I am curious as to what his view would be on, say, the positive solution to the 3n+1 problem (i.e. every 3n+1/2 sequence eventually becomes a cycle). Some of th

I am curious as to what his view would be on, say, the positive solution to the 3n+1 problem (i.e. every 3n+1/2 sequence eventually becomes a cycle). Some of these sequences may be profoundly long, so long that in his view, they may not exist. Or what if someone proves that 3 appears only finitely many times in the decimal expansion of sqrt{2} (God forbid!). How is the proof of something simple, say the solution of the Koenigsberg bridge problem by Euler any different: after all he did not enumerate all the possible paths! Even if he could, it is easy to find a manageably sized graph with too many possible paths.