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arts from the front wheel of the southbound bicycle and flies to the front wheel of the northbound one then turns around and flies to the front wheel of the southbound one again and continues in this manner till he is crushed between the two front wheels question what total distance did the fly cover the slow way to find the answer is to calculate what distance the fly covers on the first southbound leg of the trip then on the second northbound leg then on the third etc etc and finally to sum the infinite series so obtained the quick way is to observe that the bicycles meet exactly one hour after their start so that the fly had just an hour for his travels the answer must therefore be 15 miles when the question was put to von neumann he solved it in an instant and thereby disappointed the questioner oh you must have heard the trick before what trick asked von neumann all i did was sum the geometric series 452 wigner told a similar story only with a swallow instead of a fly and says it was max born who posed the question to von neumann in the 1920s 453 similarly when the first computers he was helping develop were completed simple tests like what is the lowest power of 2 that has the number 7 in the fourth position from the end were conducted to ensure their accuracy for modern computers this would take only a fraction of a second but for the first computers johnny would race against them in calculation and win 405 accolades and anecdotes were not limited to those from the physical or mathematical sciences either neurophysiologist leon harmon described him in a similar manner von neumann was a true genius the only one i ve ever known i ve met einstein and oppenheimer and teller and who s the mad genius from mit i don t mean mcculloch but a mathematician anyway a whole bunch of those other guys von neumann was the only genius i ever met the others were supersmart and great prima donnas but von neumann s mind was all encompassing he could solve problems in any domain and his mind was always working always restless 454 us president dwight d eisenhower considered him the outstanding mathematician of the time 455 while consulting for non academic projects von neumann s combination of outstanding scientific ability and practicality gave him a high credibility with military officers engineers industrialists and scientists that no other scientist could match in nuclear missilery he was considered the clearly dominant advisory figure according to herbert york whose opinions everyone took very seriously 456 even for writer arthur koestler who was not an academic von neumann was one of the few people for whom koestler entertained not only respect but reverence and he shared koestler s central european addiction to abstruse philosophical discussions political debate and dirty jokes the two of them derived considerable pleasure from discussing the state of american civilization was it in crisis or simply at the stage of adolescence the likely future of europe would there be war free will versus determinism and the definition of pregnancy the uterus taking seriously what was pointed at it in fun 457 he is often given as an example that mathematicians could do great work in the physical sciences too however r d richtmyer describes how during von neumann s time at los alamos he functioned not as a mathematician applying his art to physics problems but rather entirely as a physicist in the mind and thought except faster he describes him as a first rate physicist who knew quantum mechanics atomic molecular and nuclear physics particle physics astrophysics relativity and physical and organic chemistry as such any mathematician who does not possess the same talent as von neumann should not be fooled into thinking physics is easy just because they study mathematics 458 eidetic memory edit von neumann was also noted for his eidetic memory particularly of the symbolic kind herman goldstine writes one of his remarkable abilities was his 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 he could do it years later without hesitation he could also translate it at no diminution in speed from its original language into english on one occasion i tested his ability by asking him to tell me how a tale of two cities started whereupon without any pause he immediately began to recite the first chapter and continued until asked to stop after about ten or fifteen minutes 459 von neumann was reportedly able to memorize the pages of telephone directories he entertained friends by asking them to randomly call out page numbers he then recited the names addresses and numbers therein 41 460 in his autobiography stanislaw ulam writes that johnny s memory was auditory rather than visual he did not have to any extent an intuitive common sense for guessing what may happen in a given physical situation 461 legacy edit 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 rédei in john von neumann selected letters 462 james glimm wrote he is regarded as one of the giants of modern mathematics 463 the mathematician jean dieudonné 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 their careers maintained a steady production in both directions 14 while peter lax described him as possessing the most scintillating intellect of this century 464 in the foreword of miklós rédei s selected letters peter lax wrote to gain a measure of von neumann s achievements consider that had he lived a normal span of years he would certainly have been a recipient of a nobel prize in economics and if there were nobel prizes in computer science and mathematics he would have been honored by these too so the writer of these letters should be thought of as a triple nobel laureate or possibly a 3 1 2 fold winner for his work in physics in particular quantum mechanics 465 rota writes that he was the first to have a vision of the boundless possibilities of computing and he 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 civilization 466 he believed in the power of mathematical reasoning to influence modern civilization an idea which expressed itself through his life work he is widely regarded as one of the greatest and most influential mathematicians and scientists of the 20th century 463 467 468 302 469 470 471 mastery of mathematics edit stan ulam who knew von neumann well described his mastery of mathematics this way most mathematicians know one method for example norbert wiener had mastered fourier transforms some mathematicians have mastered two methods and might really impress someone who knows only one of them john von neumann had mastered three methods he went on to explain that the three methods were a facility with the symbolic manipulation of linear operators an intuitive feeling for the logical structure of any new mathematical theory an intuitive feeling