A (very) Brief History of John von Neumann

[Music] john von neumann was a 20th century hungarian-american mathematician and physicist he is considered to be the last representative of the great mathematicians integrating both the pure and applied sciences von neumann contributed remarkable work to many fields which included the foundations of mathematics functional analysis topology and statistics quantum mechanics hydrodynamics and nuclear physics contributing heavily to the creation of the first atomic bomb by the manhattan product in world war ii as well as on the hydrogen bomb after game theory self-replicating machines and stochastic computing he published over 150 papers with about 120 being in mathematics 20 being in physics and the remainder being on a mixture of non-mathematics and special mathematical subjects [Music] von neumann was born on december 28 1903 in budapest hungary which at that time was a part of the austro-hungarian empire he was given the name neuman janos laos and was born to a wealthy acculturated non-observant jewish family he also had two younger brothers michael and nicholas his father was neumann miksha a banker who held the doctorate in law and had moved to budapest from paige in the late 1880s his mother was margaret khan who came from a wealthy family living in large apartments above the khan heller offices von neumann's family actually lived on the top floor of this building in an 18 room space both his parents were highly intellectual so it's no surprise that they had a massive private library in this apartment on february 20th 1913 miksha paid a small fee to acquire a title of nobility for his family name being able to do so only because of his service to the austro-hungarian empire miksha ended up not changing his name but of course von neumann decided to at first he was margietai neuemanyanos but later decided to use the german name we know today john von neumann in 1911 von neumann entered the fashori evangelicos gymnasium the school was considered to be one of the best in budapest being part of a very rich school system that churned out pioneers of the 20th century known as the martians which included leo silard a hungarian german-american physicist notable for conceiving of nuclear chain reaction in 1933 paul erdosh a hungarian mathematician who is considered one of the most prolific mathematicians of the 20th century focusing heavily on previously open problems paul holmosh a hungarian-american mathematician notable for making fundamental advances in many areas of mathematics including logic and probability theory and eugene vigner a 20th century theoretical physicist notable for receiving a nobel prize for his contributions to the theory of atomic nucleus and the elementary particles wigner attended the same school as von neumann and was one year ahead they soon became friends and would remain so for the rest of von neumann's life at age 15 von neumann's father hired mathematician gabor segu notable for making fundamental contributions to the theory of orthogonal polynomials to teach von neumann advanced calculus segu was apparently brought to tears with how talented von neumann was as any problem segu proposed was apparently solved immediately in 1921 at age 19 von neumann published two major papers the second one being most notable as it provided the definition we used today for ordinal numbers the same year he graduated from the gymnasium receiving the utv prize a national prize in mathematics due to the fears his father had about the financial limitations of mathematics von neumann was being pushed towards industry thereby would have been investing his time in more financially useful endeavors in his father's eyes mathematician theodore von carmen notable for his contributions to aeronautics was asked to persuade von neumann not to take a mathematics as a major it was decided chemical engineering could be lucrative but seeing as von neumann had no knowledge in chemistry it was arranged for him to take a two-year non-degree course in the subject at the university of berlin before ultimately sitting for and passing the entrance exam at eth zurich in september 1923 it must be noted that von neumann was also studying mathematics at the university of budapest alongside his studies at the university of berlin though he never attended lectures which proved to be no problem as he passed all of his exams with flying colors the same year he began attending school in zurich von neumann had simultaneously entered pasman peter university in budapest to pursue his phd in mathematics it should come as no surprise then that he actively sought out mathematics in zurich interacting with people such as hermann weil a mathematician and physicist notable for his contributions to number theory and george poglia a mathematician notable for making fundamental contributions to combinatorics and probability theory polio was immensely impressed with von neumann apparently saying johnny was the only student i was ever afraid of if in the course of a lecture i stayed in an unsolved problem the chances were he'd come to me at the end of the lecture with the complete solution scribbled on a slip of paper [Music] but neumann presented his phd thesis in 1925. the topic being on the axiomatization of cantor's set theory and he received his degree in chemical engineering from zurich in 1926. after graduating he then went off to the university of guernigan to study under david hilbert perra grant provided by the rockefeller foundation at the end of 1927 von neumann had published 12 major mathematics papers and at the end of 1929 he'd published 32 he'd also begun lecturing at the university of berlin in 1928 under the title of