Kurt Godel: Perhaps The Smartest Man You’ve Never Heard Of
One consistency throughout the history of science is a lack of mainstream recognition for great scientists. It's impossible to avoid the names and faces of movie stars, musicians, and athletes. Most cartoons and mascots are more prominent than the winners of this year's Nobel Prizes. So let's give someone their day in the sun. Spread the story of an amazing human being who seized their life and achieved great things. I chose Kurt Godel, the mathematical logician. While not technically a scientist, leave me alone about it.
Unfortunately, Kurt's day in the sun will be marred by his 1978 death. This is another opportunity for a lesson. His area of study concerns itself with logical truths. These are true regardless of how we feel about them. Truth endures. May Kurt Godel endure too. His story can be broken into two conflicting parts. First, his strange, brilliant work. Second, his lonely, tragic existence.
Godel's Work
Mathematical logic is an alien language for nearly everyone. At least regular math has numbers. I'm going to do my best to translate Godel's genius into plain language. So hold on, because this gets quite technical. However, once his findings become clear, you'll find that they're fascinating, and even funny.
Godel is most widely acclaimed for his Incompleteness Theorems, published in 1931. A major goal at the time was to find the logical foundations of mathematics. Progress in math is based on finding proofs of theorems. A theorem is similar to a hypothesis. To prove a theorem, you take a set of statements as given, and follow them down a logical path. These given statements, which don't need to be proven, are called axioms. Great minds, like Bertrand Russell and David Hilbert, were looking for a set of axioms on which math could be grounded. They thought that all mathematics could be proven from a few initial statements. The Incompleteness Theorems ended this quest.
Godel's two Incompleteness Theorems go, basically, as follows:
A consistent logical system, capable of supporting mathematics, cannot be complete
You can't prove the consistency of axioms within their own system.
Obviously very abstract. The two key concepts here are consistency and completeness. Consistency in a logical system means that it has no contradictions. 1 + 1 can equal 2. It definitely cannot equal 2 and 3, in a consistent system. Completeness means, in a probably oversimplified way, that all true statements in the system can be proven true. We must be able to use our axioms to prove the truth of every statement that we can make in the system. Godel's claim is that any logical system capable of supporting mathematics is neither consistent or complete.
Once all of the symbols and terminology is stripped away, here is what Godel's incredible proof tells us. What he basically created was a logical statement claiming that it itself cannot be proven. If it could be proven, the statement was false. If it couldn't be proven, it was true. Godel shows that every system contains statements that are true, but cannot be proven true.
This is nearly identical to a classic language paradox. We see the same issues arise if I say to someone, 'I am a liar.' If I'm telling the truth, then I am a liar. But then why would I have initially told the truth? If I am indeed lying, then I'm not a liar. But then how can I have lied to you? Godel proved that something similar to this exists in all logical systems capable of supporting mathematics. I apologize for putting your mind through these exercises.
Godel dashed the dreams of those who believed that the world could be boiled down to logic. He exposed a fatal bug in the wiring of rational thinking. We should still understand the value of following logical steps to rational conclusions. However, we must remember that contradictions, and true but unprovable statements are inevitable. Especially because our world is far more complex than a logical system.
The Tragedy
The academic world has long praised the Incompleteness Theorems as a masterpiece in human thought. The general public couldn't be more ignorant of them. Many in Godel's position find their satisfaction from the work itself. They live for the moment of breakthrough. We can assume he did too, but the tragic degeneration of his life makes him especially sympathetic.
After publishing the Incompleteness Theorems, Godel fled the Nazis. He went to America to work at Princeton. Einstein was also at the institution at the time. Famously, the only reason he would ever visit his office was 'to have the privilege of walking home with Kurt Godel.' Godel was a quiet, private man, and Einstein was one of the few people he connected with. While introversion is common in people of great intellect, Godel's slowly deteriorated into intense paranoia.
While still in Vienna, one of Godel's mentors was assassinated by the Nazis. This awoke Godel's paranoia. He was particularly frightened of being poisoned. As he aged at Princeton, he refused food from anyone but his wife, Adele. When she was hospitalized for six months, Godel starved himself, withering to just 65 pounds at the time of his death. The logical fear of assassination by the Nazis had been perverted by paranoia. To Godel, starving to death was the only escape from being poisoned.
In his final years and death, we find Godel embodying his greatest work. The great logician, consumed by illogical paranoia. He is the ultimate contradiction. Following logical steps led him to an absurd conclusion, but he remained ever the stubborn logician. In the journey to prove the inescapable contradiction in logical systems, it seems that he found his own fatal flaw, but was blind to it. So while his accomplishments are difficult to access, let's take this moment to reflect on his tragic genius.