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"This problem is unsolvable" or "Approaches X, Y and Z are not solutions to this problem" are perfectly valid and useful contributions to science and society in general.

Or in the words of Thomas Edison: “I have not failed. I've just found 10,000 ways that won't work.”

The attainability of a solution is the product of a well-defined problem. So focus less on the "have I solved this" and focus more on the "have I made useful progress in defining the problem".




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