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Pentashagon comments on Math is Subjunctively Objective - Less Wrong
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The Pythagorean theorem and pi could both accurately be described as predictive scientific hypothesis of observed phenomenon. "In 3 dimensional space, if I measure two sides of a right triangle, the third side will be the square root of the sum of the squares of the other two sides." That is a scientific hypothesis, and it can be tested; not only that, but you lose none of the meaning of Pythagorean theorem by putting it in those terms. (Yes, if you bring relativity into it, it turns out to be a slightly inaccurate hypothesis because of the curvature of space in a gravitational field, so I suppose that puts it in the same catagory of hypothesis as Newtonian physcis.) It still seems to be an attempt to describe a feature that exists in nature, though.
(minor edits for clarification)
Ah. I wouldn't call that claim the Pythagorean theorem. To me, the Pythagorean theorem is a mathematical statement about mathematical objects called Euclidean triangles (or if we want to get really fancy, it's a statement about vectors in inner product spaces), and there is a separate claim, which is not mathematical, which asserts that a certain model which includes things like Euclidean triangles describes some part of the real world in some way.
In other words, I think it's sensible to enforce a strong separation between talking about the mathematical details of a mathematical model and the relation of that mathematical model to reality. To me this dissolves what I think your original question is (although I am not sure I have correctly understood what your original question is).
Maybe your question is secretly a question about the unreasonable effectiveness of mathematics in the natural sciences?