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First of all, my background: I've already completed all of my high school math courses including calculus, and I've been considering to pursue math at university/college starting in September. And yes I know that the way math is done in high school does not reflect what math is really all about in any way; for instance, the focus is on computation and hand-wavy arguments rather than rigorous development of the subject and proofs. However, I

**really really**like rigor and proofs when it comes to math, and I hate using mathematical results which do not come with a proof.

Here are some examples of what I found that I really liked:

1. The proofs of all the arithmetic/algebraic operations we make use of when dealing with integers and rational numbers (from the "field axioms").

2. The proofs of various results from elementary number theory.

3. Euler's proof/solution to the "Seven bridges problem".

4. Proof of irrationality of the square root of 2 (plus, the idea of a proof in general)

5. Proofs of statements from Euclidean geometry.

etc...

Now, here's my problem. Even though I really enjoy the above-mentioned aspects of mathematics, I find it hard (and I don't like) to deal with the mathematical objects which do not really have a tangible or intuitive meaning. Examples of these troublesome objects (to me) include the irrational numbers, complex numbers, infinities, vectors having more than 3 components etc. And, what's even more troublesome is that it seems to me that I'll have to accept more and more of these kinds of objects if I decide to pursue math. (By the way, I should also mention that I read the first few sections of Timothy Gower's "Mathematics - A Brief Introduction". There he says that we shouldn't bother about what these mathematical objects mean, but rather we should be concerned with what they do - that is there properties. And, I found this rather disturbing.)

To wrap it up, I'd say that I really like doing rigorous pure mathematics when dealing with mathematical objects that are meaningful/intuitive to me. But, I hate doing mathematics when dealing with hypothetical/fictional mathematical objects - those objects that I can't imagine or seem completely pointless to me. So, my question is the following: would I enjoy being a pure math major? Or will all those abstraction and fictional aspects of pure mathematics ruin my interest in math?

I'm a little lost, and I don't know what to think about or what to do. I would highly appreciate being advised (especially by those who had once been in the same situation I'm in right now).

Thanks for taking time to read such a long post.