##### Key Points:

- John Von Neumann made significant contributions to quantum mechanics by developing theories and equations such as “the Pauli spin matrix” and the “Fermi-Von Neumann equation.
- He led teams that developed computers for flight simulation for the U.S. Air Force, and for use in weather forecasting.
- In 1945 von Neumann joined the atomic bomb project, helping to develop the hydrogen bomb under Enrico Fermi at Los Alamos National Laboratory.

**Who Was John Von Neumann?**

John von Neumann (1903-1957) is best known as a mathematician and one of the leading figures in early 20th century mathematics. During World War II, he played an important role in atomic research. He worked on computational problems for the U.S. military during and after World War II, most notably on the ENIAC computer at Penn’s Moore School of Electrical Engineering.

Von Neumann later led teams that developed computers to use in weather forecasting and flight simulation for the U.S. Air Force. In 1950, he was elected permanent chairman of the influential General Advisory Committee of the newly formed Atomic Energy Commission.

**Early Life**

Von Neumann was born in Budapest, Hungary on December 28, 1903 to Neumann János Lajos (1873-1928), who was a wealthy banker, and Cecília Karsay de Felsö-Szilvás (1875-1964). The family converted to Christianity from Judaism when von Neumann was five years old.

According to Roman Catholicism at the time, it was required for his parents’ marriage that they do so. Although he remained a lifelong Catholic, John’s name change echoed through the remainder of his life. He did not like being called “John” but rather insisted on being called “Jancsi”, a nickname given to him by his mother.

Von Neumann began speaking and reading in English before Hungarian. He was particularly fond of reading about technology and science, such as Jules Verne. One of his favorite authors was H.G. Wells, who wrote War Of The Worlds , which he read when he was thirteen years old.

Von Neumann’s father died when he was six years old, and the family moved to Budapest. His mother continued her husband’s occupation in banking. Von Neumann was a very intelligent child, and quickly began learning multiplication tables at age three and four.

After graduating from his elementary school, von Neumann went on to high school in Budapest where he graduated with top marks despite not attending classes regularly; as some of his teachers were lax enough that they did not notice nor care about his absences so long as his work was up to standards.

His absenteeism concerned them more than his grades; worried that it would reflect poorly upon them should an outstanding student be cheated out of a diploma by their negligence or indifference. At this time in his life he was very interested in mathematics, and used to copy mathematical proofs from his textbooks onto slips of paper so that he could talk about them with other mathematicians.

In 1919 von Neumann enrolled in the University of Budapest and began studying chemical engineering. His father had expected him to pursue a career at the family bank but von Neumann’s passion for pure mathematics led him instead to begin taking math classes which were only offered by non-academic teachers.

He quickly proved himself as a prodigy mathematician, providing solutions two years ahead of his classmates and doing this without attending class regularly, if at all. His knowledge grew deeper over time and became more abstract. In 1922 he entered Georgikon University where he studied under the famous logician Hermann Minkowski and in 1923 he began studying under the topologist László Rátz at the University of Berlin.

**Career**

Once von Neumann graduated under Rátz, he began searching for a suitable position to continue his work. By chance, one of the mathematics professors at the University of Berlin, Jakob Rosanes happened to become aware of von Neumann’s talents and immediately hired him to assist in his research. They worked together until 1928 when Rosanes was appointed to a professorship at Göttingen. Von Neumann followed him there and continued his research on mathematical logic which he had begun studying with Minkowski.

In 1931 von Neumann went to Princeton where he met economist Oskar Morgenstern who would become his frequent collaborator over the next decade and later his good friend. He also met Albert Einstein, who influenced his thinking.

The opportunity to work with Einstein was an important factor in his decision to accept a position as professor at Princeton’s Institute for Advanced Study. He remained here from 1933 until his death, although he later managed to spend time working at the weapons laboratories during World War II. In 1945 von Neumann joined the atomic bomb project and by 1950 he had helped develop the hydrogen bomb under Enrico Fermi at Los Alamos National Laboratory.

