for example the formulas for some geometric figures like circles i dont remember other figures which i think the formulas are wrong for example the formula for a square it seems sound but for other it doesn is there a way to prove or disprove a formula or is it just guessing

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2 Answers

Just because you yourself do not know of the existence of geometrical proofs like that does not mean they in fact do not exist. The proofs you seek will be contained in any introductory textbook on *plane geometry*, and were known to the ancients.

But this is different from the question posed in the title. Mathematics is the art of quantitative reasoning. Each proof of a new mathematical fact or property is based directly on the next earlier proof in a hierarchy stretching back across thousands of years’ worth of *solved problems* in the field.

In this context, a solved problem demonstrates the correctness and hence the utility of the underlying mathematics. If math were *not* the correct way to quantitatively reason we would have known it many thousands of years ago.