119-617: The Manchester Baby , also called the Small-Scale Experimental Machine ( SSEM ), was the first electronic stored-program computer . It was built at the University of Manchester by Frederic C. Williams , Tom Kilburn , and Geoff Tootill , and ran its first program on 21 June 1948. The Baby was not intended to be a practical computing engine, but was instead designed as a testbed for the Williams tube ,
238-520: A Privatdozent at the University of Berlin in 1928. He was the youngest person elected Privatdozent in the university's history. He began writing nearly one major mathematics paper per month. In 1929, he 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
357-421: A Turing machine , a theoretical concept intended to explore the limits of mechanical computation. Turing was not imagining a physical machine, but a person he called a "computer", who acted according to the instructions provided by a tape on which symbols could be read and written sequentially as the tape moved under a tape head. Turing proved that if an algorithm can be written to solve a mathematical problem, then
476-460: A chemical engineer from ETH Zurich in 1926, and simultaneously passed his final examinations summa cum laude for his Ph.D. in mathematics (with minors in experimental physics and chemistry). However, in A Beautiful Mind by Sylvia Nasar, it's stated that Von Neumann was enrolled in chemical engineering at the University of Budapest while studying mathematics in Berlin. He then went to
595-653: A complex vector space with a Hermitian scalar product , with the corresponding norm being both separable and complete. In the same papers he also proved the general form of the Cauchy–Schwarz inequality that had previously been known only in specific examples. He continued with the development of the spectral theory of operators in Hilbert space in three seminal papers between 1929 and 1932. This work cumulated in his Mathematical Foundations of Quantum Mechanics which alongside two other books by Stone and Banach in
714-612: A lieutenant in the U.S. Army's Officers Reserve Corps . He passed the exams but was rejected because of his age. Klára and John von Neumann were socially active within the local academic community. His white clapboard house on Westcott Road was one of Princeton's largest private residences. He always wore formal suits. He enjoyed Yiddish and "off-color" humor. In Princeton, he received complaints for playing extremely loud German march music ; Von Neumann did some of his best work in noisy, chaotic environments. According to Churchill Eisenhart , von Neumann could attend parties until
833-579: A mercury column, the device's temperature had to be very carefully controlled, as the velocity of sound through a medium varies with its temperature. Williams had seen an experiment at Bell Labs demonstrating the effectiveness of cathode-ray tubes (CRT) as an alternative to the delay line for removing ground echoes from radar signals. While working at the TRE, shortly before he joined the University of Manchester in December 1946, he and Tom Kilburn had developed
952-487: A von Neumann architecture stores program data and instruction data in the same memory, while a computer with a Harvard architecture has separate memories for storing program and data. However, the term stored-program computer is sometimes used as a synonym for the von Neumann architecture. Jack Copeland considers that it is "historically inappropriate, to refer to electronic stored-program digital computers as 'von Neumann machines'". Hennessy and Patterson wrote that
1071-416: A Hilbert space, as distinct from self-adjoint operators , which enabled him to give a description of all Hermitian operators which extend a given Hermitian operator. He wrote a paper detailing how the usage of infinite matrices , common at the time in spectral theory, was inadequate as a representation for Hermitian operators. His work on operator theory lead to his most profound invention in pure mathematics,
1190-645: A Turing machine can execute that algorithm. Konrad Zuse 's Z3 was the world's first working programmable , fully automatic computer, with binary digital arithmetic logic, but it lacked the conditional branching of a Turing machine. On 12 May 1941, the Z3 was successfully presented to an audience of scientists of the Deutsche Versuchsanstalt für Luftfahrt ("German Laboratory for Aviation") in Berlin . The Z3 stored its program on an external tape, but it
1309-478: A blueprint for all Air Force long-range missile programs. Many people who had known von Neumann were puzzled by his relationship to the military and to power structures in general. Stanisław Ulam suspected that he had a hidden admiration for people or organizations that could influence the thoughts and decision making of others. He also maintained his knowledge of languages learnt in his youth. He knew Hungarian, French, German and English fluently, and maintained
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#17327734061401428-400: A branch of mathematics that involves the states of dynamical systems with an invariant measure . Of the 1932 papers on ergodic theory, Paul Halmos wrote that even "if von Neumann had never done anything else, they would have been sufficient to guarantee him mathematical immortality". By then von Neumann had already written his articles on operator theory , and the application of this work
1547-485: A broader class of theorems. By 1927, von Neumann was involving himself in discussions in Göttingen on whether elementary arithmetic followed from Peano axioms . Building on the work of Ackermann , he began attempting to prove (using the finistic methods of Hilbert's school ) the consistency of first-order arithmetic . He succeeded in proving the consistency of a fragment of arithmetic of natural numbers (through
