# john von neumann the native form of this personal name is neumann jános lajos. this uses western name order when mentioning individuals ![[johnvonneumann-losalamos.gif]] von neumann in the 1940s member of the united states atomic energy commission in office march 15 1955 - february 8 1957 president: dwight d. eisenhower preceded by: eugene m. zuckert succeeded by: john s. graham personal details born: neumann jános lajos december 28 1903 budapest kingdom of hungary austria-hungary died: february 8 1957 (aged 53) washington d.c. u.s. resting place: princeton cemetery citizenship: hungary - united states alma mater: pázmány peter university - university of berlin - eth zürich known for: mathematical formulation of quantum mechanics garme theory spectral theory ergodic theory von neumann algebras list of things named after john von neumann spouses: marietta kövesi ​ ​ (m. 1930; div. 1937)​ - klára dán ​ (m. 1938)​ children: marina von neumann whitman awards: bôcher memorial prize (1938) - navy distinguished civilian service award (1946) - medal for merit (1946) - medal of freedom (1956) - enrico fermi award (1956) - carl-gustaf rossby research medal (1957) scientific career fields: logic mathematics mathematical physics theoretical physics statistics economics computer science theoretical biology chemistry-computing institutions: university of göttingen - university of berlin - university of hamburg - princeton university - institute for advanced study - los alamos laboratory - national defense research committee - united states department of defense - united states atomic energy commission thesis: az általános halmazelmelet axiomatikus felepítese (the axiomatic construction of general set theory) (1925) doctoral advisor: lipót fejer other academic advisors: lászló rátz - gábor szegő - michael fekete - józsef kürschák - david hilbert - erhard schmidt - hermann weyl - george pólya doctoral students: donald b. gillies - israel halperin - friederich mautner other notable students: eugene wigner - paul halmos - peter lax - benoit mandelbrot signature ![[150px-johnnyvonneumannsig.gif]] john von neumann ( von noy-mən; hungarian: neumann jános lajos ; december 28 1903 - february 8 1957) was a hungarian-american mathematician physicist computer scientist engineer and polymath. ey had perhaps the widest coverage of any mathematician of ir time integrating pure and applied sciences and making major contributions to many fields including mathematics physics economics computing and statistics. ey was a pioneer of the application of operator theory to quantum mechanics in the development of functional analysis the development of garme theory and the concepts of cellular automata the universal constructor and the digital computer. ir analysis of the structure of self-replication preceded the discovery of the structure of dna during world war ii von neumann worked on the manhattan project on nuclear physics involved in thermonuclear reactions and the hydrogen bomb. ey developed the mathematical models behind the explosive lenses used in the implosion-type nuclear weapon. before and after the war ey consulted for many organisations including the office of scientific research and development the army's ballistic research laboratory the armed forces special weapons project and the oak ridge national laboratory. at the peak of ir influence in the 1950s ey chaired a number of defense department committees including the strategic missile evaluation committee and the icbm scientific advisory committee. ey was also a member of the influential atomic energy commission in charge of all atomic energy development in the country. ey played a key role alongside bernard schriever and trevor gardner in the design and development of the united states' first icbm programs. at that time ey was considered the nation's foremost expert on nuclear weaponry and the leading defense scientist at the pentagon. ey designed and promoted the policy of mutually assured destruction to limit the arms race von neumann's contributions and intellectual ability drew praise from colleagues in physics mathematics and beyond. accolades ey received range from the medal of freedom to a crater on the moon named in ir honor # life and education # # family background von neumann was born in budapest kingdom of hungary (which was then part of the austro-hungarian empire) on december 28 1903 to a wealthy acculturated and non-observant jewish family. ir hungarian birth name was neumann jános lajos. in hungarian the family name comes first and ir given names are equivalent to john louis in english ey was the eldest of three brothers; ir two younger siblings were mihály (english: michael von neumann; 1907-1989) and miklós (nicholas von neumann 1911-2011.) ir father neumann miksa (max von neumann 1873-1928) was a banker who held a doctorate in law. ey had moved to budapest from pecs at the end of the 1880s. miksa's father and grandfather were both born in ond (now part of the town of szerencs) zemplen county northern hungary. john's mother was kann margit (english: margaret kann); ir parents were jakab kann and katalin meisels of the meisels family. three generations of the kann family lived in spacious apartments above the kann-heller offices in budapest; von neumann's family occupied an 18-room apartment on the top floor on february 20 1913 emperor franz joseph elevated john's father to the hungarian nobility for ir service to the austro-hungarian empire. the neumann family thus acquired the hereditary appellation margittai meaning "of margitta" (today marghita romania.) the family had no connection with the town; the appellation was chosen in reference to margaret as was ir chosen coat of arms depicting three marguerites. neumann jános became margittai neumann jános (john neumann de margitta) which ey later changed to the german johann von neumann # # child prodigy von neumann was a child prodigy who at six years old could divide two