Perhaps it's the fact that I'm an experimentalist, but I still don't see the difference. A mathematician considers a theory "right" if only it is self-consistent. By contrast, "right" or "wrong" for a scientific theory also addresses the question of whether or not it applies to the real world. But I can also apply the same standards to mathematical theorems: an experimental test of Euclid's theorems shows that they don't apply to real spaces as well as Riemann's do. To me, Riemann is "right" where Euclid is "wrong". Apples to apples, you understand.
So you see, it isn't that the word "theory" is used differently in mathematics and physics, but that the standards of "right" and "wrong" are different.
I can't tell whether you honestly don't understand what I'm saying, or are just being intentionally obtuse for the purposes of prolonging the argument.
In brief: Scientific theories contain statements which may be falsified upon further data; mathematical "theories" consist of nothing but true statements (theorems). Scientific theories can be disproved and mathematical theories can't. That's the difference.
After making me frame this difference in plain English for the third or fourth time, for you to protest that you "don't see the difference" is to say nothing more and nothing less that you don't understand English. The main difference for this discussion consists of the second-to-last sentence of the preceding paragraph; if you still "don't see the difference" at this point all I can ask you to do is to read that sentence again until you do, or get tired.
To be sure, I understand (and already agreed to) the very minor point that if you view things abstractly enough then "mathematical theories" and "scientific theories" are similar, in the sense that they are both "theories". (Duh.) But this only goes so far. There are still those pesky adjectives "mathematical" and "scientific" in front of the two terms, and you can't just ignore them. Adjectives have a funny way of modifying the nouns they precede, and this can lead to precision and differentiation. It's like you don't understand this, or are pretending not to, for some reason.
It is precisely as if I was posting on a thread about ice cream cones. Post after post discusses this type of cone vs. that type of cone - some prefer waffle, others prefer the pointed kind, whatever. In one post I say "boy oh boy, yessirree, I sure do love all these kinds of cones."
Then Doctor Stochastic chimes in, "Oh yeah? What about pine cones?" This is a superficially clever type of comment, but only for a moment, and in particular only from seven-year-olds. All that is required to say is, "that's not the kind of 'cones' we've been talking about. Sorry." And that's what I did say, come to think of it.
The problem is that now, you, "Physicist", have valiantly rushed to Doctor Stochastic's aid, for some reason. "Are too! They're both cones! I don't see the difference!"
Now look, I guess I agree that viewed abstractly enough, both ice cream cones and pine cones are types of cones (very roughly speaking), and so, there ya go. (One comes to this dazzling conclusion by ignoring the modifiers "ice cream" and "pine", just as you've ignored the modifiers "mathematical" and "scientific".) But you'd never say "So therefore I don't see the difference between ice cream cones and pine cones!" And I'm also pretty sure you wouldn't eat a pine cone.
Now, I've stated several times that "mathematical theories" and "scientific theories" differ in that the former may never be disproven, placing them in stark contrast to the latter. The former make predictions about the real world, and the latter don't. And you're saying you "don't see" the difference.
I think the only thing left to decide is whether you do this out of denseness or just to be a nuisance.
A mathematician considers a theory "right" if only it is self-consistent. By contrast, "right" or "wrong" for a scientific theory also addresses the question of whether or not it applies to the real world.
Let me get this straight, you're trying to help me prove my point right? After all here you are detailing a way in which "mathematical theories" and "scientific theories" differ (standards of "rightness"). So why all that disingenuous crap about pretending not to understand the difference?
But I can also apply the same standards to mathematical theorems: an experimental test of Euclid's theorems shows that they don't apply to real spaces as well as Riemann's do.
"Don't apply to real spaces" means they are false (or at least inadequate) as "scientific theories" meant to describe the real world.
In the meantime, the mathematical theorems, or "the theory of Euclidean geometry" if you will, are just as true as ever - and will ever remain thus.
You're still helping me illustrate my point.
To me, Riemann is "right" where Euclid is "wrong".
As scientific theories, perhaps you are right. As mathematical theories, of course you are wrong.
This is an illustration of precisely my point, which was that scientific theories are different from mathematical theories.
So you see, it isn't that the word "theory" is used differently in mathematics and physics, but that the standards of "right" and "wrong" are different.
Sigh. So my earlier comments that "scientific theories can be proven wrong, mathematical theories can't" is wrong in your eyes, because, see, what I'm supposed to do is to switch the definition of "right" around when I switch from the "scientific" to the "mathematical" contexts, even if I do so in the same sentence. Thus leading to a construction like this: "mathematical theories are always right, according to the mathematical definition of 'right'. Scientific theories are always right, according to the scientific definition of 'right'." You require that I say this sentence, instead of the sentence I said.
The problem is that the sentence I did say is still true, and you know it. I wasn't using the scientific definition of "right" in the first place, and I won't apologize for this.
I guess one implication of the definition of "right" you'd force me to use is that, say, Newton's theories were "right" back in the 1700s, just not now. In fact, all scientific theories are "right" as long as they gain consensus acceptance for a reasonable period of time. I guess I could protest about all this, about why you think it disproves anything I said (hint: it doesn't; you switched definitions on me), and in particular just how the heck it's supposed to related to putting "evolution is a theory" in front of science textbooks, but you know what?
I get bored. I don't think you have an actual point to make anyway.