@tao@mathstodon.xyz would deeply appreciate a bit of elaboration on “to the point where one can no longer discern its geometry to the extent that promising questions can be extracted within the range of applicability of the tool. Often this is counteracted by the ability of such a tool to enlarge the radius …” The metaphor is of concentric circles where the interior of inner circle’s geometry has been flattened by this new tool but area b/w the outer circle and inner circle still has sufficient ‘curvature’ to identify promising questions? and here, is promising in more than (just) understanding the difficulty boundaries of the tool? E.g. difficulty topography is a compass to other qualities of interest.