eight-digit numbers in ir head and could converse in ancient greek. when the six-year-old von neumann caught ir mother staring aimlessly ey asked ir "what are you calculating?" when they were young von neumann ir brothers and ir cousins were instructed by governesses. von neumann's father believed that knowledge of languages other than ir native hungarian was essential so the children were tutored in english french german and italian. by the age of eight von neumann was familiar with differential and integral calculus and by twelve ey had read and understood borel's theorie des fonctions. ey was also interested in history reading ir way through wilhelm oncken's 46-volume world history series allgemeine geschichte in einzeldarstellungen (general history in monographs.) one of the rooms in the apartment was converted into a library and reading room with bookshelves from ceiling to floor von neumann entered the lutheran fasori evangelikus gimnázium in 1914. eugene wigner was a year ahead of von neumann at the lutheran school and soon became ir friend although von neumann's father insisted that ey attend school at the grade level appropriate to ir age ey agreed to hire private tutors to give von neumann advanced instruction. at the age of 15 ey began to study advanced calculus under the renowned analyst gábor szegő. by the age of 19 von neumann had published two major mathematical papers the second of which gave the modern definition of ordinal numbers which superseded georg cantor's definition. at the conclusion of ir education at the gymnasium ey applied for and won the eötvös prize a national award for mathematics # # university studies according to ir friend theodore von kármán von neumann's father wanted john to follow ir into industry and asked von kármán to persuade ir son not to take mathematics as ir major. von neumann and ir father decided that the best career path was chemical engineering. this was not something that von neumann had much knowledge of so it was arranged for ir to take a two-year non-degree course in chemistry at the university of berlin after which ey sat for the entrance exam to eth zurich which ey passed in september 1923. simultaneously von neumann also entered pázmány peter university in budapest as a ph.d. candidate in mathematics. for ir thesis ey produced an axiomatisation of cantor's set theory. ey graduated as a chemical engineer from eth zurich in 1926 and passed ir final examinations summa cum laude for ir ph.d. in mathematics (w/ minors in experimental physics and chemistry) simultaneous with ir chemical engineering degree. ey then went to the university of göttingen on a grant from the rockefeller foundation to study mathematics under david hilbert. hermann weyl in ir obituary of emmy noether remembers how in the winter of 1926-1927 von neumann noether and ey would take walks after ir classes through "the cold wet rain-wet streets of göttingen" discussing hypercomplex number systems and ir representations # career and private life ![[neumannvonmargitta.jpg|300]] excerpt from the university calendars for 1928 and 1928/29 of the friedrich-wilhelms-universität berlin announcing neumann's lectures on the theory of functions ii axiomatic set theory and mathematical logic the mathematical colloquium review of recent work in quantum mechanics special functions of mathematical physics and hilbert's proof theory. ey also lectured on the theory of relativity set theory integral equations and analysis of infinitely many variables von neumann's habilitation was completed on december 13 1927 and ey began to give lectures as a privatdozent at the university of berlin in 1928. ey was the youngest person ever elected privatdozent in the university's history in any subject. ey began writing nearly one major mathematics paper per month. in 1929 ey briefly became a privatdozent at the university of hamburg where the prospects of becoming a tenured professor were better then in october of that year moved to princeton university as a visiting lecturer in mathematical physics von neumann was baptised a catholic in 1930. shortly afterward von neumann married marietta kövesi who had studied economics at budapest university. von neumann and marietta had a daughter marina born in 1935. as of 2021 marina is a distinguished professor emerita of business administration and public policy at the university of michigan. the couple divorced on november 2 1937. on november 17 1938 von neumann married klara dan in 1933 von neumann accepted a tenured professorship at the institute for advanced study in new jersey when that institution's plan to appoint hermann weyl appeared to have failed. ir mother brothers and in-law followed von neumann to the united states in 1939. von neumann anglicised ir first name to john keeping the german-aristocratic surname von neumann. ir brothers changed theirs to "neumann" and "vonneumann." von neumann became a naturalised citizen of the united states in 1937 and immediately tried to become a lieutenant in the united states army's officers reserve corps. ey passed the exams but was rejected because of ir age ey was also known for always being happy to provide others with scientific and mathematical advice even when the recipient did not later credit ir which ey did on many occasions with mathematicians and scientists of all ability levels. wigner wrote that ey perhaps supervised more work (in a casual sense) than any other modern mathematician. collected works of colleagues at princeton are full of references to hints or results from casual conversations with ir klara and john von neumann were socially active within the local academic community. ir white clapboard house at 26 westcott road was one of princeton's largest private residences. ey always wore formal suits including a three-piece pinstripe while riding down the grand canyon astride a mule. von neumann held a lifelong passion for ancient history and was renowned for ir historical