Kurt Gödel (1906-1978) was an Austrian mathematician and logician who came to the United States in 1938 to escape Nazi rule; Gödel was baptized Lutheran, but his close ties to Jewish friends and colleagues put him at risk.  He took a position at the Institute for Advanced Study and became a close friend of Einstein, who said that he sometimes came in to the office just to have the pleasure of walking home with Gödel.  With two exceptions Gödel has received little public mention.  The first was in the 1994 movie IQ starring Tim Robbins, Meg Ryan, and Walter Matthau where he was Einstein’s bumbling sidekick.  In real life he was even stranger than portrayed in the movie.  For example, in 1948 when Gödel went to take his citizenship exam, Einstein insisted on going with him.  Gödel had found a contradiction in the Constitution, which in his mind allowed for a dictator like Hitler, and Einstein was worried (fortunately needlessly) that Gödel could sidetrack his own exam.  The second instance was in 1999, when leading up to the new millennium Time magazine named him one of the 100 most important persons of the previous century.  Some of the others on the list were Winston Churchill, Franklin Roosevelt, Adolf Hitler, Albert Einstein, Henry Ford, the Wright brothers, and Mother Teresa.

            The primary reason Gödel was chosen for Time’s list was his 1931 Incompleteness Theorem.  In the previous fifty years mathematicians had been trying to base all of mathematics on a formal structure.  If you’ve taken a geometry course, you can think of this as being like Euclid’s system of axioms and postulates.  Gödel’s Theorem showed that there was a serious obstruction.  The statement of the theorem is too technical for us here (and irrelevant), but some of its consequences are of interest.  The first is that it shows that in any such formal structure for mathematics, it is impossible to show that mathematics is consistent; that is, that there are no contradictions.  And if there are contradictions in mathematics, I don’t want to fly in any airplane that used math in its design process, and that’s all of them.  What a bummer!  In a more positive vein, the theorem shows that in mathematics there are true statements that can’t be proved.  Since they are true, you cannot disprove them either.  There will always be things in mathematics that we cannot decide, and you probably won’t know if a given statement is one of these.  This is sort of an unemployment insurance for mathematicians.  By the way, until COVID-19 I had no problems with flying.

            It is always dangerous to use results from on field in another where they don’t directly apply (I always cringe at false applications of the Second Law of Thermodynamics).  Making analogies to another area, while not a valid form of argument, can sometimes can help us gain understanding.  As a math person, I identify with the Apostle Thomas; I want proof.  Hence, I think that archeological and historical research into the beginning of Christianity is very important, and textual scholarship is crucial to determining the most accurate rendering of the Bible.  But if even in my chosen field of mathematics it is impossible to prove or decide everything, how can I expect it not to be the same in religion?  The need for faith is inescapable.  How then are we convinced of essential truths?  One important way is looking to the lives of the faithful.  This is the content of one of my favorite chapters of the Bible, chapter 11 of Hebrews, which is often called the faith chapter.  Please read it and remember:  God loves YOU unconditionally.

Jim