Von Neumann held positions of authority in charge of research and development teams dedicated to furthering progress on these two projects until he died unexpectedly in 1957. Although he did not live long enough to witness it, von Neumann contributed significantly – especially through his leadership – towards the advancement of nuclear physics technology which is responsible for the massive nuclear arms race that continues to this day.

**What Is John Von Neumann Known For?**

John von Neumann is one of those people who are best described as a polymath. His intellect was astounding, and he was known to have an incredible memory as well. He could memorize the digits of large numbers easily, recite long passages verbatim from books he had read years before, and even solve complicated mathematical equations without lifting a pencil or paper; instead using only his mind to calculate the results in his head while casually chatting with other professors during lunch breaks at university.

As far back as high school von Neumann spent time thinking about pure mathematics; something which most children tend to avoid like the plague due to its dryness. Although it was regarded by many adults of the day as impractical, von Neumann saw educational merit in pure mathematics that was not taught in high school or even college and decided to go down the path of self-directed study.

**Set Theory and Quantum Mechanics**

In his early twenties, von Neumann’s research on set theory and logic began to gain popularity among other mathematicians. This led to an invitation from Italian mathematician Giuseppe Peano, whom he had met through Minkowski when visiting Berlin, for him to come work at the University of Turin as a professor upon finishing his studies. He took this position instead of staying at Göttingen where Rátz had also offered him a professorship and spent six years there developing mathematical logic further through group theory into higher dimensions.

During this time he developed more interest in game theory, particularly in using it to model nuclear proliferation. Von Neumann then went on to write a book titled Theory of Games and Economic Behavior which became so highly respected that it is still included in most undergraduate courses on economics, today. He also contributed to the theory of computation with his seminal work Mathematical Foundations of Quantum Mechanics , published in 1932, which led to further insights into quantum physics; specifically the wave function.

His towering intellect was not limited to just mathematics or science as von Neumann spent time reading literature and philosophy too. In fact, he authored over 100 papers on various subjects throughout his lifetime, from economics to linguistics.

In addition to this astounding intellect, von Neumann had amazing physical attributes which could have undoubtedly contributed greatly to his talent, had he been born in a different era. He was an avid sportsman and excelled at many physically demanding activities; such as tennis, skiing, swimming and even diving with the U.S. Navy’s Underwater Demolition Team where he taught himself to hold his breath for three minutes while searching submerged targets off the coast of Borneo during World War II.

**Manhattan Project**

When it came time to join the Manhattan Project he did not balk at the opportunity; choosing instead to resign from his professorship at Princeton despite having just married Marietta Kovesi (a fellow mathematician), worked on creating nuclear weapons for nearly three years, helped develop the hydrogen bomb under Fermi after two more years, and spent two more consulting with the Atomic Energy Commission when he was finished.

**Personal Life**

John Von Neumann was married to his first wife, Marietta Kovesi for eight years until her death in 1953 when he was 48. He then married Marina Berberova and they remained together until his death in 1957 at the age of 53.

With all of his accomplishments it seems that von Neumann’s life is best summed up not by what he did but rather by what he accomplished . He contributed enormously to mathematics and physics during a time when most other universities were closing their doors to Jews; effectively saving himself from almost certain death as well as many others including Einstein and Fermi who worked with him on the Manhattan Project. His innovations had a tremendous impact on economics, computer science and game theory which are still highly utilized today despite being over 50 years old.

Von Neumann was primarily focused on math throughout his entire life which resulted in him being an extremely singular individual with no close friends except for Kovesi. In fact President Kennedy had to make a private call to get him to attend the first meeting of his Science Advisory Committee.

Not much is known about his family except that he and his mother never got along very well, and when she died he refused to go to her funeral. He was described as a stern looking man with dark eyes and an olive complexion who did everything he could do to be physically fit.