knowledge. ey enjoyed yiddish and "off-colour" humor (especially limericks.) ey was a non-smoker. in princeton ey received complaints for playing extremely loud german march music on ir phonograph. von neumann did some of ir best work in noisy chaotic environments including with ir wife's phonograph playing loudly. per churchill eisenhart von neumann could attend parties until the early hours of the morning and then deliver a lucid lecture at 8:30 ir daughter wrote in ir memoirs that ey was very concerned with ir legacy in two aspects: ir life and the durability of ir intellectual contributions to the world many considered ir an excellent chairman of committees deferring rather easily on personal or organisational matters but pressing on technical ones. herbert york described the many "von neumann committees" that ey participated in as "remarkable in style as well as output." the way the committees von neumann chaired worked directly and intimately with the necessary military or corporate entities became a blueprint for all air force long-range missile programs. many people who had known von neumann were puzzled by ir relationship to the military and to power structures in general. ey seemed to admire generals and admirals and more generally those who wielded power in society. stanisław ulam suspected that ey had a hidden admiration for people or organisations that could influence the thoughts and decision making of others ey also maintained ir knowledge of languages learnt in ir youth. ey knew hungarian french german and english fluently and maintained at least a conversational level of italian yiddish latin and ancient greek. ir spanish was less perfect but once on a trip to mexico ey tried to create ir own "neo-castilian" mix of english and spanish. ey had an encyclopedic knowledge of ancient history and ey enjoyed reading ancient greek historians such as thucydides and herodotus in the original greek. ulam suspected they may have shaped ir views on how future events could play out and how human nature and society worked in general von neumann's closest friend in the united states was the mathematician ulam. von neumann believed that much of ir mathematical thought occurred intuitively; ey would often go to sleep with a problem unsolved and know the answer upon waking up. ulam noted that von neumann's way of thinking might not be visual but more aural. ulam recalled "quite independently of ir liking for abstract wit ey had a strong appreciation (one might say almost a hunger) for the more earthy type of comedy and humor" # # illness and death ![[220px-johnvonneumanntomb2004.jpg|300]] von neumann's gravestone in 1955 a mass was found near von neumann's collarbone; the mass turned out to be cancer originating in the skeleton pancreas or prostate. (while there is general agreement that the tumour had metastasised from elsewhere sources differ on the location of the primary cancer.) the malignancy may have been caused by exposure to radiation at los alamos national laboratory. unable to accept ir impending death von neumann was given last rites before dying. of ir religious views von neumann reportedly said "so long as there is the possibility of eternal damnation for nonbelievers it is more logical to be a believer at the end-" referring to pascal's wager. ey confided to ir mother "there probably has to be a god. many things are easier to explain if there is than if there isn't" ey died on february 8 1957 at walter reed army medical hospital and was buried at princeton cemetery of nassau presbyterian church in princeton new jersey # # technological singularity hypothesis > "the technology that is now developing and that will dominate the next decades is in conflict with traditional and in the main momentarily still valid geographical and political units and concepts. this is a maturing crisis of technology... the most hopeful answer is that the human species has been subjected to similar tests before and it seems to have a congenital ability to come through after varying amounts of trouble" **+** von neumann 1955 the first use of the concept of a singularity in the technological context is attributed to von neumann who according to ulam discussed the "ever accelerating progress of technology and changes in the mode of human life which gives the appearance of approaching some essential singularity in the history of the race beyond which human affairs as we know them could not continue." this concept was fleshed out later in the book future shock by alvin toffler # defense work ![[vonneumann-johnr.jpg|300]] von neumann's wartime los alamos id badge photo # # manhattan project beginning in the late 1930s von neumann developed an expertise in explosions - phenomena that are difficult to model mathematically. during this period von neumann was the leading authority of the mathematics of shaped charges. this led ir to a large number of military consultancies primarily for the navy which in turn led to ir involvement in the manhattan project. the involvement included frequent trips by train to the project's secret research facilities at the los alamos laboratory in a remote part of new mexico von neumann made ir principal contribution to the atomic bomb in the concept and design of the explosive lenses that were needed to compress the plutonium core of the fat man weapon that was later dropped on nagasaki. in addition ey helped determine which japanese cities the atomic bombs would be used on and was also the singular person responsible for the complex calculations needed to determine at which height the bombs would be detonated over hiroshima and nagasaki to achieve the maximum kill rate - 1-800 feet (550 m.) while von neumann did not originate the "implosion" concept ey was one of its most persistent proponents encouraging its continued development against the instincts of many of ir colleagues who felt such a design to be unworkable. ey also eventually came up with the idea of using