Were the world’s most “difficult” math problems constructed to be unsolvable?
In: Mathematics
They’re not designed to be unsolvable on purpose. It’s rather the opposite.
The problems are *basically* unsolvable using *today’s techniques*, but some kind of solution *probably* exists. The hope is that by the time we solve them, we will have invented new clever techniques and interesting theories of math.
Just knowing the yes/no answer to every problem wouldn’t be very useful to us, so e.g. chugging the problem into a supercomputer and having it make 1000-page proof that e.g. P=NP would actually not advance our understanding of mathematics that much. Rather, the problems are a milestone that indicate that our general math intelligence (achieved through new theories and new ways of looking at the world) is now much more powerful than before. Being able to solve those problems has much greater practical use than merely having the answer.
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