private dotsent which granted him permission to teach subjects at the highest possible level and he was the youngest the university had ever elected to that title in their history the following year in 1929 von neumann ended up at the university of hamburg as a private docent as the prospects of being a tenured professor were higher this was very brief as he was offered a position at princeton that october so he ended up moving to america but he still held academic posts in germany until 1933. while lecturing at princeton from 1930 to 1933 it was expressed that his students had a difficult time following his mathematical explanations largely because he was a speed demon but apparently he was crystal clear when teaching physics going a bit deeper into his contributions over the next few years will first take a step back and discuss his phd thesis the 1925 paper demonstrated two techniques to exclude sets that are sets of themselves the first is the axiom of regularity which states that every non-empty set a contains an element that is disjoined from a and the second is the notion of class a class being a collection of sets that can be unambiguously defined by a property that all its members share the arguments made with these techniques patched up contradictions that arose in earlier set theoretic systems like russell's paradox which is stated as follows let a set r be defined as x such that x does not belong to itself then we have that r belongs to itself if and only if r does not belong to itself in 1928 von neumann basically kicked off game theory with his proof of the mini max theorem which in game theoretic terms established that in zero-sum games with perfect information there exists a pair of strategies for both players that allows each to minimize his maximum losses he showed many maxes are equal in absolute value and contrary by sign later on von neumann expanded upon the theorem to also account for games lacking perfect information and to account for games with greater than two players this expansion can be found in the 1944 work theory of games and economic behavior authored by both von neumann and oscar morgenstern a 20th century economist notable for co-founding game theory with von neumann in this work it is declared that economic theory needed to use functional analysis rather than traditional differential calculus emphasizing heavy use of methods found in differential topology in 1932 von neumann made foundational contributions to ergotic theory which is the study of invariant measures in dynamical systems an invariant measure being a measure that is preserved by some function hal mosh wrote that if von neumann's only contributions to mathematics have been these series of papers that would have been plenty to provide mathematical immortality [Music] the same year von neumann published mathematical foundations of quantum mechanics it was the first work to establish a rigorous mathematical framework for quantum which are coined the darak von neumann axioms he began work on this axiomatization after his phd thesis realizing in 1926 the state of quantum mechanics could be represented by a point in a complex hilbert space that generally could be infinite dimensional even for a single particle in von neumann's formalization of quantum observable quantities such as position or momentum are represented as linear operators acting on the hilbert space associated with the quantum system thus the physics of quantum mechanics was reduced to the mathematics of hilbert spaces and linear operators acting upon them a prime example of this is the uncertainty principle which is the principle according to which the determination of the position of a particle prevents the determination of its momentum and vice versa von neumann's formalization translated this into non-communicativity of the two corresponding operators this abstract treatment permitted him to also confront the foundational issue of determinism versus non-determinism presenting a proof that the statistical results of quantum could not possibly be averages underlying a set of determined hidden variables contrary to classical statistical mechanics this proof launched a line of research that ultimately led to the demonstration that quantum mechanics either requires the notion of reality in a substantially different way from that of classical physics or must include non-locality and an apparent violation of special relativity non-locality being the phenomenon by which the measurement statistics of a multipartite quantum system do not admit an interpretation in terms of a local realistic theory aside from his contributions to mathematics and physics von neumann was one of the founding figures of computing when alan touring visited princeton in the 1930s him and von neumann worked on the philosophy of artificial intelligence together in 1945 von neumann wrote a 23-page sorting program for the electronic discrete variable automatic computer in inc which is referred to as the merge sort algorithm where the first and second halves of an array are each sorted recursively and then merged [Music] when neumann made strides in simulation theory developing simulations on his digital computers for hydrodynamic computations when working on the hydrogen bomb he ended up contributing heavily to the development of the monte carlo method allowing for solutions of complicated problems to be approximated using random numbers due to the issue of producing a set of random numbers being too computationally intensive von neumann created one of the earlier methods of pseudorandom number generation by the middle square method it was criticized as crude which von neumann already knew but he justified it as being