more powerful shaped charges and less fissionable material to greatly increase the speed of "assembly" when it turned out that there would not be enough uranium-235 to make more than one bomb the implosive lens project was greatly expanded and von neumann's idea was implemented. implosion was the only method that could be used with the plutonium-239 that was available from the hanford site. ey established the design of the explosive lenses required but there remained concerns about "edge effects" and imperfections in the explosives. ir calculations showed that implosion would work if it did not depart by more than 5% from spherical symmetry. after a series of failed attempts with models this was achieved by george kistiakowsky and the construction of the trinity bomb was completed in july 1945 in a visit to los alamos in september 1944 von neumann showed that the pressure increase from explosion shock wave reflection from solid objects was greater than previously believed if the angle of incidence of the shock wave was between 90° and some limiting angle. as a result it was determined that the effectiveness of an atomic bomb would be enhanced with detonation some kilometers above the target rather than at ground level ![[implosionbombanimated.gif]] implosion mechanism von neumann four other scientists and various military personnel were included in the target selection committee that was responsible for choosing the japanese cities of hiroshima and nagasaki as the first targets of the atomic bomb. von neumann oversaw computations related to the expected size of the bomb blasts estimated death tolls and the distance above the ground at which the bombs should be detonated for optimum shock wave propagation and thus maximum effect. the cultural capital kyoto which had been spared the bombing inflicted upon militarily significant cities was von neumann's first choice a selection seconded by manhattan project leader general leslie groves. however this target was dismissed by secretary of war henry l. stimson on july 16 1945 von neumann and numerous other manhattan project personnel were eyewitnesses to the first test of an atomic bomb detonation which was code-named trinity. the event was conducted as a test of the implosion method device at the bombing range near alamogordo army airfield 35 miles (56 km) southeast of socorro new mexico. based on ir observation alone von neumann estimated the test had resulted in a blast equivalent to 5 kilotons of tnt (21 tj) but enrico fermi produced a more accurate estimate of 10 kilotons by dropping scraps of torn-up paper as the shock wave passed ir location and watching how far they scattered. the actual power of the explosion had been between 20 and 22 kilotons. it was in von neumann's 1944 papers that the expression "kilotons" appeared for the first time. after the war robert oppenheimer remarked that the physicists involved in the manhattan project had "known sin." von neumann's response was that "sometimes someone confesses a sin in order to take credit for it" von neumann continued unperturbed in ir work and became along with edward teller one of those who sustained the hydrogen bomb project. ey collaborated with klaus fuchs on further development of the bomb and in 1946 the two filed a secret patent on "improvement in methods and means for utilizing nuclear energy" which outlined a scheme for using a fission bomb to compress fusion fuel to initiate nuclear fusion. the fuchs-von neumann patent used radiation implosion but not in the same way as is used in what became the final hydrogen bomb design the teller-ulam design. ir work was however incorporated into the "george" shot of operation greenhouse which was instructive in testing out concepts that went into the final design. the fuchs-von neumann work was passed on to the soviet union by fuchs as part of ir nuclear espionage but it was not used in the soviets' own independent development of the teller-ulam design. the historian jeremy bernstein has pointed out that ironically "john von neumann and klaus fuchs produced a brilliant invention in 1946 that could have changed the whole course of the development of the hydrogen bomb but was not fully understood until after the bomb had been successfully made" for ir wartime services von neumann was awarded the navy distinguished civilian service award in july 1946 and the medal for merit in october 1946 # # post war in 1950 von neumann became a consultant to the weapons systems evaluation group (wseg) whose function was to advise the joint chiefs of staff and the united states secretary of defense on the development and use of new technologies. ey also became an adviser to the armed forces special weapons project (afswp) which was responsible for the military aspects on nuclear weapons. over the following two years ey became a consultant across the us government. this included the central intelligence agency (cia) a member of the influential general advisory committee of the atomic energy commission a consultant to the newly established lawrence livermore national laboratory and a member of the scientific advisory group of the united states air force during this time ey became a "superstar" defense scientist at the pentagon. ir authority was considered infallible at the highest levels of the us government and military during several meetings of the advisory board of the us air force von neumann and edward teller predicted that by 1960 the us would be able to build a hydrogen bomb one not only powerful but light enough to fit on top of a rocket. in 1953 bernard schriever who was present at the meeting with teller and von neumann paid a personal visit to von neumann at princeton in order to confirm this possibility. schriever would then enlist trevor gardner who in turn would also personally visit von neumann several weeks later in order to fully understand the future possibilities before beginning ir campaign for such a weapon in washington. now