Ray Monk in Prospect:
We are sometimes inclined to make celebrities out of intellectuals despite—or perhaps precisely because of—their producing work we can never hope to understand. Bertrand Russell’s oddly old-fashioned dress sense and aristocratic bearing remain familiar features on the cultural landscape, as are Albert Einstein’s friendly face and shock of white hair. Indeed, such was the popularity of the aging Einstein that he was, decades after coming up with relativity theory, offered the (largely ceremonial) presidency of Israel. The elder Russell, meanwhile, was invited on to radio and television to give his opinion on everything from communism to what kind of lipstick women should wear. The reason he was invited on to the media was not, of course, that he was an authority on these subjects, but that he had, in his younger days, written abstruse things on mathematical logic and the philosophy of mathematics. The most notable of these, Principia Mathematica—in which he and his co-author Alfred North Whitehead put forward an axiomatic system of logic upon which they hoped to build, first arithmetic and then the whole of mathematics—is considered formidably difficult even by experts in the field.
The logician and philosopher Kurt Gödel passes the Einstein/Russell test, in doing work whose importance is beyond argument, but can also seem beyond comprehension as well. If you wanted to make the case that he should join them as a celebrated public figure, you could point out that among his work is an important contribution to the interpretation of Einstein’s relativity theory, and that he pulled the rug out from under the project on which Russell spilled most sweat.