Transcript for:
John von Neumann: A Mathematical Genius

John von Neumann was smarter than the smartest. Hans Bethe, who won the Nobel  Prize in Physics, remarked: “I have sometimes wondered whether a brain like von Neumann’s does not indicate a  species superior to that of man.” He had a profound impact on quantum mechanics, the atomic bomb, the modern computer, game  theory, and self-replicating machines. The basis for all these contributions was  his exceptional understanding of mathematics. Growing up in Budapest, Johnny,  or Jancsi, as he was called, could reportedly multiply two eight-digit  numbers together in his head when he was six! His well-off Jewish parents fostered  an environment for learning. His father, Max, an economic  adviser to the Hungarian government, hosted intellectual dinners that  greatly influenced young Johnny The “von” was added to their surname after the  Austro-Hungarian Emperor elevated Max to nobility. Although times were good,  Max felt they wouldn’t last. As anti-Semitism spread through  Europe in the early 20th century, Max wanted to prepare his three  sons in case they needed to move. So, Johnny studied French, Italian,  English, Ancient Greek, and Latin. But his greatest strength lay in mathematics. Soon after enrolling in an elite prep school, his math teacher Gábor Szego was brought  to tears after their first meeting, as he had never experienced a mind like  Johnny’s. Lutheran school, Fasori Gimnázium But Max didn’t want his son  studying math at university, believing, “Mathematics does not make money.” So a compromise of sorts was struck. Johnny studied chemistry at the  University of Berlin for two years before enrolling at ETH Zurich, where he  earned his chemical engineering degree. At the same time, he completed his PhD in  mathematics at the University of Budapest, where he wrote his thesis on set theory. Set theory is the study of sets, which are  collections of objects, including numbers. They form the fundamental  building blocks of mathematics. Ananyo Bhattacharya, author of the  biography The Man From the Future, uses a great example to explain set theory: Imagine building a tower with Lego bricks. The 1st level has a single brick representing  the empty set, the foundation of all sets. The 2nd level includes the brick from  the 1st level and adds another brick, representing the set containing the empty set. The 3rd level builds on the previous two levels and adds another brick to represent  a new set containing these sets. After completing his formal education,  Johnny headed to Göttingen, Germany, the center of the math world, to study  under the esteemed David Hilbert. At the time, scientists and  mathematicians were trying to understand the strange behavior of particles  at the smallest scales, like electrons. Werner Heisenberg and Erwin  Schrödinger came up with two different ways to describe  how these particles behaved. Heinsenberg’s approach used a grid  with columns and rows representing the different energy states of electrons. Schrödinger described particles  as waves spread through space. Oddly, when these waves are observed, the wave function collapses,  and they behave like particles. It was as if they were talking  about two different things. Scientists like Paul Dirac had tried  to prove that the two were the same, but were not entirely successful. Johnny was. He proved that the two were  mathematically equivalent. Still in his early twenties, he  was already regarded as a legend. He received an offer to lecture  at the University of Berlin, where he enjoyed the cabaret shows  as much as the academic work. His next stint at the University  of Hamburg was also a short stay, as his chances of becoming a  tenured professor were slim. Then came an invitation from America to become a visiting lecturer in mathematical  physics at Princeton University. Oswald Veblen, a math professor at Princeton, wanted to entice Europe’s top talent  with huge salaries, in some cases, offering more than seven times what they  made in Germany. (In the case of Wigner) Germany was the leading scientific nation in the world, while the U.S. was considered  second-rate and wanted to catch up. Before accepting the position at Princeton, he married Mariette Kövesi also from a prosperous  Jewish family, whom he had known since childhood. Upon arriving in America with his wife in  January 1930, Johnny quickly settled in. Though, he did face an unexpected problem  when he tried to get a driver’s license. He failed his driving test so many times  that he had to bribe an examiner to pass him. An intersection at Princeton  University was nicknamed “von Neumannn corner” due to his  frequent accidents there. He’d have