Gödel's Theorem states that there will always be unanswerable questions. In relation to the beliefs of Ludwig Wittgenstein- a logician who believed that not all things could be spoken about logically, such as things that cannot be fathomed (the universe, infinity). Because one cannot form a picture of the unfathomable, then we cannot make claims upon what can't be imagined [please correct me if I did not properly convey his philosophy]- Gödel's Theorem does not completely deny what Wittgenstein believed in. But, in that case of Bertrand Russell, a life's work had been obliterated. Russell longed for a complete understanding which Gödel had denied the existence of.
Being a man of reason, Russell did not futilely resist. It's odd how one man can disprove what we as mankind have been looking for for a ridiculously long time. At the beginning of the book, mathematicians sneered at Russell's wish to perfectly combine logic and math, the mathematicians continued what, generally, they've been notorious for for many years; an air of stubbornness and superiority. I do not blame the mathematicians though, they're feelings are equal to that of most people- upon finally finding solid grounds to stand upon, people refuse to or reluctantly move to potentially shaky ground. Many resist revisions in math and science because those are meant to be things that were already completely reliable.
The quest of Bertrand Russell embodies the human struggle of finding reason and ethics, logic and math. Humans are curious beings. We search for the answers to our pondering and are not satisfied until an adequate solution if reached. But what if the solution is the fact that there is no solution? Sounds like a Russell's Paradox to me!
http://en.wikipedia.org/wiki/Russel%27s_paradox