1666-411: A conversational level of Italian, Yiddish, Latin and Ancient Greek. His Spanish was less perfect. He had a passion for and encyclopedic knowledge of ancient history, and he enjoyed reading Ancient Greek historians in the original Greek. Ulam suspected they may have shaped his views on how future events could play out and how human nature and society worked in general. Von Neumann's closest friend in
1785-507: A digital computer was ... Where I got this knowledge from I've no idea. Jack Copeland explains that Kilburn's first (pre-Baby) accumulator-free (decentralized, in Jack Good's nomenclature) design was based on inputs from Turing, but that he later switched to an accumulator-based (centralized) machine of the sort advocated by von Neumann, as written up and taught to him by Jack Good and Max Newman. The Baby's seven operation instruction set
1904-510: A form of electronic memory known as the Williams tube or Williams–Kilburn tube, based on a standard CRT: the first electronic random-access digital storage device. The Baby was designed to show that it was a practical storage device by demonstrating that data held within it could be read and written reliably at a speed suitable for use in a computer. For use in a binary digital computer, the tube had to be capable of storing either one of two states at each of its memory locations, corresponding to
2023-461: A hunger) for the more earthy type of comedy and humor". In 1955, a mass was found near von Neumann's collarbone, which turned out to be cancer originating in the skeleton , pancreas or prostate . (While there is general agreement that the tumor had metastasised , sources differ on the location of the primary cancer.) The malignancy may have been caused by exposure to radiation at Los Alamos National Laboratory . As death neared he asked for
2142-494: A meteor". Von Neumann combined traditional projective geometry with modern algebra ( linear algebra , ring theory , lattice theory). Many previously geometric results could then be interpreted in the case of general modules over rings. His work laid the foundations for some of the modern work in projective geometry. His biggest contribution was founding the field of continuous geometry . It followed his path-breaking work on rings of operators. In mathematics, continuous geometry
2261-770: A new, ingenious proof for the Radon–Nikodym theorem . His lecture notes on measure theory at the Institute for Advanced Study were an important source for knowledge on the topic in America at the time, and were later published. Using his previous work on measure theory, von Neumann made several contributions to the theory of topological groups , beginning with a paper on almost periodic functions on groups, where von Neumann extended Bohr's theory of almost periodic functions to arbitrary groups . He continued this work with another paper in conjunction with Bochner that improved
2380-549: A paper outlining his design for an electronic stored-program computer to be known as the Automatic Computing Engine (ACE). This was one of several projects set up in the years following the Second World War with the aim of constructing a stored-program computer. At about the same time, EDVAC was under development at the University of Pennsylvania 's Moore School of Electrical Engineering , and
2499-728: A positive charge 1. The charge dissipated in about 0.2 seconds, but it could be automatically refreshed from the data picked up by the detector. The Williams tube used in Baby was based on the CV1131, a commercially available 12-inch (300 mm) diameter CRT, but a smaller 6-inch (150 mm) tube, the CV1097, was used in the Mark I. After developing the Colossus computer for code breaking at Bletchley Park during World War II, Max Newman
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#17327734061402618-470: A power consumption of 3500 watts. The arithmetic unit was built using EF50 pentode valves, which had been widely used during wartime. The Baby used one Williams tube to provide 32 by 32-bit words of random-access memory (RAM), a second to hold a 32-bit accumulator in which the intermediate results of a calculation could be stored temporarily, and a third to hold the current program instruction along with its address in memory. A fourth CRT, without
2737-409: A priest, and converted to Catholicism , though the priest later recalled that von Neumann found little comfort in his conversion, and in receiving the last rites – he remained terrified of death and unable to accept it. Of his 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
2856-461: A set as a class that belongs to other classes, while a proper class is defined as a class that does not belong to other classes. On the Zermelo–Fraenkel approach, the axioms impede the construction of a set of all sets that do not belong to themselves. In contrast, on von Neumann's approach, the class of all sets that do not belong to themselves can be constructed, but it is a proper class , not
2975-530: A set of 32 buttons and switches known as the input device to set the value of each bit of each word to either 0 or 1. The Baby had no paper-tape reader or punch . Three programs were written for the computer. The first, consisting of 17 instructions, was written by Kilburn, and so far as can be ascertained first ran on 21 June 1948. It was designed to find the highest proper factor of 2 (262,144) by trying every integer from 2 − 1 downwards. The divisions were implemented by repeated subtractions of
