Einstein once told everyone that he came to his office at Princeton University just for the privilege of walking home with Kurt Gödel.
In 1933, Einstein arrived in the United States and spent the last 25 years of his life in Princeton, New Jersey. Working at the Institute for Advanced Study (IAS), he walked daily from his home at 115 Mercer Street to his office.
About a decade later, locals often saw him walking alongside a young colleague. They conversed in German. Einstein regarded this young man as his equal. That young man was Kurt Gödel – the mathematician who discovered the Incompleteness Theorem at just 25 years old.
Gödel announced the Incompleteness Theorem at just 25. (Photo: Getty).
The scientific community regards the Incompleteness Theorem as the most profound revolution in understanding in the 20th century.
In June 1975, the White House Press Secretary’s Office announced that President Gerald R. Ford had chosen the recipients of the National Medal of Science. Among them was Austrian-born mathematician Kurt Gödel. Besides his nickname Mr. Why, Gödel was also known by the acronym God.
In 2000, Time magazine listed him among the 100 most influential people of the century. Gödel’s Incompleteness Theorem was recognized as the number one mathematical discovery of the 20th century, on par with Einstein’s Theory of Relativity and Heisenberg’s Uncertainty Principle.
Youth of Gödel and the Incompleteness Theorem
Gödel was born on April 28, 1906, in the city of Brno (now in the Czech Republic). His father managed a large textile factory.
As a child, his parents called him Mr. Why because he asked many questions. Gödel showed his talent early on, excelling in all subjects, especially mathematics, languages, and theology.
By the age of 18, he had mastered mathematics at the university level. Although he pursued theoretical physics at the University of Vienna (Austria), he still attended lectures in mathematics and philosophy. Later, he became captivated by mathematical logic.
According to Gödel, mathematical logic is “a science that precedes all other sciences, containing the thoughts and fundamental principles of all science.”
In 1930, he received his Ph.D. in mathematics. The content of his doctoral thesis is known as Gödel’s Completeness Theorem. However, that was just the beginning.
A year later, Gödel published a work containing his most important and famous theorems titled: “On Formally Undecidable Propositions of Principia Mathematica and Related Systems.”
In this work, he logically proved that for any set of axioms strong enough to describe the arithmetic of natural numbers, the following conclusions are always true: 1/ The system cannot be both consistent and complete. 2/ The consistency of the axiomatic system cannot be proven within that system.
This is the essence of the Incompleteness Theorem. Incompleteness is evident in the existence of propositions that cannot be decided, proven, or disproven. In other words, in mathematics, there exist truths that cannot be known.
Gödel’s work dealt a significant blow to scientism. It created an unprecedented revolution in mathematical understanding. The theorem showed that mathematics is as incomplete as any other system of understanding, rather than being an absolutely certain logical system, which most of humanity mistakenly believed.
In simpler terms, Gödel’s Incompleteness Theorem states that no logical system is perfect enough to allow us to explain all truths. Gödel himself stated: “Explaining everything is impossible.”
Commenting on this work during the honorary doctorate ceremony for Gödel, Princeton University declared: “His revolutionary work has shaken the foundations of our understanding of human thought.”
Meanwhile, Professor Jonathan David Farley of Stanford University remarked: “20th-century science was shaken by three tsunamis: 1/ Einstein’s formula E = mc2, explaining the principle of the atomic bomb and why the sun shines; 2/ The discovery by Francis Crick, James Watson, and Rosalind Franklin, showing that all life originates from the double helix; 3/ The discovery of a young Austrian mathematician showing that we can never be certain that 1 does not equal 0. That mathematician was Kurt Gödel.”
In the fall of 1938, Gödel married Adele, his longtime girlfriend who was six years older and had been previously married.
Gödel and Einstein
After publishing the Incompleteness Theorem at age 25, Mr. Why etched his name into the list of “Immortal Stars” in the mathematical community. This success caught the attention of Princeton University (New Jersey, USA), which invited him to work there.
It was there that Gödel met Einstein, and the two quickly became close friends. This was also one of the reasons why Gödel decided to settle and obtain U.S. citizenship in 1947.
Einstein and Gödel became lifelong friends, often conversing together. (Photo: Getty).
According to The New Yorker, locals often saw Einstein walking alongside Gödel. Each morning, they would walk to their offices together, conversing in German. In the afternoon, they would stroll home together.
In terms of personality and interests, they seemed to be opposites. While Einstein was older, extroverted, active, cheerful, sociable, and always smiling, the younger Gödel appeared introverted, solitary, and reserved.
However, it seemed that Einstein found no one who understood him better than Gödel. He even told people that he came to his office at Princeton University “just for the privilege of walking home with Gödel.”
Additionally, another reason might be that Gödel was not intimidated by Einstein’s stature. Freeman Dyson, a member of Einstein’s and Gödel’s research institute, noted: “Gödel was the only colleague here who could walk and talk on equal terms with Einstein.”
After the Incompleteness Theorem, Gödel achieved many other remarkable successes, particularly during his time at Princeton University.
In his later years, Gödel’s health deteriorated. After suffering from bleeding due to a duodenal ulcer, he had to follow a very strict diet that led to significant weight loss. Adele, Gödel’s wife, was always there to care for him.
When Gödel developed paranoid delusions, always suspecting someone was plotting to poison him, he refused to eat anything except the meals prepared by his wife.
However, by the end of 1977, Adele fell seriously ill, was hospitalized for six months, and could no longer prepare food for her husband. Ultimately, Gödel starved to death at Princeton Hospital on January 14, 1978, at the age of 71, weighing only 29 kg at the time of his passing.
