kitchen—his notebooks it was no different.

It was Einstein's physical insight and intuition that gave him his greatest successes, and when he had no new insights and relied on the beauty of mathematics, as in his futile quest for a unified theory, he got absolutely nowhere.

Smolin draws the lesson:

The lesson is that the task of formulating a physical principle must come first—only when we have one in hand do we have a basis to look for new mathematics to express the new principle.

The physical principles "that Einstein invented such as the principle of equivalence and the principle of the relativity of inertial frames"..."are directly about nature."

They constrain, and can be falsified by, individual experiments. They require no mathematics to express them: their contents can be entirely captured in a verbal description of an experiment. Historians talk of “thought experiments”, but in fact the principles invented by the young Einstein referred to genuinely doable experiments.

All very good, but then Smolin goes on to propose that background independence ("...the laws of nature should be statable in a form that does not rely on the specification of a fixed geometry of spacetime") might be one such physical principle. Here, I'm lost. This seems to me to be a statement the real content of which can only be expressed in mathematics. I'm hard-pressed to think of genuinely doable experiments that test this principle.

Smolin weighs in on the holography principle: "This says that a model world with gravity can be described as if it were a world without gravity, with one fewer dimension, where that surface theory has one degree of freedom per Planck area", and says that this principle does not have the physical content of the principles of relativity and equivalence, and cannot be tested in single experiment.

So color me puzzled. But it suits my particular inclination that physics proceeds with physical insight, not with mathematics. Of course, if we're stuck with no unexplained anomalous observations or experimental results, and we have no good physical principle, then we can only pay attention to the mathematics, and hope that it leads to something. The history of the last forty years of particle physics is that this is a slender straw to cling to.