3094-476: A set. Overall, von Neumann's major achievement in set theory was an "axiomatization of set theory and (connected with that) elegant theory of the ordinal and cardinal numbers as well as the first strict formulation of principles of definitions by the transfinite induction ". Building on the Hausdorff paradox of Felix Hausdorff (1914), Stefan Banach and Alfred Tarski in 1924 showed how to subdivide
3213-472: A short paper giving the first derivation of a given norm from an inner product by means of the parallelogram identity . His trace inequality is a key result of matrix theory used in matrix approximation problems. He also first presented the idea that the dual of a pre-norm is a norm in the first major paper discussing the theory of unitarily invariant norms and symmetric gauge functions (now known as symmetric absolute norms). This paper leads naturally to
3332-633: A single hardwired program. As there were no program instructions, no program storage was necessary. Other computers, though programmable, stored their programs on punched tape , which was physically fed into the system as needed, as was the case for the Zuse Z3 and the Harvard Mark I , or were only programmable by physical manipulation of switches and plugs, as was the case for the Colossus computer . In 1936, Konrad Zuse anticipated in two patent applications that machine instructions could be stored in
3451-679: 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. His mother, brothers and in-laws followed von Neumann to the United States in 1939. Von Neumann anglicized his name to John, keeping the German-aristocratic surname von Neumann. Von Neumann became a naturalized U.S. citizen in 1937, and immediately tried to become
3570-479: A theory of noncommutative integration, something that von Neumann hinted to in his work but did not explicitly write out. Another important result on polar decomposition was published in 1932. Between 1935 and 1937, von Neumann worked on lattice theory , the theory of partially ordered sets in which every two elements have a greatest lower bound and a least upper bound. As Garrett Birkhoff wrote, "John von Neumann's brilliant mind blazed over lattice theory like
3689-668: A three-dimensional ball into disjoint sets , then translate and rotate these sets to form two identical copies of the same ball; this is the Banach–Tarski paradox . They also proved that a two-dimensional disk has no such paradoxical decomposition. But in 1929, von Neumann subdivided the disk into finitely many pieces and rearranged them into two disks, using area-preserving affine transformations instead of translations and rotations. The result depended on finding free groups of affine transformations, an important technique extended later by von Neumann in his work on measure theory . With
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3808-419: A visiting lecturer in mathematical physics . Von Neumann was baptized a Catholic in 1930. Shortly afterward, he married Marietta Kövesi, who had studied economics at Budapest University. Von Neumann and Marietta had a daughter, Marina , born in 1935; she would become a professor. The couple divorced on November 2, 1937. On November 17, 1938, von Neumann married Klára Dán . In 1933 Von Neumann accepted
3927-437: A von Neumann computer depended on the availability of a suitable memory device on which to store the program. During the Second World War researchers working on the problem of removing the clutter from radar signals had developed a form of delay-line memory , the first practical application of which was the mercury delay line, developed by J. Presper Eckert . Radar transmitters send out regular brief pulses of radio energy,
4046-501: A wide range of problems, but its program was held in the state of switches in patch cords, rather than machine-changeable memory, and it could take several days to reprogram. Researchers such as Turing and Zuse investigated the idea of using the computer's memory to hold the program as well as the data it was working on, and it was mathematician John von Neumann who wrote a widely distributed paper describing that computer architecture, still used in almost all computers. The construction of
4165-427: A word from memory, giving an instruction execution rate of about 700 per second. The main store was refreshed continuously, a process that took 20 milliseconds to complete, as each of the Baby's 32 words had to be read and then refreshed in sequence. The Baby represented negative numbers using two's complement , as most computers still do. In that representation, the value of the most significant bit denotes
4284-481: Is isomorphic to the subspace-lattice of an n {\displaystyle {\mathit {n}}} -dimensional vector space V n ( F ) {\displaystyle V_{n}(F)} over a (unique) corresponding division ring F {\displaystyle F} . This is known as the Veblen–Young theorem . Von Neumann extended this fundamental result in projective geometry to
4403-489: Is a computer that stores program instructions in electronically, electromagnetically, or optically accessible memory. This contrasts with systems that stored the program instructions with plugboards or similar mechanisms. The definition is often extended with the requirement that the treatment of programs and data in memory be interchangeable or uniform. In principle, stored-program computers have been designed with various architectural characteristics. A computer with
4522-440: Is a substitute of complex projective geometry , where instead of the dimension of a subspace being in a discrete set 0 , 1 , . . . , n {\displaystyle 0,1,...,{\mathit {n}}} it can be an element of the unit interval [ 0 , 1 ] {\displaystyle [0,1]} . Earlier, Menger and Birkhoff had axiomatized complex projective geometry in terms of
