What is your favorite current scientific theory?

Holographic universe cosmology.

Not because I think it is true (I am not qualified to judge, anyway), but just because it shows how completely off the rails modern science is at the margins. We've reached a place where for some theories, the distinction between "this is just a useful mathematical tool" and "this is something real about the universe that the theory accurately describes" collapse into one another.

Good one and good reason!

The EM Drive. While not an FTL, it would give us access to our solar system
that we never thought would be possible. Just imagine going to the moon in about the same time it takes to get from NYC to LA, or a trip to Mars taking less time than it took the Pilgrims to travel to America.

Not really on the mark science, yet if there existed a parallel universe, it would only be scientifically reasoned to have to assume there'd be millions of them. Why would there only exist a single parallel universe simply because it's easiest to imagine.

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We've reached a place where for some theories, the distinction between "this is just a useful mathematical tool" and "this is something real about the universe that the theory accurately describes" collapse into one another.Didn't we reach that way back with the "sun-centered universe" (solar system, as we now call it)?

Didn't we reach that way back with the "sun-centered universe" (solar system, as we now call it)?

Not quite what I had in mind.

Here is what I am thinking of:

The guy who first discovered quarks thought that they were not real the way photons or electrons are, but merely a mathematical trick that he had discovered. He didn't think his model described something out there in the universe. Turns out he was wrong and quarks really do exist the way photons and electrons do.

Holographic cosmology suggests that the universe around us is a projection in three dimensions from a very distant two dimensional surface. Does the model describe something factual and real in the way electrons and quarks are real, or does it just produce accurate calculations? And how can we tell the difference, if at all?

I tread cautiously, because I know you are far more knowledgable about science than I. And you are thorough at destroying those who fail to present a genuine argument.

What I was thinking of was that I recall hearing that way back when the Church was arguing against the sun-centered model of the "universe", the math was plainly irrefutable, so they said, well......OK, so it's "just a useful mathematical tool", but definitely NOT, no way, uh-uh, we repeat, NOT how the "universe" actually IS!! Ultimately, however, it had to be conceded the sun-centered model IS the reality (of its context).

Then there's the example of quarks that you cite. Their discoverer originally thought they were a mere "mathematical trick"; but later...golly, they ARE real!

So, do we EVER actually have a distinction between "mathemetical models" and "reality"? Does the working out of the math initially "blow our minds", and only later do we come to accept it as reality? What I might ask for here is if you know of any examples where the math has been firmly held to be JUST that, and NOT reality? This may seem silly if you do know of obvious examples. Or maybe my whole question is just one big fail!

So, do we EVER actually have a distinction between "mathemetical models" and "reality"?

In science, models are really all you get. You use them to understand and refer to elements of reality, but it is always a mistake to think they are reality in itself.

But especially in physics, there are cases where the models have elements which don't appear to refer to objective entities in the universe and are merely artifacts used to perform calculations.

What I might ask for here is if you know of any examples where the math has been firmly held to be JUST that, and NOT reality?

I can't provide any examples where debate has been settled one way or another, but someone who is better educated than I probably could.

Examples I think of would be the strings in string theory, fields in physics, the wave function in quantum physics. Experts are all over the map on these. My personal opinion at the moment is that these are probably all mathematical artifacts.