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April 28 1906 – Mathematician Kurt Goedel is Born

by Vishul Malik

Though most would think the foundation of philosophy and mathematics do not intertwine, a man born on April 28, 1906 in the small Austro-Hungarian town of Brunn (modern Brno, Czech…

April 28 1906 - Mathematician Kurt Goedel is Born

Though most would think the foundation of philosophy and mathematics do not intertwine, a man born on April 28, 1906 in the small Austro-Hungarian town of Brunn (modern Brno, Czech Republic) would redefine the relationship between them. Kurt Goedel, who eventually emigrated to the United States and rubbed elbows with Albert Einstein, is regarded by many as perhaps the most influential thinker in logic since the Greek scholar Aristotle. By his death in 1978, his theories had rocked accepted science and exploded the concept of time. At the turn of the 20th century, Brunn was very much an Austrian city: the majority of the population considered German their native tongue and the culture reflected these cues. Growing up, Goedel was exposed to the riches of his hometown, enjoying a legacy of attachment to the community’s arts scene passed down through the family. (His grandfather, Joseph, was a locally-recognized singer.) Either owing to this access to knowledge or simply a natural curiosity, the young boy soon earned the nickname Herr Warum (“Mr. Why”) from his parents due to his constant questions. To Goedel, each day was a platform for discovery, an attitude that served him well as he worked his way through the education system. After World War I, Brunn became a part of the newly-created nation of Czechoslovakia and was renamed Brno. The change frustrated Goedel, forcing him to feel like a stranger in his homeland — he was an Austrian through and through, yet the country had changed around him and his birth citizenship fell within the updated borders of Czechoslovakia. He buried himself in books to pass the time, focusing on mathematics, religion and philosophy in his mid-teens. By the time he graduated from Deutsches Staats-Realgymnasium in 1924, Goedel was considered one of the brightest prospective students any university admissions officer could find. He opted to attend the University of Vienna, where his brother was studying medicine, immediately immersing himself in the mathematics department. His advanced understanding of the subject allowed him to converse with his professors at a level far beyond his classmates, a fact that allowed him to attend meetings of the Vienna Circle, a collection of eminent thinkers in the Austrian capital led by Moritz Schlick and Hans Hahn. Goedel found college life enchanting. The flow of new ideas stimulated his brain immensely, but none more than the concept of mathematical logic. In his estimation, this “science prior to all the others” served as the foundation for study in every discipline known to man. Without a sensible approach to understanding how calculations could be made — or, in other words, how everything literally added together to create something — there would be no real comprehension of anything. Now aged 22 and working toward his doctoral thesis, Goedel dove into the idea of deductive reasoning. When he submitted his dissertation in 1929, he had formulated a concept for verifying the truth of a calculation based on the formal proof for it. In very simple terms, if a scientist wanted to discern the direction of a moving car, the ability to do so without drawing from outside calculations would make his or her work more “complete.” The speed of the car, departure location and destination would all be more reliable in this case than information about the flow of traffic on the opposite side of the road. Granted a PhD in 1930 for his “completeness theorem,” Goedel published two papers the following year that stunned his chosen field. Building on his previous work, he assigned numbers to the constants and formulas present in mathematical logic, then showed that no system was complete or consistent — there was always some measure of uncertainty if observations were made from within that defined set of rules. In other words, logic-based algorithms — whether for personal decision-making or computer programming — cannot resist periodically coming to conclusions where both possible answers are true at the same time. This is famously demonstrated by the problem of Schroedinger’s Cat, a physics problem which asks whether a cat sealed in a box is alive or dead. According to Goedel’s “incompleteness theorem,” until a person opens the box to determine for sure, the animal is both alive and dead. The implications of this idea have a wide-ranging reach, affecting everything from high-level physics to basic computers. Now employed by the University of Vienna, Goedel’s work took him to the U.S. in 1933, where he met Albert Einstein. As if two peas from the same pod, the brilliant minds developed a deep friendship nearly immediately. Knowing his friend had escaped the rise of Nazism by taking an appointment at Princeton University, Goedel increasingly wondered when the time would come for him to abandon his home — with Adolf Hitler and his sympathizers gaining influence with each passing year, it seemed inevitable. Even as Goedel visited Einstein annually at the Institute for Advanced Study (IAS), lecturing Princeton students on the intricacies of his mathematics, academic life in Austria devolved further. Friedrich Albert Moritz Schlick, Goedel’s mentor and friend, was killed by a student in 1936, leaving Goedel to wonder if he might be a target. The situation wore him down emotionally, forcing him to spend a year away from the university. By 1938, the Nazi annexation of Austria was official and Goedel was forced to apply for a new job after his position was eliminated by the pro-Nazi leadership at the University of Vienna. While reviewing his information, the board noticed Goedel’s connection to Schlick, Hahn and the Vienna Circle. Since the club consisted of several Jewish scholars, the mathematician was denied a professorship. In September 1939, just weeks later, German tanks rumbled into Poland. Unable to serve as a soldier, the writing was on the wall: Goedel and his wife were bound for America as soon as possible. In the spring of 1940, the Goedels made Princeton their home. Offered the opportunity to join Einstein on staff at IAS, Goedel accepted and went right to work. He quickly published a fresh set of theories on the axiom of choice and theorized about the “constructible universe,” a concept by which more complex systems must be built with the foundation of simpler pieces. As the years passed, Einstein and Goedel continued to talk daily, often walking around Princeton’s campus so engaged in conversation it seemed as if they were the only two people for miles. When Goedel applied for US citizenship late in 1947, Einstein joined his friend at the ceremony. By the end of his life, the eminent physicist had benefited from Goedel’s mathematics — they proved that Einstein’s relativity rendered time a variable dimension instead of a set measurement — and found because “his own work no longer meant much, that he came to the Institute merely…to have the privilege of walking home with Goedel.” In his later years, Goedel moved away from mathematics and consumed philosophy. Honored by his peers with the first Albert Einstein Award and a National Medal of Science, he battled questions about his mental health as he neared retirement. Ever since Schlick’s death, Goedel believed someone might attempt to poison him. He refused to ingest anything not prepared by his beloved wife Adele and, when she was hospitalized for several months, Goedel promptly stopped eating altogether. On January 14, 1978, he died at the age of 71, having starved himself while waiting for her to be able to cook again. Also On This Day: 1192 – Conrad of Montferrat, King of Jerusalem for just two days, is assassinated in Tyre by Hashshashin. 1503 – Spanish soldiers using small arms loaded with gunpowder register a victory at the Battle of Cerignola, the first time the weapons prove decisive in human history. 1932 – A vaccine for yellow fever is announced. 1952 – After more than 15 years, the Second Sino-Japanese War comes to an end when China and Japan sign the Treaty of Taipei. 2001 – Dennis Tito, an American multimillionaire, becomes the first space tourist by joining the crew of Soyuz TM-32 for an eight-day mission aboard the International Space Station.