4641-566: Is the change of group that makes a difference, not the change of space." Around 1942 he told Dorothy Maharam how to prove that every complete σ-finite measure space has a multiplicative lifting; he did not publish this proof and she later came up with a new one. In a number of von Neumann's papers, the methods of argument he employed are considered even more significant than the results. In anticipation of his later study of dimension theory in algebras of operators, von Neumann used results on equivalence by finite decomposition, and reformulated
4760-543: The Bell System , a development that started in earnest by c. 1954 with initial concept designs by Erna Schneider Hoover at Bell Labs . The first of such systems was installed on a trial basis in Morris, Illinois in 1960. The storage medium for the program instructions was the flying-spot store , a photographic plate read by an optical scanner that had a speed of about one microsecond access time. For temporary data,
4879-767: The EDSAC in Cambridge ran its first program, making it another electronic digital stored-program computer. It is sometimes claimed that the IBM SSEC , operational in January 1948, was the first stored-program computer; this claim is controversial, not least because of the hierarchical memory system of the SSEC, and because some aspects of its operations, like access to relays or tape drives, were determined by plugging. The first stored-program computer to be built in continental Europe
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4998-826: The Medal of Freedom to a crater on the Moon named in his honor. Von Neumann was born in Budapest , Kingdom of Hungary (then part of the Austro-Hungarian Empire ), on December 28, 1903, to a wealthy, non-observant Jewish family. His birth name was Neumann János Lajos. In Hungarian, the family name comes first, and his given names are equivalent to John Louis in English. He was the eldest of three brothers; his two younger siblings were Mihály (Michael) and Miklós (Nicholas). His father Neumann Miksa (Max von Neumann)
5117-868: 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 his influence in the 1950s, he chaired a number of Defense Department committees including the Strategic Missile Evaluation Committee and the ICBM Scientific Advisory Committee. He was also a member of
5236-590: The University of Cambridge Mathematical Laboratory was working on EDSAC . The NPL did not have the expertise to build a machine like ACE, so they contacted Tommy Flowers at the General Post Office 's (GPO) Dollis Hill Research Laboratory . Flowers, the designer of Colossus, the world's first programmable electronic computer, was committed elsewhere and was unable to take part in the project, although his team did build some mercury delay lines for ACE. The Telecommunications Research Establishment (TRE)
5355-534: The University of Göttingen on a grant from the Rockefeller Foundation to study mathematics under David Hilbert . Hermann Weyl remembers how in the winter of 1926–1927 von Neumann, Emmy Noether , and he would walk through "the cold, wet, rain-wet streets of Göttingen" after class discussing hypercomplex number systems and their representations . Von Neumann's habilitation was completed on December 13, 1927, and he began to give lectures as
5474-508: The identity operator . The von Neumann bicommutant theorem shows that the analytic definition is equivalent to a purely algebraic definition as being equal to the bicommutant . After elucidating the study of the commutative algebra case, von Neumann embarked in 1936, with the partial collaboration of Murray, on the noncommutative case, the general study of factors classification of von Neumann algebras. The six major papers in which he developed that theory between 1936 and 1940 "rank among
5593-604: The lattices of subspaces of inner product spaces ): Dimension is determined, up to a positive linear transformation, by the following two properties. It is conserved by perspective mappings ("perspectivities") and ordered by inclusion. The deepest part of the proof concerns the equivalence of perspectivity with "projectivity by decomposition"—of which a corollary is the transitivity of perspectivity. For any integer n > 3 {\displaystyle n>3} every n {\displaystyle {\mathit {n}}} -dimensional abstract projective geometry
5712-481: The universal constructor and the digital computer . His 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 . He developed the mathematical models behind the explosive lenses used in the implosion-type nuclear weapon . Before and after the war, he consulted for many organizations including
5831-549: The "circuit man" for a new computer project for which he had secured funding from the Royal Society . Having secured the support of the university, obtained funding from the Royal Society, and assembled a first-rate team of mathematicians and engineers, Newman now had all elements of his computer-building plan in place. Adopting the approach he had used so effectively at Bletchley Park, Newman set his people loose on
5950-523: The "problem is essentially group-theoretic in character": the existence of a measure could be determined by looking at the properties of the transformation group of the given space. The positive solution for spaces of dimension at most two, and the negative solution for higher dimensions, comes from the fact that the Euclidean group is a solvable group for dimension at most two, and is not solvable for higher dimensions. "Thus, according to von Neumann, it