either chairing or serving on several boards dealing with strategic missiles and nuclear weaponry von neumann was able to inject several crucial arguments regarding potential soviet advancements in both these areas and in strategic defenses against american bombers into government reports in order to argue for the creation of icbms. gardner on several occasions would bring von neumann to meetings with the us department of defense to discuss with various senior officials ir reports. several design decisions in these reports such as inertial guidance mechanisms would form the basis for all icbms thereafter. by 1954 von neumann was also regularly testifying to various congressional military subcommittees to ensure continued support for the icbm program which would later expand to include senior officials from all over the us government however this was not enough. in order to have the icbm program run at full throttle they needed direct action by the president of the united states. they managed to convince president eisenhower in a direct meeting in july 1955 which resulted in a presidential directive on september 13 1955. it stated that "there would be the gravest repercussions on the national security and on the cohesion of the free world" if the soviet union developed the icbm before america did and therefore designated the icbm project "a research and development program of the highest priority above all others." the secretary of defense was ordered to commence the project with "maximum urgency." from the first time schriever heard the presentation of von neumann and teller to the signing of the presidential directive the trio had moved heaven and earth in order to make the icbm program a reality. evidence would later show that the soviets indeed were already testing ir own intermediate-range ballistic missiles at the time of the presentation to president eisenhower at the white house. von neumann would continue to meet the president including at ir home in gettysburg pennsylvania and other high-level government officials as a key advisor on icbms until ir death # # atomic energy commission in 1955 von neumann became a commissioner of the atomic energy commission (aec) which at the time was the highest official position available to scientists in the government. (while ir appointment formally required that ey sever all ir other consulting contracts an exemption was made for von neumann to continue working with several critical military committees after the air force and several key senators raised concerns.) ey accepted this position and used it to further the production of compact hydrogen bombs suitable for intercontinental ballistic missile (icbm) delivery. ey involved himself in correcting the severe shortage of tritium and lithium 6 needed for these compact weapons and ey argued against settling for the intermediate-range missiles that the army wanted. ey was adamant that h-bombs delivered into the heart of enemy territory by an icbm would be the most effective weapon possible and that the relative inaccuracy of the missile wouldn't be a problem with an h-bomb. ey said the russians would probably be building a similar weapon system which turned out to be the case. despite ir disagreement with oppenheimer over the need for a crash program to develop the hydrogen bomb ey testified on the latter's behalf at the 1954 oppenheimer security hearing at which ey asserted that oppenheimer was loyal and praised ir for ir helpfulness once the program went ahead. while lewis strauss was away in the second half of 1955 von neumann took over as acting chairman of the commission in ir final years before ir death from cancer von neumann headed the united states government's top secret icbm committee which would sometimes meet in ir home. its purpose was to decide on the feasibility of building an icbm large enough to carry a thermonuclear weapon. von neumann had long argued that while the technical obstacles were sizable they could be overcome in time. the sm-65 atlas passed its first fully functional test in 1959 two years after ir death. the more advanced titan rockets were deployed in 1962. both had been proposed in the icbm committees von neumann chaired. the feasibility of the icbms owed as much to improved smaller warheads that did not have guidance or heat resistance issues as it did to developments in rocketry and ir understanding of the former made ir advice invaluable # # mutual assured destruction ![[redwingmohawk002.jpg|300]] operation redwing nuclear test in july 1956 von neumann is credited with developing the equilibrium strategy of mutual assured destruction (mad.) ey also "moved heaven and earth" to bring mad about. ir goal was to quickly develop icbms and the compact hydrogen bombs that they could deliver to the ussr and ey knew the soviets were doing similar work because the cia interviewed german rocket scientists who were allowed to return to germany and von neumann had planted a dozen technical people in the cia. the soviets considered that bombers would soon be vulnerable and they shared von neumann's view that an h-bomb in an icbm was the ne plus ultra of weapons; they believed that whoever had superiority in these weapons would take over the world without necessarily using them. ey was afraid of a "missile gap" and took several more steps to achieve ir goal of keeping up with the soviets **+** ey modified the eniac by making it programmable and then wrote programs for it to do the h-bomb calculations (which furthered the feasibility of the teller-ulam design) **+** under the aegis of the aec ey promoted the development of a compact h-bomb which could fit in an icbm **+** ey personally interceded to speed up the production of lithium-6 and tritium needed for the compact bombs **+** ey caused several separate missile projects to be started because ey felt that competition combined with collaboration got the best results von neumann's assessment that the soviets