[abdullahkhalids]

Yes. But I think this is because, any area of study in which such disagreements can happen are, are by definition excluded from pure mathematics.

What is surprising is that what remains to be studied is vast and beautiful and highly effective when borrowed by other disciplines.

[pmiller2]

I don't particularly think it's surprising that results from the study of structure end up applying to other disciplines. The wonder of the "unreasonable effectiveness of mathematics" is really that we've managed to find those bits that line up the best between mathematics and other fields.