6069-466: The "problem of measure" for an n -dimensional Euclidean space R may be stated as: "does there exist a positive, normalized, invariant, and additive set function on the class of all subsets of R ?" The work of Felix Hausdorff and Stefan Banach had implied that the problem of measure has a positive solution if n = 1 or n = 2 and a negative solution (because of the Banach–Tarski paradox ) in all other cases. Von Neumann's work argued that
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#17327734061406188-448: The Baby had performed about 3.5 million operations (for an effective CPU speed of about 1100 instructions per second ). The first design for a program-controlled computer was Charles Babbage 's Analytical Engine in the 1830s, with Ada Lovelace conceiving the idea of the first theoretical program to calculate Bernoulli numbers . A century later, in 1936, mathematician Alan Turing published his description of what became known as
6307-658: 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 his 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
6426-567: The TRE. Williams led a TRE development group working on CRT stores for radar applications, as an alternative to delay lines. Williams was not available to work on the ACE because he had already accepted a professorship at the University of Manchester , and most of his circuit technicians were in the process of being transferred to the Department of Atomic Energy. The TRE agreed to second a small number of technicians to work under Williams' direction at
6545-430: The United States was the mathematician Stanisław Ulam . Von Neumann believed that much of his mathematical thought occurred intuitively; he 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 his liking for abstract wit, he had a strong appreciation (one might say almost
6664-615: The analyst Gábor Szegő . By 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 his education at the gymnasium, he applied for and won the Eötvös Prize, a national award for mathematics. According to his friend Theodore von Kármán , von Neumann's father wanted John to follow him into industry, and asked von Kármán to persuade his son not to take mathematics. Von Neumann and his father decided that
6783-582: The best career path was chemical engineering . This was not something that von Neumann had much knowledge of, so it was arranged for him to take a two-year, non-degree course in chemistry at the University of Berlin , after which he sat for the entrance exam to ETH Zurich , which he passed in September 1923. Simultaneously von Neumann entered Pázmány Péter University in Budapest, as a Ph.D. candidate in mathematics . For his thesis, he produced an axiomatization of Cantor's set theory . He graduated as
6902-452: The binary digits ( bits ) 0 and 1. It exploited the positive or negative electric charge generated by displaying either a dash or a dot at any position on the CRT screen, a phenomenon known as secondary emission . A dash generated a positive charge, and a dot a negative charge, either of which could be picked up by a detector plate in front of the screen; a negative charge represented 0, and
7021-699: The construction of a more practical computer, the Manchester Mark 1 , work on which began in August 1948. The first version was operational by April 1949, and it in turn led directly to the development of the Ferranti Mark 1 , the world's first commercially available general-purpose computer. In 1998, a working replica of the Baby, now on display at the Museum of Science and Industry in Manchester ,
7140-437: The contributions of von Neumann to sets, the axiomatic system of the theory of sets avoided the contradictions of earlier systems and became usable as a foundation for mathematics, despite the lack of a proof of its consistency . The next question was whether it provided definitive answers to all mathematical questions that could be posed in it, or whether it might be improved by adding stronger axioms that could be used to prove
7259-580: The detailed work while he concentrated on orchestrating the endeavor. Following his appointment to the Chair of Electrical Engineering at Manchester University, Williams recruited his TRE colleague Tom Kilburn on secondment. By the autumn of 1947 the pair had increased the storage capacity of the Williams tube from one bit to 2,048, arranged in a 64 by 32-bit array, and demonstrated that it was able to store those bits for four hours. Engineer Geoff Tootill joined
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#17327734061407378-475: The difficult problem of characterizing the class of C G ( F ) {\displaystyle {\mathit {CG(F)}}} (continuous-dimensional projective geometry over an arbitrary division ring F {\displaystyle {\mathit {F}}\,} ) in abstract language of lattice theory. Von Neumann provided an abstract exploration of dimension in completed complemented modular topological lattices (properties that arise in
7497-484: The divisor. The Baby took 3.5 million operations and 52 minutes to produce the answer (131,072). The program used eight words of working storage in addition to its 17 words of instructions, giving a program size of 25 words. Geoff Tootill wrote an amended version of the program the following month, and in mid-July Alan Turing — who had been appointed as a reader in the mathematics department at Manchester University in September 1948 — submitted
7616-494: The early 1930s he proved the existence of proper invariant subspaces for completely continuous operators in a Hilbert space while working on the invariant subspace problem . With I. J. Schoenberg he wrote several items investigating translation invariant Hilbertian metrics on the real number line which resulted in their complete classification. Their motivation lie in various questions related to embedding metric spaces into Hilbert spaces. With Pascual Jordan he wrote
