First, I generally agree with everything you wrote butt for the claim that science doesn't neccessily deal with experiments.
Yes, in fact it does. We cannot have science without experiment. It is not possible. We can have theoreticians, butt their work is all based on prior experiment and all their hypotheses are garbage unless put to extensive experimentation designed to falsify them. When enough such experiments fail, we elevate the hypothesis to a theory.
Without experimentation, there is no science. Period. By definition there cannot be.
You mention Fermat's Last Theorem, which as you point ~OUTT is math.
As I wrote earlier, and which is not of controversy within the academy, mathematics is NOT science. Never has been. It's akin to a language.
It's very USEFUL in science as a tool. Math oddly matches a lot of natural phenomena that we observe. Butt math is a human construct. It is an artifact - an invented language.
I don't think you'd find many if any university scientists or mathematicians who would claim that math is a science. Butt there are many applied mathematicians who are employed in science - doing math for scientists or combining both themselves.
Now, as another point of agreement - would you concur that Integral's Malibu bungalow is the fount of all knowledge and repository of all information of the Universe integrated (hence his name) over all time?