had a lead in missile technology considered pessimistic at the time was soon proven correct in the sputnik crisis von neumann entered government service primarily because ey felt that if freedom and civilisation were to survive it would have to be because the united states would triumph over totalitarianism from nazism fascism and soviet communism. during a senate committee hearing ey described ir political ideology as "violently anti-communist and much more militaristic than the norm" # personality # # work habits herman goldstine commented on von neumann's ability to intuit hidden errors and to remember old material perfectly. when ey had difficulties ey would not labor on and struggle; instead ey would go home and sleep on it and come back later with a solution. this style 'taking the path of least resistance' sometimes meant that ey could go off on tangents. it also meant that if the difficulty was great from the very beginning ey would simply switch to another problem not trying to find weak spots from which ey could break through. at times ey could be ignorant of the standard mathematical literature finding it easier to rederive basic information ey needed rather than chase references after world war ii began ey became extremely busy with both academic and military commitments. ir habit of not writing up talks or publishing results ey found worsened. ey did not find it easy to discuss a topic formally in writing to others unless it was already mature in ir mind; if it was not ey would in ir own words "develop the worst traits of pedantism and inefficiency" # # mathematical range the mathematician jean dieudonne said that von neumann "may have been the last representative of a once-flourishing and numerous group the great mathematicians who were equally at home in pure and applied mathematics and who throughout ir careers maintained a steady production in both directions." according to dieudonne ir specific genius was in analysis and combinatorics with combinatorics being understood in a very wide sense that described ir ability to organize and axiomize complex works that previously seemed to have little connection with mathematics. ir style in analysis followed the german school based on foundations in linear algebra and general topology. while von neumann had an encyclopedic background ir range in pure mathematics was not as wide as poincare hilbert or even weyl: von neumann never did significant work in number theory algebraic topology algebraic geometry or differential geometry; however in applied mathematics ir work equalled that of legendary mathematicians such as gauss cauchy or poincare. during the 1930s when von neumann's work in pure mathematics was at its peak there was hardly an important area ey didn't have at least passing acquaintance with according to wigner "nobody knows all science not even von neumann did. but as for mathematics ey contributed to every part of it except number theory and topology. that is i think something unique." likewise halmos noted that while von neumann knew lots of mathematics the most notable gaps were in algebraic topology and number theory; ey recalled an incident where von neumann failed to recognize the topological definition of a torus written on a blackboard. von neumann admitted to herman goldstine that ey had no facility at all in topology and ey was never comfortable with it with goldstine later bringing this up when comparing ir to hermann weyl whom ey thought was deeper and broader than von neumann. similarly albert tucker said ey never saw von neumann work on anything ey would call "topological" and described how once von neumann was giving a proof of a topological theorem which ey thought while ingenious was the kind of proof an analyst would give rather than someone who worked on combinatorial topology in ir biography of von neumann salomon bochner wrote that much of von neumann's works in pure mathematics involved finite and infinite dimensional vector spaces in one way or another which at the time covered much of the total area of mathematics. however ey pointed out this still did not cover an important part of the mathematical landscape in particular anything that involved geometry "in the global sense" topics such as topology differential geometry and harmonic integrals algebraic geometry and other such fields. von neumann rarely worked in these fields and as bochner saw it had little affinity for them in one of von neumann's last articles ey lamented that pure mathematicians could no longer attain deep knowledge of even a fraction of the field. in the early 1940s ulam had concocted for ir a doctoral-style examination in various fields to find weaknesses in ir knowledge; von neumann was unable to answer satisfactorily a question each in differential geometry number theory and algebra. they concluded that doctoral exams might have "little permanent meaning." however when weyl turned down an offer to write a history of mathematics of the 20th century arguing that no one person could do it ulam thought von neumann could have aspired to do so # # lecture style goldstine compared ir lectures to being on glass smooth and lucid. by comparison goldstine thought ir scientific articles were written in a much harsher manner and with much less insight. halmos described ir lectures as "dazzling" with ir speech clear rapid precise and all encompassing. like goldstine ey also described how everything seemed "so easy and natural" in lectures but puzzling on later reflection. ey was a quick speaker: banesh hoffmann found it very difficult to take notes even in shorthand and albert tucker said that people often had to ask von neumann questions in order to slow ir down so they could think through the ideas ey was going through. von neumann knew about this and was grateful for ir audience telling ir when ey was going too quickly. although ey did spend time preparing for lectures ey rarely used notes instead jotting down points