If ones who asks this question have a phone in their pocket or a tablet in their hands, I say: You would not have that, and we would not have this information society if Kurt Gödel & co. hadn’t in the 20’s and 30’s thought profoundly about the questions of the foundations of logic and arithmetic. The concepts and theories of formal languages and calculation arose from these ideas, and then in turn programming languages and algorithmic computation.

The second world war forced Alan Turing and Johann von Neumann to create programmable computers, one for cracking the secret code of the German submarines, the other for the numerical calculation of the explosion of an atomic bomb. Here is some “societal impact” of basic research, but with the criteria of science policy today, Gödel & co. wouldn’t have gotten a schilling for their esoteric research!