faster than any other available method noting that any problems that arise in generation are clearly visible contrary to other methods von neumann is considered to be the father of computer virology he used mathematical analysis for the structure of self-replication preceding the discovery of dna structure creating the field of cellular automata using a pencil and graph paper to construct the first self-replicating automata in 1949 this design was used for a self-reproducing computer program and is considered the world's first computer virus in 1953 von neumann published a paper that introduced the world to stochastic computing a collection of techniques that represent continuous values by streams of random bits reducing complex computations to simple bitwise operations of streams though revolutionary none of its techniques could be implemented at the time due to the limited computing power it wouldn't be until the 1960s well after his death that computing would advance enough [Music] working on the meteorological program a project funded by the u.s navy in 1946 von neumann wrote the world's first climate modeling software this was used to perform the world's first numerical weather forecasts and the results were published in his 1950 work titled numerical integration of the barotropic vorticity equation his research in weather systems and meteorological prediction led him to propose manipulating the environment by spreading coolants on the polar ice caps to enhance solar radiation basically inducing global warming he proposed a theory of global warming as a result of human activity noting earth was six fahrenheit colder during the last glacial period and in 1955 he wrote that carbon dioxide released into the atmosphere by industries burning of coal and oil more than half of it during the last generation may have changed the atmosphere's composition sufficiently to account for a general warming of the world by about one degree fahrenheit he urged caution in any program of intentional human weather manufacturing emphasizing it could be done but questioned whether it should be done [Music] during the 1930s von neumann had developed an expertise in explosions which were notoriously difficult to model mathematically he was a leading authority at the time of the mathematics of shaped charges landing him many military consultancies primarily with the navy ultimately this led him to the manhattan project the program beginning in the late 1930s that produced the world's first nuclear weapons his role was pivotal as he actually made the most important contribution of the bomb that was eventually dropped on nagasaki coined fat man he came up with the concept and design of explosive lenses needed to compress the plutonium core of the bomb working on the manhattan project von neumann had to take frequent trips by train to secret research facilities at the los alamos laboratory in a remote part of new mexico on a visit in september 1944 von neumann showed that the pressure increase from an explosion shock wave reflection from solid objects was greater than previously believed if the angle of incidence of the wave is between 90 degrees and some limiting angle thus the effectiveness of an atom bomb is greatly increased with detonation some kilometers above the designated target rather than at ground level because of how significant von neumann's contributions were him and a few other scientists were chosen as members of a target selection committee with various military personnel the mission being to choose which japanese cities to have as the first targets of the atom bomb von neumann oversaw the computations related to expected size of the bomb blasts estimation of death tolls and the optimal distance above the ground at which bombs should be detonated on july 16 1945 von neumann was one of the eyewitnesses of the first ever test of an atom bomb detonation codenamed trinity the testing site was about 35 miles south east of socorro new mexico less than a month later on august 9th is when fat man was dropped on nagasaki after the war ended von neumann continued his work without issue working with klaus fuchs on further development of the hydrogen bomb project him and fuchs filed a secret patent in 1946 titled improvement in methods and means for utilizing nuclear energy outlining the scheme for using a fission bomb to compress fusion fuel to initiate nuclear fission fuchs ended up passing on this work to the soviets as part of his nuclear espionage though it ended up not being used by the soviets as it didn't seem to be understood that well until after the creation of the hydrogen bomb by the teller ulam design for his contributions during wartime services in 1946 von neumann was awarded both the medal for merit and the navy distinguished civilian service award [Music] as is quite well known the cold war began about two years after world war ii ended von neumann is credited with developing the equilibrium strategy of mutually assured destruction to ensure the war stayed cold mutually sure destruction entailed that if one side attacked the other side would attack and both sides would be destroyed von neumann's goal was to quickly develop intercontinental ballistic missiles as well as compact hydrogen bombs that they could deliver to the ussr he knew the soviets were doing similar work as the cia gathered intel from german rocket scientists who were allowed to return to germany being afraid of a missile gap von neumann made sure the us and allies were quite a few steps ahead of the soviets there was initial speculation over his concerns about the soviets but they were quickly dismissed due to the sputnik crisis which was mass hysteria of a perceived technological