7735-474: The early Harvard machines were regarded as "reactionary by the advocates of stored-program computers". The concept of the stored-program computer can be traced back to the 1936 theoretical concept of a universal Turing machine . Von Neumann was aware of this paper, and he impressed it on his collaborators. Many early computers, such as the Atanasoff–Berry computer , were not reprogrammable. They executed
7854-440: The early hours of the morning and then deliver a lecture at 8:30. He was known for always being happy to provide others of all ability levels with scientific and mathematical advice. Wigner wrote that he perhaps supervised more work (in a casual sense) than any other modern mathematician. His daughter wrote that he was very concerned with his legacy in two aspects: his life and the durability of his intellectual contributions to
7973-422: The end," referring to Pascal's wager . He confided to his mother, "There probably has to be a God. Many things are easier to explain if there is than if there isn't." He died on February 8, 1957, at Walter Reed Army Medical Hospital and was buried at Princeton Cemetery . At the beginning of the 20th century, efforts to base mathematics on naive set theory suffered a setback due to Russell's paradox (on
8092-434: The existence of a set that belongs to itself. In his 1925 doctoral thesis, von Neumann demonstrated two techniques to exclude such sets—the axiom of foundation and the notion of class . The axiom of foundation proposed that every set can be constructed from the bottom up in an ordered succession of steps by way of the Zermelo–Fraenkel principles. If one set belongs to another, then the first must necessarily come before
8211-439: The first truly random-access memory . Described as "small and primitive" 50 years after its creation, it was the first working machine to contain all the elements essential to a modern electronic digital computer. As soon as the Baby had demonstrated the feasibility of its design, a project was initiated at the university to develop it into a full-scale operational machine, the Manchester Mark 1 . The Mark 1 in turn quickly became
8330-555: The influential Atomic Energy Commission in charge of all atomic energy development in the country. He 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 he was considered the nation's foremost expert on nuclear weaponry and the leading defense scientist at the U.S. Department of Defense . Von Neumann's contributions and intellectual ability drew praise from colleagues in physics, mathematics, and beyond. Accolades he received range from
8449-401: The machine calculated the highest proper divisor of 2 (262,144), by testing every integer from 2 downwards. This algorithm would take a long time to execute—and so prove the computer's reliability, as division was implemented by repeated subtraction of the divisor. The program consisted of 17 instructions and ran for about 52 minutes before reaching the correct answer of 131,072, after
8568-685: The machine's storage was described with the least significant digits to the left; thus a one was represented in three bits as "100", rather than the more conventional "001". The awkward negative operations were a consequence of the Baby's lack of hardware to perform any arithmetic operations except subtraction and negation . It was considered unnecessary to build an adder before testing could begin as addition can easily be implemented by subtraction, i.e. x + y can be computed as −(− x − y ). Therefore, adding two numbers together, X and Y, required four instructions: Programs were entered in binary form by stepping through each word of memory in turn, and using
8687-473: The masterpieces of analysis in the twentieth century"; they collect many foundational results and started several programs in operator algebra theory that mathematicians worked on for decades afterwards. An example is the classification of factors . In addition in 1938 he proved that every von Neumann algebra on a separable Hilbert space is a direct integral of factors; he did not find time to publish this result until 1949. Von Neumann algebras relate closely to
8806-486: The positive, and in later papers with Stone discussed various generalizations and algebraic aspects of this problem. He also proved by new methods the existence of disintegrations for various general types of measures. Von Neumann also gave a new proof on the uniqueness of Haar measures by using the mean values of functions, although this method only worked for compact groups . He had to create entirely new techniques to apply this to locally compact groups . He also gave
8925-411: The problem of measure in terms of functions. A major contribution von Neumann made to measure theory was the result of a paper written to answer a question of Haar regarding whether there existed an algebra of all bounded functions on the real number line such that they form "a complete system of representatives of the classes of almost everywhere-equal measurable bounded functions". He proved this in
9044-400: The properties of its lattice of linear subspaces . Von Neumann, following his work on rings of operators, weakened those axioms to describe a broader class of lattices, the continuous geometries. While the dimensions of the subspaces of projective geometries are a discrete set (the non-negative integers ), the dimensions of the elements of a continuous geometry can range continuously across