to buy a new car every  year after totaling the previous one, though was never seriously injured. He humorously explained his accidents this way: “I was proceeding down the road. The trees  on the right were passing me in orderly fashion at 60 miles an hour. Suddenly one  of them stepped in my path. Boom!” (page 66) Johnny picked a good time to leave Germany  as the Nazi party was growing in popularity. In January 1933, Hitler rose  to power and became Chancellor. Some lost half their staff overnight. German science never recovered. That same year, Johnny joined the recently  formed Institute for Advanced Study, a research institute in Princeton, New Jersey, where the greatest scientific minds, including  Einstein, were free to explore their ideas. He was the youngest recruit at 29 years old  and was often mistaken for a grad student. One of his most significant  contributions around this time was providing mathematical  proof of the ergodic hypothesis. This hypothesis suggests that a system will  eventually explore and visit all the possible states it can occupy. Imagine gas in a box. Over time, the gas particles will spread  out and fill every part of the box. This work was crucial for predicting the  long-term behavior of physical systems. While working away at the IAS, his  mind wandered as he was preoccupied with the looming war back home. He wrote to Hungarian physicist Rudolf Ortvay in 1935, “There will be  a war in Europe in the next decade.” He was also correct when he  predicted that America would enter the war if Great Britain were in trouble. He feared that European Jews  would suffer a genocide similar to the Armenians under the Ottoman Empire. Johnny lobbied for America's involvement, writing to a congressman in September 1941,  “The present war against Hitlerism is not a foreign war, since the principles for which it is  being fought are common to all civilized mankind.” Between his preoccupation with  his work and the inevitable war, Johnny wasn’t an attentive husband or father. His daughter Marina reflected in her memoirs: “Although he genuinely adored my mother, my  father’s first love in life was thinking, a pursuit that occupied most of his waking hours,  and, like many geniuses, he tended to be oblivious to the emotional needs of those around him.” He was surprised when his wife left him. A year after their divorce, he married Klára Dán, or Klari, in 1938, after meeting her  at a casino in Monte Carlo earlier. She was also from a wealthy Jewish Budapest  family and had left her husband for Johnny. They threw wild parties at their home every  week, and Johnny, with his remarkable memory, amassed a vast collection of  jokes to entertain their guests. At the start of the war, Johnny  researched explosives and ballistics, determining how their shape  affected their force and direction. His expertise led him to  something far more catastrophic. In December 1938, German scientists  discovered that uranium could be split. Physicist Enrico Fermi, who had fled  fascist Italy, understood the significance, declaring: “A little bomb like  that and it would all disappear.” Robert Oppenheimer, then at  the University of California, Berkeley, led the secretive American  effort to beat Germany to the bomb. Johnny played a key role in the Manhattan  Project by perfecting the implosion device. He improved the arrangement  of explosives for the “Fat Man” bomb by suggesting wedge-shaped  charges around the plutonium core. When detonated simultaneously, these  charges produced focused jets of energy, compressing the core more rapidly and  uniformly than conventional explosives. The implosion had to be so symmetrical  that it was compared to crushing a beer can without splattering any beer. Achieving this symmetry resulted  in a powerful nuclear explosion. By the time the atomic bomb was fully  developed and tested in July 1945, Germany had already surrendered. The war in Europe was over. But Japan refused to yield. Johnny had no qualms about bombing  Japan as he feared the threat of Stalin’s Soviet Union and wanted  America to send a strong message. He was part of the team that shortlisted  the Japanese cities to drop bombs on. Despite his willingness to use the bomb, he was fully aware of the devastating  power he had helped to create. “What we are creating now is a monster  whose influence is going to change history, provided there is any history left, yet it  would be impossible not to see it through, not only for the military reasons, but it  would also be unethical from the point of view of the scientists not to do what they  know is feasible, no matter what terrible consequences it may have. And this is only the  beginning! The energy source