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I am writing a math thesis.

I want to provide a result in chapter 2, but formally prove this result in chapter 8. This is because I am introducing a bunch of definitions in between these chapters and they cannot be moved in front of or within chapter 2.

Can I say something like, "as we will see in chapter 8, this result in chapter 2 is true"? In other words, can you allude to the proof of a result that will be given only later in the thesis?

I don't feel like it is good practice because it sorts of destroys the "surprise factor", and it also makes the reader jump 100 pages to see the result. How should I handle this?

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    Yes. It's bad if you don't do that. Your thesis should minimize the "surprise factor" for maximum clarity. You should also use dynamic cross-referencing so you can put in something like (see p. 135) and have that page number automatically update as pagination changes.
    – WBT
    Commented Jun 18, 2017 at 19:02

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Is it appropriate to allude to results obtained later on?

Yes, please not only "allude" to later results, but make it absolutely clear at any point of your thesis what all the components of your argument are. You can, and sometimes should, defer the explanation of those components to a later part of your thesis. Just don't make your reader think "Huh? Something is missing here".

If you feel it is too much to ask your readers to accept a statement until it is explained in more detail, you can provide a very short and abstract version earlier. But this "preview" should only serve the purpose of making the reader aware of a part of the argument that will be explained later on; it should not be a duplicate explanation. (This could be just one or two sentences if possible, but two or three paragraphs at most and only if necessary.)

A thesis is not a suspense story. A crime novel aims for surprising plot twist; a thesis aims for a natural flow of the argument. If your readers are surprised at any point, your writing is not consistent enough.

This is also why in the standard format of research papers in most disciplines, the last part of the introduction is an outline of the entire argument.

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    This reminds me of a great linguistics prof I had whose partner is an English lit prof. "Our essays are very different," she told us one day. "With his essays, you slowly figure out what he's getting at and start to understand what he's saying when he finally reveals it at the end. In linguistics, you just put what you mean at the beginning and spend the rest of the time explaining how you got there." I think the second, more scientific approach, is more suitable for math.
    – Luke Sawczak
    Commented Jun 18, 2017 at 19:04
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    Seconded. It doesn't even have to be complicated - a simple statement of "A formal proof of this [theorem/assumption/brain fart] can be found in Chapter 6" essentially says it all.
    – NGTOne
    Commented Jun 19, 2017 at 5:27
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    There's a good shorthand for this that I was taught to bear in mind whenever writing (or making presentations): "Tell them [the reader/audience] what you're going to tell them. Then tell them. Then tell them what you've told them."
    – owjburnham
    Commented Jul 4, 2017 at 19:45
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Can I say something like, "as we will see in chapter 8, this result in chapter 2 is true"?

How about: "Thesis outline: In Chapter 1 we will etc. In chapter 2 we will present the first main result of this research, the Foo theorem. In Chapter 3 we will develop some machinery for etc. etc. etc. Having done (whatever), in Chapter 8 we will utilize (something) to prove the Foo theorem described in chapter 2."

Refer. Or refer not. There is no "allude".

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