This being Less Wrong, this might be the point where you bring up whether P=NP and that solutions are often much easier to verify than compute. Easier does not necessarily mean easy or even within human cognitive capabilities. And if it does in whatever example comes to mind, just keep pushing to harder problems until we need not only tools to solve the problem but also meta-tools to tell us what our tools are telling us. And you can keep pushing that meta. (Did I mention that Blindsight is a very Less Wrong book?)

We trust our tools because we trust the process we used to develop our tools, and we trust the previous generation of tools used to develop those tools and processes, and we trust... At some point, you look at the edifice of knowledge and realize your life depends on a lot of interdependencies, and that can be scary.

And then I trust Google Maps to get me most places, because I know it has a much better direction sense than me and it knows things like construction and traffic conditions.