for the combinatorial superstructure of new theories 472 as an example of the last point eugene wigner described how once he did not understand a mathematical theorem and asked von neumann for help von neumann would ask wigner whether he knew several other different but related theorems and then he would then explain the problematic theorem based off what wigner already knew using such circular paths he could make even the most difficult concepts easy 473 on another occasion he wrote nobody knows all science not even von neumann did but as for mathematics he advanced every part of it except number theory and topology that is i think something unique 474 likewise halmos noted that while von neumann knew lots of mathematics the most notable gaps were in algebraic topology and number theory describing a story of how von neumann once was walking by and saw something on the blackboard he didn t understand upon asking halmos told him it was just the usual identification for a torus while elementary even for modern graduate students this kind of work never crossed his path and thus he did not know it 475 one time he admitted to herman goldstine that he had no facility at all in topology and he was never comfortable with it with goldstine later bringing this up when comparing him to hermann weyl whom he thought was deeper and broader than von neumann 430 similarly albert tucker said he never saw von neumann work on anything he would call topological and described how once von neumann was giving a proof of a topological theorem which he thought while ingenious was the kind of proof an analyst would give rather than someone who worked on combinatorial topology 423 towards the end of his life he deplored to ulam the fact that it no longer felt possible for anyone to have more than passing knowledge of one third of the field of pure mathematics 476 in fact in the early 1940s ulam himself concocted for him at his suggestion a doctoral style examination in various fields in order to find weaknesses in his knowledge he did find them with von neumann being unable to answer satisfactorily a question each in differential geometry number theory and algebra this may also tend to show that doctoral exams have little permanent meaning was their conclusion however while 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 johnny could have aspired to do so 477 in his biography of von neumann salomon bochner describes how 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 he 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 in these fields he said von neumann worked on rarely and had very little affinity for it in his thinking 139 likewise jean dieudonné noted in his biographical article that while he had an encyclopedic background his range in pure mathematics was not as wide as poincaré hilbert or even weyl his specific genius was in analysis and combinatorics with combinatorics being understood in a very wide sense that described his ability to organize and axiomize complex works a priori that previously seemed to have little connection with mathematics his style in analysis was not of the traditional english or french schools but rather of the german one where analysis is based extensively on foundations in linear algebra and general topology as with bochner he noted von neumann never did significant work in number theory algebraic topology algebraic geometry or differential geometry however for his limits in pure mathematics he made up for in applied mathematics where his work certainly equalled that of legendary mathematicians such as gauss cauchy or poincaré dieudonné notes that during the 1930s when von neumann s work in pure mathematics was at its peak there was hardly an important area he didn t have at least passing acquaintance with 126 honors and awards edit the von neumann crater on the far side of the moon the john von neumann theory prize of the institute for operations research and the management sciences informs previously tims orsa is awarded annually to an individual or group who have made fundamental and sustained contributions to theory in operations research and the management sciences 478 the ieee john von neumann medal is awarded annually by the institute of electrical and electronics engineers ieee for outstanding achievements in computer related science and technology 479 the john von neumann lecture is given annually at the society for industrial and applied mathematics siam by a researcher who has contributed to applied mathematics and the chosen lecturer is also awarded a monetary prize 480 the crater von neumann on the moon is named after him 481 asteroid 22824 von neumann was named in his honor 482 483 the john von neumann center in plainsboro township new jersey was named in his honor 484 the professional society of hungarian computer scientists john von neumann computer society was named after von neumann 485 486 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 487 the john von neumann award of the rajk lászló college for advanced studies was named in his honor and has been given every year since 1995 to professors who have made an outstanding contribution to the exact social sciences and through their work have strongly influenced the professional development and thinking of the members of the college 488 john von neumann university hu neumann jános egyetem was established in kecskemét hungary in 2016 as a successor to kecskemét college 489 the may 1958 issue of the bulletin of the american mathematical society was dedicated as a memorial volume in an act without precedent to von neumann and several articles were written about him and his work by friends and colleagues 490 491 a large number of books have been dedicated to him from a wide variety of fields 492 493 a large number of scientific papers have been dedicated to him from a wide variety of fields 494 495 496 many events have been dedicated to him from a wide variety of fields 497 twice invited speaker at the international congress of mathematicians 498 a list of the following awards and honors was drawn from various biographic statements given by von neumann 499 500 385 awards 1926 rockefeller fellowship 1937 bôcher prize american mathematical society 1947 medal for merit presidential award 1947 distinguished civilian service award u s navy 1955 science award air force association 1956 medal of freedom presidential award 1956 albert einstein commemorative award 1956 enrico fermi award u s atomic energy commission 1957 american meteorological society award for extraordinary scientific accomplishment 1997 air force space and missile pioneers award posthumous 1997 hall of fame space command headquarters peterson air force base posthumous co editorship 1933 1957 annals of mathematics 1935 1957 compositio mathematica 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