Saying the same thing in a slightly different way:
Today we see math and science as inseparable. But at their most basic, they're worlds apart. Math relies on deductive reasoning. We start with basic principles then logically deduce their consequences. In the world of math, if you believe what you start with - sets, numbers, addition, and so on - there's no uncertainty about your conclusions. None.
Science doesn't work that way. Scientists observe the world around them, then reach inductive conclusions. If every swan a scientist observes is white, he may reasonably theorize that all swans are white. However, if a black swan shows up at the party, his theory needs to be modified or discarded. Einstein's theory of general relativity showed how Newton's theory of gravity was wrong - or at least incomplete. Yet Newton rightly remains one of the most highly esteemed scientists in history.
Or we could say pirouetting around Godel:
Be it a theory of government or a scientific theory, math-like reasoning can't stand front and center. Devoid of grounding in observed facts, such reasoning is all sound and fury, signifying nothing. Descartes. The scholastics. The shores of history are riddled with the remains of those seduced by the precision of math. For all math's beauty, power, and even perfection, when it comes to science, math's but a humble servant - though admittedly a pretty good one. Our universe, it turns out, is surprisingly mathematical.Although he sticks the landing:
Which is why, even today, scientists are sometimes tempted by the siren call. They offer up infinite universes we can't interact with; bona-fide physical dimensions beyond three that can't be experimentally verified. "But the math," goes the argument, "is too compelling to ignore." Is it? Or are we once again falling into that age-old trap?
I'm not quite sure how Descartes or the Scholastics wind up in there; but even though the universe is surprisingly mathematical, the universe is not everything. Even Descartes understood the power of doubt, and the limit of thought. Anglo-American philosophers and Continental phenomenologists are still wrangling over that one.