Isn't it the case that mathematics could, and in my opinion does seem to be, just a useful fiction as you mentioned in your debate? You say something along the lines of "this wouldn't explain how nature seems to be written in the language of mathematics". Isn't it also the case that if mathematical concepts are useful fictions, then they would describe (accurately if well thought out) the universe as apprehended by our perceptions? Shouldn't we expect that our useful fictions would be useful precisely because they accurately describe our observations?
I have thought that perhaps I am missing the point of the argument though. Perhaps it is the case that you aren't saying God must exist because our useful fictions, particularly those of mathematics describing reality, would just be happy coincidence. Indeed, what kind of coincidence would it be that our tools were designed for the purpose they serve? Perhaps you are making the point that without God the universe wouldn't necessarily exhibit these extremely logical properties.
Maybe I'm just completely wrong headed on this. Could you please set me straight?
Here is a quote from Dr William Lane Craig's Answer:
Your question is about the argument from the applicability of mathematics to the physical world. Question of the Week #277 is about the only place where I have reflected on this question, and I refer you there. Again, it was reading Rosenberg’s own book that prompted me to put this into the form of the theistic argument. For mathematics lies at the foundation of physics, at whose altar Rosenberg bows. Given his scientism (epistemological naturalism), he cannot dismiss applied mathematics as illusory. Rosenberg also emphasizes that naturalism simply cannot tolerate cosmic coincidences. But then what explanation can the naturalist offer for why mathematics is applicable to the physical world, that is to say, for why the physical world is imbued with the complex mathematical structure that physics discovers. Naturalism founders in this regard, whereas theism has an easy answer: God created the universe on the mathematical structure that He had in mind.
I think reading the full response is a good idea. I have to say that I have often thought that the fact that we can use mathematics to model the universe is good evidence that there is a rational mind that not only brought the universe into being but holds it together. I've been fascinated by the fact that so many physical constants contain numbers and multiples of Pi, 2, and 3. It seems beyond rationality to concluded this is just a coincidence not a fingerprint or a signature.
God and the Applicability of Mathematics | Reasonable Faith