An indispensability argument for math

I just need to get this on the table, because it's basic to the topics that I'm currently learning more about. I'm going to quickly present the Quine-Putnam argument indispensability argument here, so that I can build off of it and delve deeper in future posts. Just to experiment with form a little bit here, I'm going to make it into a series of dialogues.
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A: Zebras exist.
B: What makes you say that?
A: Well, I observed a bunch of zebras. I saw them. They're over there [points to zebras].
B: So what? That's inconclusive. You could be hallucinating.
A: That's hardly the best explanation of the fact that I observed those zebras. The best explanation is that I'm not hallucinating, and that there's a bunch of things over there, and those things are called zebras.
B: Fair point. You're always justified in believing things if belief in them is necessary for the best explanation you have of the evidence.
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A: Electrons exist.
B: What makes you say that?
A: Well, I observed a bunch of stuff [note: I don't know physics], and the best explanation I have of it is that there is something that exists that we hadn't previously known of. I call it an electron.
B: Oh, fair point. After all, it's the best explanation that you have of the evidence, and that explanation requires you to believe that electrons exist.
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A: Numbers don't exist.
B: Wait a second, that doesn't sound right.
A: Why not?
B: You believe in zebras and electrons because your best explanation of the world requires your belief in their existence, right?
A: Right.
B: And what does it mean for your explanation to "require you to believe in their existence"?
A: I can clarify that. In order to give my best explanation of the world, I have to speak as if zebras and electrons exist. So if I'm committed to my explanation, I can't really avoid being committing to talking as if zebras and electrons exist. I think that this justifies my belief that zebras and electrons exist.
B: Is the law of gravity an important part of your best explanation of the world?
A: Sure--as long as it's up to date with current research...
B: Now, here's the important question for my argument: when you talk about the law of gravitation in your best explanation, is there any way that you can avoid talking as if numbers exist.
A: Well, errrm, no. How else can I talk about distances?
B: That's my point, then. Your best explanation of the world requires you to talk as if numbers exist. But that's the exact same justification you gave for why you believe that zebras and electrons exist. So if you're justified in believing that zebras exist, then you're justified in believing that numbers exist too.
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