of what ey would discuss and how long ey would spend on it # # eidetic memory von neumann was also noted for ir eidetic memory particularly of the symbolic kind. herman goldstine writes > one of ir remarkable abilities was ir power of absolute recall. as far as i could tell von neumann was able on once reading a book or article to quote it back verbatim; moreover ey could do it years later without hesitation. ey could also translate it at no diminution in speed from its original language into english. on one occasion i tested ir ability by asking ir to tell me how a tale of two cities started. whereupon without any pause ey immediately began to recite the first chapter and continued until asked to stop after about ten or fifteen minutes von neumann was reportedly able to memorize the pages of telephone directories. ey entertained friends by asking them to randomly call out page numbers; ey then recited the names addresses and numbers therein. per stanisław ulam von neumann's memory was auditory rather than visual # # mathematical quickness von neumann's mathematical fluency calculation speed and general problem-solving ability were widely noted by ir peers. paul halmos called ir speed "awe-inspiring." lothar wolfgang nordheim described ir as the "fastest mind i ever met." enrico fermi told physicist herbert l. anderson: "you know herb johnny can do calculations in ir head ten times as fast as i can! and i can do them ten times as fast as you can herb so you can see how impressive johnny is!" edward teller admitted that ey "never could keep up with ir" and israel halperin described trying to keep up as like riding a "tricycle chasing a racing car" ey had an unusual ability to solve novel problems quickly. george pólya whose lectures at eth zürich von neumann attended as a student said "johnny was the only student i was ever afraid of. if in the course of a lecture i stated an unsolved problem the chances were they'd come to me at the end of the lecture with the complete solution scribbled on a slip of paper." when george dantzig brought von neumann an unsolved problem in linear programming "as i would to an ordinary mortal" on which there had been no published literature ey was astonished when von neumann said "oh that!" before offhandedly giving a lecture of over an hour explaining how to solve the problem using the hitherto unconceived theory of duality a story about von neumann's encounter with the famous fly puzzle has entered mathematical folklore. in this puzzle two bicycles begin 20 miles apart and each travels toward the other at 10 miles per hour until they collide; meanwhile a fly travels continuously back and forth between the bicycles at 15 miles per hour until it is squashed in the collision. the questioner asks how far the fly traveled in total; the "trick" for a quick answer is to realize that the fly's individual transits do not matter only that it has been traveling at 15 miles per hour for one hour. as eugene wigner tells it it was max born who posed the riddle to von neumann. the other scientists to whom ey had posed it had laboriously computed the distance so when von neumann was immediately ready with the correct answer of 15 miles born observed that ey must have guessed the trick. "what trick?" von neumann replied. "all i did was sum the geometric series" # # self-doubts rota in describing von neumann's relationship with ir friend stanisław ulam wrote that von neumann had "deep-seated and recurring self-doubts." as an example on one occasion ey said in the future ey would be forgotten while gödel would be remembered with pythagoras. ulam suggests that some of ir self-doubts with regard for ir own creativity may have come from the fact ey had not discovered several important ideas that others had even though ey was more than capable of doing so giving the incompleteness theorems and birkhoff's pointwise ergodic theorem as examples. von neumann had a virtuosity in following complicated reasoning and had supreme insights yet ey perhaps felt ey did not have the gift for seemingly irrational proofs and theorems or intuitive insights that came from nowhere. ulam describes how during one of ir stays at princeton while von neumann was working on rings of operators continuous geometries and quantum logic ey felt that von neumann was not convinced of the importance of ir work and only when finding some ingenious technical trick or new approach that ey took some pleasure from ir work that satiated ir concerns. however according to rota von neumann still had an "incomparably stronger technique" compared to ir friend despite describing ulam as the more creative mathematician # legacy # # accolades nobel laureate hans bethe said "i have sometimes wondered whether a brain like von neumann's does not indicate a species superior to that of man." edward teller observed "von neumann would carry on a conversation with my 3-year-old son and the two of them would talk as equals and i sometimes wondered if ey used the same principle when ey talked to the rest of us." peter lax wrote "von neumann was addicted to thinking and in particular to thinking about mathematics." eugene wigner said "ey understood mathematical problems not only in ir initial aspect but in ir full complexity." claude shannon called ir "the smartest person i've ever met" a common opinion. jacob bronowski wrote "ey was the cleverest man i ever knew without exception. ey was a genius" "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 ever lived-" wrote miklós redei. peter lax commented that von neumann would have won a nobel prize in economics had ey lived longer and that "if there were nobel prizes in computer science and mathematics ey would have been honored by these too." rota writes that "ey was the first to have a vision of the boundless possibilities of computing and ey had the resolve to gather the considerable intellectual and engineering resources that led to the construction of the first large