which is now being made available will make scientists the most hated  and also the most wanted citizens of any country.” On August 6, 1945, the U.S. dropped the "Little  Boy” bomb on Hiroshima, killing 78,000 people instantly, with tens of thousands more dying  later from radiation poisoning and burns. Three days later, American forces dropped  the second bomb, "Fat Man," on Nagasaki. It used the implosion mechanism  Johnny had developed, resulting in the deaths of 70,000 people. Japan surrendered unconditionally. Toward the end of the war, engineers  at the University of Pennsylvania began working on a revolutionary  machine known as the ENIAC. Initially designed to calculate artillery  firing tables, ENIAC’s first task was determining whether it was possible to build a  more powerful bomb. Referring to hydrogen bomb John Mauchly and J. Presper Eckert created  the world’s first programmable electronic computer for the U.S. Army's Ballistic Research  Laboratory. Moore School of Electrical Engineering ENIAC, which took up an entire room, could  perform more than 300 multiplications per second, which was thousands of times  faster than its predecessors. Johnny joined the project as a consultant. But he wasn’t satisfied with a machine that could merely calculate. He envisioned computers that could store information and instructions  in their memory, whereas the ENIAC required manual reconfiguration for each new task. Johnny played a key role in developing the ENIAC’s successor, the EDVAC, which introduced  the concept of a stored-program computer. This design allowed data and instructions to be  stored in memory and manipulated by the machine, a foundational concept of  modern computing technology. The dissemination of Johnny’s 1945  report spread these revolutionary ideas. However, Eckert and Mauchly were furious that  the report bearing only John von Neumann’s name had been shared before they could  patent their digital computing device. Mathematician Herman Goldstine distributed  the report to dozens of scientists and engineers to further the development of  high-speed computers, as Johnny intended. Johny explained that “...this was perfectly proper  and in the best interests of the United States.” His ideas from EDVAC guided the design of the  IAS machine at the Institute for Advanced Study. IBM's first commercially successful  electronic computer, the IBM 701, was based on Johny’s stored-program architecture. Leading a bitter Eckert to complain: “He sold  all our ideas through the back door to IBM.” In a landmark verdict on October 19, 1973,  a judge ruled that the basic concepts of the electronic digital computer were in the  public domain and could not be patented. So, one of the most valuable inventions of  the 20th century was declared public property, a significant step towards what would  become the open-source movement. As if his schedule weren’t full enough, Johnny  also developed game theory during the war years, desiring to find neat mathematical  solutions to real-world problems at a tumultuous time in history. He explained to mathematician Jacob Bronowski during a London cab ride that  game theory was different from chess: “Chess is not a game. Chess is a well-defined  form of computation.Real life is not like that. Real life consists of bluffing,  of little tactics of deception, of asking yourself what is the other  man going to think I mean to do. And that is what games are about in my theory.” as  recounted in Bronowski’s “The Ascent of Man” Game theory encompasses various models, each  addressing different decision-making scenarios. A classic example related to fair  division is the cake-cutting problem. If two people share a cake, what’s the  best way to ensure it’s divided fairly? One person cuts it, and the  other chooses the first piece, ensuring a fair division since the cutter  will aim to make both pieces equal. Another example is the zero-sum  game known as “matching pennies.” In this game, each player has a penny and  must secretly turn it to heads or tails, then reveal their choices simultaneously. If the pennies match, one player  wins and keeps both pennies. If they don't match, the other player wins. This game illustrates that one player’s gain is exactly the other’s loss,  making it a zero-sum game. Johnny viewed the Cold War between the U.S. and  the U.S.S.R. as two players in a zero-sum game. He supported the development of the hydrogen bomb, which was exponentially more  powerful than the atomic bomb. Initially, he was a proponent of “preventive war”  and recommended the U.S. launch a nuclear strike at Moscow, knowing it was only a matter of time  before the Soviet Union became a nuclear power. Confident that