I have read many times that some problems or logical propositions do not have solutions or are outright impossible. These are three examples of such problems:
[The Russell's paradox] which is deemed as contradictory with no possible solutions
[The Liar's paradox] which is similar to Russell's paradox in the sense that it is also contradictory and no logical solution can be found out of it
Some mathematical impossibilities like trying to find a positive integer number to divide a prime number (e.g. 2, 7, 53, 181...) other than 1 and itself
However, is it really true that no solutions exist for these situations? Could we solve these problems using alternative axioms of logic and mathematics? Or perhaps our brains need to develop or evolve more to conceive such solutions?