gap between the us and russia kicking off when the soviets launched the world's first artificial satellite sputnik won considering all the work von neumann did with the military he clearly had strong political views he ended government work primarily because he felt that the only way for freedom and civilization to survive was having the united states triumph over totalitarian nazism fascism and soviet communism he described his ideology as violently anti-communist and much more militaristic than the norm and he is quoted as saying if you say why not bomb the soviets tomorrow i say why not today if you say today at five o'clock i say why not one o'clock [Music] in 1937 von neumann became a naturalized citizen of the u.s he immediately tried to become a lieutenant in the us army's reserve corps but was ultimately rejected because of his age despite stellar exam scores by 1939 much of von neumann's immediate family had moved to the us as well it was at this point that von neumann began using the first name john instead of janus but still kept vaughn when neumann married marietta kuveshi on january 1st 1930 a woman who he'd met at the university of budapest while she studied economics they had a daughter together in 1935 named marina who is now a distinguished professor of business administration and public policy at the university of michigan alas the marriage between von neumann and marietta was short-lived they divorced in 1937. von neumann remarried fast marrying clara dawn in 1938 a woman who he'd met during one of his last trips back to budapest prior to the outbreak of world war ii him and clara were very social in the local academic community which was especially helped by them throwing many huge parties at their princeton home parties which were claimed to be famous and long von neumann seemed to do his best work when it was wildly noisy when he would work at home he preferred to work in the living room while his wife watched very loud television never using a quiet study that clara had prepared for him when he worked in his princeton office he would often blast loud german march music on his gramophone receiving many complaints from those in offices neighboring his including that of albert einstein [Music] despite how intelligent von neumann was he was quite reckless with his driving to give an extreme example he loved to read while at the wheel he was arrested a handful of times and had a few accidents cuthbert heard the man who hired von neumann as a consultant for ibm discreetly paid off many of his fines for the majority of his life von neumann was agnostic despite being baptized as catholic in 1930 after his father died the year prior one could argue he was agnostic and know that he died but it appears he tried to dig into catholic faith a bit once he had to truly process his own mortality he had a consultation with a catholic priest named father anselm street mata which didn't seem to actually help him process but when neumann is stated as saying so long as there is the possibility of eternal damnation for non-believers it is more logical to be a believer at the end he apparently said to his mother too that there probably has to be a god many things are easier to explain if there is than if there isn't in 1955 von neumann was diagnosed with cancer the cancer being either bone pancreatic or prostate the realization of his own death and so soon greatly affected him instilling great fear a breakdown of his reaction to his own mortality is quoted as follows from legendi and centivani's book life and work of john von neumann his mind the amulet on which he had always been able to rely was becoming less dependable then came complete psychological breakdown panic screams of uncontrollable terror every night his friend edward teller said i think that von neumann suffered more when his mind would no longer function than i have ever seen any human being suffer but neumann's sense of invulnerability or simply the desire to live was struggling with unalterable facts he seemed to have a great fear of death until the last no achievements and no amount of influence could save him now as they always had in the past johnny von neumann who knew how to live so fully did not know how to die [Music] despite any mental decline from the cancer his mind was still surprisingly powerful on his deathbed with a prime example being him reciting a few lines of each page from memory of gold's faust to his brother for entertainment von neumann died on february 8 1957 at the age of 53 at walter reed army medical center in washington dc under military security in the off chance that he revealed any military secrets while heavily medicated his burial took place at the princeton cemetery in princeton mercer county new jersey well there you have it a glimpse into the life of john von neumann i end on a quote from miklos radai it seems fair to say that if the influence of a scientist is interpreted broadly enough to include impact on fields beyond science proper then john von neumann was probably the most influential mathematician who has ever lived i hope you guys enjoyed and i'll catch you next time [Music] you

Channel: moderndaymath

Views: 51,027

Keywords: john von neumann, von neumann, neumann, atomic bomb, atom bomb, nuclear, quantum mechanics, quantum, cantor, dirac, erdos, polya, soviet, soviets, mutually assured destruction, ww2, wwII, world war, axioms, axiomatization, einstein, wigner, klara dan, cathburt herd, mortality, ergodic, game theory, hydrogen bomb, ballistic missiles, manhattan project, weather forecasting, global warming, computer virus, stochastic, turing

Id: QhBvuW-kCbM

Length: 25min 44sec (1544 seconds)

Published: Mon Jun 29 2020