the Russian spy network had  obtained details of the atomic bomb design, he was convinced that war with  the Soviet Union was inevitable. He recognized the urgency of the situation and  remarked: “If you say why not bomb them tomorrow, I say why not today? If you say today at  5 o'clock, I say why not one o'clock?” However, he abandoned his idea of a pre-emptive  strike once the Soviet Union had enough bombs to retaliate, leading to the doctrine  of mutually assured destruction (MAD). Deterrence is the art of producing in  the mind of the enemy the fear to attack. He is said to have inspired the character  Dr. Strangelove in Stanley Kubrick’s film, “How I Learned to Stop  Worrying and Love the Bomb”. He used game theory to model  the Cold War interaction, helping military strategists consider when they  should and should not push the nuclear button. Ironically, Johnny defended Oppenheimer during  secret hearings to determine whether he posed a security risk due to his close ties  to those with Communist affiliations. Meanwhile, Johnny had pushed for a pre-emptive  strike against the Communist Soviet Union. While Johnny’s mind was racing,  his health was breaking down. Bone cancer metastasized through his body. It’s been suggested that the disease resulted  from his radiation exposure when he witnessed the hydrogen bomb tests conducted in  the Marshall Islands. Bikini Atoll Although Johnny believed that mathematicians  typically did their best work by the age of 26, he produced some of his most unique  contributions after his health declined. In his later years, he became fascinated by  the concept of self-replicating machines. He theorized about machines  that could reproduce themselves, with information copied and passed to  offspring separately from the machine itself – a vision that anticipated the  discovery of DNA's structure in 1953. His theories have profoundly  influenced artificial intelligence, inspiring the development of systems that  self-improve through training on data, as seen in machine learning  algorithms and neural networks. John von Neumann’s ideas were far ahead of  his time, but sadly, his life was cut short. He passed away on February  8, 1957, at the age of 53. Despite being agnostic all his life, on  his deathbed, he converted to Catholicism. In a 1950s article for Fortune magazine,  Johnny questioned the future of technology, recognizing its potential for good and evil. He wrote, "The problems of the future of humanity cannot be resolved by a single prescription,  but only in reliance on day-to-day opportunistic measures, and reliance on the human qualities  required: patience, flexibility, intelligence.” Despite his many contributions to math  and science, John von Neumann was acutely aware of the gaps in education that  could hinder future advancements. He once addressed a young man's question  about whether America was educating enough people to operate advanced machines. Is there enough people to do it? I’m glad that you’re asking this question  because it’s really a very good one. No, we don’t take enough people, and we better do  something about it. And I hesitate to say that we better do something about it quickly, but  rather, we’d better do something about it both quickly and then continuously. In other words,  we need more training in science on all levels, in college, in the high schools, and  more training of high school teachers. Well, one great way to learn STEM and  bridge this gap is through Brilliant. Brilliant is an amazing platform  for brushing up on your math skills, starting at your level and helping you  advance—and it’s FREE for you to try out. Each lesson is filled with hands-on  problem-solving that lets you play with concepts— which is way more  effective than watching lecture videos. Brilliant recently launched a ton of new  interactive content in AI and programming. Their “How LLMs Work” course gives you hands-on  experience with language models and helps you understand how they generate text that's  nearly indistinguishable from human writing. Brilliant’s “Programming with Python” is perfect  for building a strong foundation in programming. You’ll start writing your own programs on day  one, using their built-in drag-and-drop editor. There’s something for everyone no  matter your area of interest in STEM. Brilliant is FREE for you to try out for 30 days. Just scan my custom QR code on your screen or click my custom link in the video  description: brilliant.org/newsthink If you sign up with my code or link, you’ll  receive a 20% discount on Brilliant’s annual Premium subscription, which gives you access  to all of their interactive offerings. Thanks for watching. For Newsthink, I’m Cindy Pom.