9163-466: The prototype for the Ferranti Mark 1 , the world's first commercially available general-purpose computer. The Baby had a 32- bit word length and a memory of 32 words (1 kilobit , 1,024 bits). As it was designed to be the simplest possible stored-program computer, the only arithmetic operations implemented in hardware were subtraction and negation ; other arithmetic operations were implemented in software. The first of three programs written for
9282-449: The reflections from which are displayed on a CRT screen. As operators are usually interested only in moving targets, it was desirable to filter out any distracting reflections from stationary objects. The filtering was achieved by comparing each received pulse with the previous pulse, and rejecting both if they were identical, leaving a signal containing only the images of any moving objects. To store each received pulse for later comparison it
9401-435: The remaining 16 bits were unused. The Baby's single operand architecture meant that the second operand of any operation was implicit: the accumulator or the program counter (instruction address); program instructions specified only the address of the data in memory. A word in the computer's memory could be read, written, or refreshed, in 360 microseconds. An instruction took four times as long to execute as accessing
9520-566: The rooms in the apartment was converted into a library and reading room. Von Neumann entered the Lutheran Fasori Evangélikus Gimnázium in 1914. Eugene Wigner was a year ahead of von Neumann at the school and soon became his friend. Although von Neumann's father insisted that he attend school at the grade level appropriate to his age, he agreed to hire private tutors to give von Neumann advanced instruction. At 15, he began to study advanced calculus under
9639-606: The same storage used for data. In 1948, the Manchester Baby , built at University of Manchester , is generally recognized as world's first electronic computer that ran a stored program—an event on 21 June 1948. However the Baby was not regarded as a full-fledged computer, but more a proof of concept predecessor to the Manchester Mark 1 computer, which was first put to research work in April 1949. On 6 May 1949
9758-429: The same year were the first monographs on Hilbert space theory. Previous work by others showed that a theory of weak topologies could not be obtained by using sequences . Von Neumann was the first to outline a program of how to overcome the difficulties, which resulted in him defining locally convex spaces and topological vector spaces for the first time. In addition several other topological properties he defined at
9877-429: The second in the succession. This excludes the possibility of a set belonging to itself. To demonstrate that the addition of this new axiom to the others did not produce contradictions, von Neumann introduced the method of inner models , which became an essential demonstration instrument in set theory. The second approach to the problem of sets belonging to themselves took as its base the notion of class , and defines
9996-615: The sense of the metric defined by the Hilbert norm and is a vector ψ {\displaystyle \psi } which is such that V t ( ψ ) = ψ {\displaystyle V_{t}(\psi )=\psi } for all t {\displaystyle t} . This was proven in the first paper. In the second paper, von Neumann argued that his results here were sufficient for physical applications relating to Boltzmann's ergodic hypothesis . He also pointed out that ergodicity had not yet been achieved and isolated this for future work. Later in
10115-406: The sense that they cannot prove every truth expressible in their language. Moreover, every consistent extension of these systems necessarily remains incomplete. At the conference, von Neumann suggested to Gödel that he should try to transform his results for undecidable propositions about integers. Less than a month later, von Neumann communicated to Gödel an interesting consequence of his theorem:
10234-409: The set of all sets that do not belong to themselves). The problem of an adequate axiomatization of set theory was resolved implicitly about twenty years later by Ernst Zermelo and Abraham Fraenkel . Zermelo–Fraenkel set theory provided a series of principles that allowed for the construction of the sets used in the everyday practice of mathematics, but did not explicitly exclude the possibility of
10353-404: The sign of a number; positive numbers have a zero in that position and negative numbers a one. Thus, the range of numbers that could be held in each 32-bit word was −2 to +2 − 1 (decimal: −2,147,483,648 to +2,147,483,647). The Baby's instruction format had a three-bit operation code field, which allowed a maximum of eight (2) different instructions. In contrast to the modern convention,
10472-411: The spectral theory of Hermitian operators from the bounded to the unbounded case. Other major achievements in these papers include a complete elucidation of spectral theory for normal operators , the first abstract presentation of the trace of a positive operator , a generalisation of Riesz 's presentation of Hilbert 's spectral theorems at the time, and the discovery of Hermitian operators in
10591-403: The storage electronics of the other three, was used as the output device, able to display the bit pattern of any selected storage tube. Each 32-bit word of RAM could contain either a program instruction or data. In a program instruction, bits 0–12 represented the memory address of the operand to be used, and bits 13–15 specified the operation to be executed, such as storing a number in memory;
