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|Friedrich Waismann Suchen und Finden in der Mathematik 1938 in Kursbuch 8 Mathematik 1967
E.g. Is it possible to search for an integer between 1 and 2? This is pointless.
Is not the search for the threefold division of the angle meaningless? For the threefold division is impossible. That would be a very forced answer. After all, mathematicians have been looking for it for more than 2,000 years.
We can also ask: why does the search cease when the proof for the impossibility is found? The ordinary idea is that "the solution was already impossible even when one was searching for it." This is a deception. It was possible.
E.g. misleading comparison: If something sought is found in a completely different room. It seems to us as if the evidence has already searched the whole route. But this is a misunderstanding: the proof goes a very different way than the search.
One might say that, when he was looking for the threefold division, he searched for this and that and it does not exist. But one can truthfully say: he did not search for it. The seeker is not yet clear about what he really wants. (How he wants to divide the angle in three parts.)
The proof of the impracticability thus first of all changes the goal of the search. In the end, the goal disappears, in that the purpose of the task is clarified. If one surveys all the evidence, one can see that it actually gives the strict explanation of the concept "solvable with the help of square roots," and with this strict explanation the goal disappears.
In fact, it was a process that led me from one symbolism to another. When searching in the room, I have simply stopped searching, in our search in mathematics the goal changes.
The proof changes our way of thinking._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.
Einführung in das mathematische Denken Darmstadt 1996
Logik, Sprache, Philosophie Stuttgart 1976