True, mathematicians are important people who solve problems in the real world.
Mathematics is the science that deals with the logic of shape, quantity and arrangement. Math is all around us, in everything we do.
Mathematicians spent thousands of years trying to solve problems that turned out to be impossible however with these years of solving impossible problems along the way they are able to discover new things like mathematical principles, methods, and constructions.
In mathematics, a proof of impossibility, also known as negative proof, proof of an impossibility theorem, or negative result is a proof demonstrating that a particular problem cannot be solved as described in the claim, or that a particular set of problems cannot be solved in general.
Proofs of impossibility often put decades or centuries of work attempting to find a solution to rest.
To prove that something is impossible is usually much harder than the opposite task, as it is often necessary to develop a theory.
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