The biggest example I can think of is Fermat's Last Theorem. Uncounted mathematicians devoted years of their lives to the theorem, and the developments they mad

The biggest example I can think of is Fermat's Last Theorem. Uncounted mathematicians devoted years of their lives to the theorem, and the developments they made along the way may have some applications. But I have yet to hear of any physical truths derived from the fact that a^n + b^n != c^n for n > 2. Most math is like this - beautiful, and useless. The motivation of most non-applied mathematicians is aesthetic, much like the motivation of someone in the arts. It's done for its own sake ("mathematical beauty"), not because it has any practical application. Mathematics might turn out to be "useful" more often than the average novel - but that doesn't mean the math was done with any use in mind. For example many developments in differential geometry made in the 19th century were inapplicable to anything physical for decades until Einstein applied them to create general relativity. Plenty of math becomes useful long after its development, and plenty more never finds any practical application.