Of any one thing most people can say they are truly proud, but John Von Neumann seemed more proud of the fact that Kovesi was able to teach herself English by reading textbooks than anything else in his life. This mentality seems odd at first until you realize exactly what kind of a mind it takes to be accepted into Princeton’s mathematics program after only 2 years of college and then go on to become one of the most accomplished minds of all time.

**Achievements**

From his earliest days Von Neumann was always extremely precocious, publishing a paper in 1920 at the age of 19 that corrected a previously overlooked error made by German mathematician David Hilbert . He received his Ph.D from the University of Budapest at 20 with an award winning dissertation on sets which he had begun working on before he even arrived there.

His thesis examiner remarked that it would have been more appropriate for him to be awarded two degrees instead; one in mathematics and another in philosophy given that it contained so many philosophical implications. In 1922 he obtained a position as an instructor at the University of Berlin where he taught classes until 1924 when he was appointed ordinarius professor in mathematics at the University of Budapest.

### von Neumann Architecture

Von Neumann Architecture (otherwise known as the von Neumann Model or Princeton architecture) is a computer system that contains the following elements:

- External mass storage
- Memory with data storage
- A control unit
- A processing Unit
- Input and output mechanisms

An example of von Neumann Architecture is shown below:

The idea has morphed and is now used interchangeably with any stored-program computer, and compares favorably to the more complicated Harvard architecture. The Harvard architecture system differs from the von Neumann system in that it has multiple data buses compared to just one in von Neumann’s design.

**Contributions to Mathematics**

Von Neumann is best known for his work in set theory which was primarily motivated by a letter from English mathematician George D. Birkhoff . Von Neumann looked into ways on how to axiomatize statements about equality, proving the completeness theorem , deriving his own system called “The Theory of Types” and writing a lengthy treatise named “Mathematical Foundations of Quantum Mechanics”.

In addition to categories he wrote three other major publications summarizing his research including The General and Logical Theory of Sets , A Survey of Modern Algebra and On Groups and Their Arithmetic which combined constitute over 600 pages worth of material.

He was also heavily influential in the creation of game theory which he co-authored with Oskar Morgenstern . Von Neumann proved that certain non-linear optimization problems were difficult to solve even for simple systems; thus, his work set the stage for the development of linear programming and is still utilized today.

**Contributions to Physics/Mathematical Physics**

Von Neumann made significant contributions to quantum mechanics such as explaining why angular momentum is quantized when it should have been continuous according to general relativity — proving that there are actually two different types of degenerate quantum states, introducing a new state representation now known as “the Pauli spin matrix”, and deriving an equation that would later become very useful in explaining nuclear fission known as the “Fermi-Von Neumann equation”. However Von Neumann was perhaps best known for his work in game theory and economics.

He formulated mathematical models to predict the economic behavior of a system which helped him make millions on Wall Street. This ultimately became the basis of his theory of games which laid out how rational players would play a game when given certain odds and what could be expected from their moves.

In addition Von Neumann devised methods that allowed him to analytically solve systems of nonlinear ordinary differential equations and partial differential equations at least up until 1960 when such techniques were no longer valid due to advances in computers.

**Awards and Recognitions**

Von Neumann was one of the most highly decorated scientists of his time. In 1930 he was awarded the second highest honor in mathematics, the Fields Medal for his work in set theory. He received two Guggenheim Fellowships and an honorary doctorate from Harvard University .

Von Neumann also became a member of the Hungarian Academy of Sciences as well as corresponding member to the Bavarian Academy of Sciences and Humanities , both for being some of Europe’s most prestigious academies at that time.

**Published Works**

Produced a collected three-volume set containing all of his works including On the Theory of Games, The Collected Works of John von Neumann, in addition to another published work entitled “Theory of Self-Reproducing Automata.”

In 1956 von Neumann wrote his (posthumously published) book *The Computer and the Brain*

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