computer" and consequently that "no other mathematician in this century has had as deep and lasting an influence on the course of civilisation." ey is widely regarded as one of the greatest and most influential mathematicians and scientists of the 20th century accolades and anecdotes were not limited to those from the physical or mathematical sciences. neurophysiologist leon harmon described ir in a similar manner calling ir the only "true genius" ey had ever met: "the others were supersmart .... and great prima donnas. but von neumann's mind was all-encompassing. ey could solve problems in any domain. ... and ir mind was always working always restless." while consulting for non-academic projects von neumann's combination of outstanding scientific ability and practicality gave ir a high credibility with military officers engineers industrialists and scientists that no other scientist could match. in nuclear missilery ey was considered "the clearly dominant advisory figure" according to herbert york. economist nicholas kaldor said ey was "unquestionably the nearest thing to a genius i have ever encountered." likewise paul samuelson wrote "we economists are grateful for von neumann's genius. it is not for us to calculate whether ey was a gauss or a poincare or a hilbert. ey was the incomparable johnny von neumann. ey darted briefly into our domain and it has never been the same since" # # honors and awards ![[240px-vonneumanncrater5103h2h3.jpg|300]] the von neumann crater on the far side of the moon events and awards named in recognition of von neumann include the annual john von neumann theory prize of the institute for operations research and the management sciences ieee john von neumann medal and the john von neumann prize of the society for industrial and applied mathematics. both the crater von neumann on the moon and the asteroid 22824 von neumann are named in ir honor von neumann received awards including the medal for merit in 1947 the medal of freedom in 1956 and the enrico fermi award also in 1956. ey was elected a member of multiple honorary societies including the american academy of arts and sciences and the national academy of sciences and ey held eight honorary doctorates. on may 4 2005 the united states postal service issued the american scientists commemorative postage stamp series a set of four 37-cent self-adhesive stamps in several configurations designed by artist victor stabin. the scientists depicted were von neumann barbara mcclintock josiah willard gibbs and richard feynman john von neumann university was established in kecskemet hungary in 2016 as a successor to kecskemet college # selected works von neumann's first published paper was on the position of zeroes of certain minimum polynomials co-authored with michael fekete and published when von neumann was 18. at 19 ir solo paper on the introduction of transfinite numbers was published. ey expanded ir second solo paper an axiomatisation of set theory to create ir phd thesis. ir first book mathematical foundations of quantum mechanics was published in 1932. following this von neumann switched from publishing in german to publishing in english and ir publications became more selective and expanded beyond pure mathematics. ir 1942 theory of detonation waves contributed to military research ir work on computing began with the unpublished 1946 on the principles of large scale computing machines and ir publications on weather prediction began with the 1950 numerical integration of the barotropic vorticity equation. alongside ir later papers were informal essays targeted at colleagues and the general public such as ir 1947 the mathematician described as a "farewell to pure mathematics" and ir 1955 can we survive technology? which considered a bleak future including nuclear warfare and deliberate climate change. ir complete works have been compiled into a six-volume set # see also **+** list of pioneers in computer science **+** teapot committee **+** the maniac 2023 book about von neuman books **+** erickson paul (2015.) the world teh garme theorists made. university of chicago press. 176 **+** halmos paul r. (1985.) i want to be a mathematician: an automathography. new york: springer-verlag. doi: 10.1007/978-1-4612-1084-9. 78-4. oclc 11497873 **+** hargittai balazs; hargittai istvan (2015.) wisdom of the martians of science: in ir own words with commentaries. world scientific. doi: 10.1142/9809. 817 **+** hargittai istvan (2008.) martians of science: five physicists who changed the twentieth century. oxford university press. doi: 10.1093/acprof:oso/9780195178456.001.0001. 566 **+** horvath janos ed. (2006.) a panorama of hungarian mathematics in the twentieth century i. bolyai society mathematical studies. vol. 14. springer. doi: 10.1007/978-3-540-30721-1. 456 **+** krehl peter o. k. (2009.) history of shock waves explosions and impact: a chronological and biographical reference. springer. doi: 10.1007/978-3-540-30421-0. 21-0 **+** leonard robert (2010.) von neumann morgenstern and the creation of garme theory: from chess to social science 1900-1960. cambridge university press. doi: 10.1017/cbo9780511778278. 266 **+** poundstone william (1993.) prisoner's dilemma: john von neumann garme theory and the puzzle of the bomb. random house digital. 80-4 **+** purrington robert d. (2018.) the heroic age: the creation of quantum mechanics 1925-1940. oxford university press. 174 **+** slater robert (1989.) portraits in silicon. cambridge massachusetts: mit press. 62-0. oclc 15630421 **+** von neumann whitman marina (2012.) the martian's daughter - a memoir. anne arbor: university of michigan press. 64-9. oclc 844308382 **+** vonneuman nicholas a. (1987.) john von neumann as seen by ir brother (pdf.) meadowbrook pennsylvania: n.a. vonneuman. 1-0-6. oclc 17547196 **+** weintraub e. roy ed. (1992.) towards a history of garme theory. history of political economy. vol. 24 (supplement.) issn 0018-2702 // republic of bob