10710-541: The study of nuclear operators on Banach spaces was among the first achievements of Alexander Grothendieck . Previously in 1937 von Neumann published several results in this area, for example giving 1-parameter scale of different cross norms on l 2 n ⊗ l 2 n {\displaystyle {\textit {l}}\,_{2}^{n}\otimes {\textit {l}}\,_{2}^{n}} and proving several other results on what are now known as Schatten–von Neumann ideals. Von Neumann founded
10829-409: The study of rings of operators, through the von Neumann algebras (originally called W*-algebras). While his original ideas for rings of operators existed already in 1930, he did not begin studying them in depth until he met F. J. Murray several years later. A von Neumann algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains
10948-445: The study of symmetric operator ideals and is the beginning point for modern studies of symmetric operator spaces . Later with Robert Schatten he initiated the study of nuclear operators on Hilbert spaces, tensor products of Banach spaces , introduced and studied trace class operators, their ideals , and their duality with compact operators , and preduality with bounded operators . The generalization of this topic to
11067-431: The study of von Neumann algebras and in general of operator algebras . His later work on rings of operators lead to him revisiting his work on spectral theory and providing a new way of working through the geometric content by the use of direct integrals of Hilbert spaces. Like in his work on measure theory he proved several theorems that he did not find time to publish. He told Nachman Aronszajn and K. T. Smith that in
11186-408: The system used a barrier-grid electrostatic storage tube . John von Neumann John von Neumann ( / v ɒ n ˈ n ɔɪ m ən / von NOY -mən ; Hungarian : Neumann János Lajos [ˈnɒjmɒn ˈjaːnoʃ ˈlɒjoʃ] ; December 28, 1903 – February 8, 1957) was a Hungarian and American mathematician , physicist , computer scientist and engineer . Von Neumann had perhaps
11305-443: The team on loan from TRE in September 1947, and remained on secondment until April 1949. Now let's be clear before we go any further that neither Tom Kilburn nor I knew the first thing about computers when we arrived at Manchester University ... Newman explained the whole business of how a computer works to us." Kilburn had a hard time recalling the influences on his machine design: [I]n that period, somehow or other I knew what
11424-482: The theory of almost periodicity to include functions that took on elements of linear spaces as values rather than numbers. In 1938, he was awarded the Bôcher Memorial Prize for his work in analysis in relation to these papers. In a 1933 paper, he used the newly discovered Haar measure in the solution of Hilbert's fifth problem for the case of compact groups . The basic idea behind this
11543-560: The third program, to carry out long division . Turing had by then been appointed to the nominal post of Deputy Director of the Computing Machine Laboratory at the university, although the laboratory did not become a physical reality until 1951. Williams and Kilburn reported on the Baby in a letter to the Journal Nature , published in September 1948. The machine's successful demonstration quickly led to
11662-399: The time (he was among the first mathematicians to apply new topological ideas from Hausdorff from Euclidean to Hilbert spaces) such as boundness and total boundness are still used today. For twenty years von Neumann was considered the 'undisputed master' of this area. These developments were primarily prompted by needs in quantum mechanics where von Neumann realized the need to extend
11781-684: The town; the appellation was chosen in reference to Margaret, as was their chosen coat of arms depicting three marguerites . Neumann János became margittai Neumann János (John Neumann de Margitta), which he later changed to the German Johann von Neumann. Von Neumann was a child prodigy who at six years old could divide two eight-digit numbers in his head and converse in Ancient Greek . He, his brothers and his cousins were instructed by governesses. Von Neumann's father believed that knowledge of languages other than their native Hungarian
11900-412: The unit interval [ 0 , 1 ] {\displaystyle [0,1]} . Von Neumann was motivated by his discovery of von Neumann algebras with a dimension function taking a continuous range of dimensions, and the first example of a continuous geometry other than projective space was the projections of the hyperfinite type II factor . In more pure lattice theoretical work, he solved
12019-429: The university, and to support another small group working with Uttley at the TRE. Although some early computers such as EDSAC, inspired by the design of EDVAC, later made successful use of mercury delay-line memory , the technology had several drawbacks: it was heavy, it was expensive, and it did not allow data to be accessed randomly. In addition, because data was stored as a sequence of acoustic waves propagated through
12138-631: The use of restrictions on induction ). He continued looking for a more general proof of the consistency of classical mathematics using methods from proof theory . A strongly negative answer to whether it was definitive arrived in September 1930 at the Second Conference on the Epistemology of the Exact Sciences , in which Kurt Gödel announced his first theorem of incompleteness : the usual axiomatic systems are incomplete, in
12257-421: The usual axiomatic systems are unable to demonstrate their own consistency. Gödel replied that he had already discovered this consequence, now known as his second incompleteness theorem , and that he would send a preprint of his article containing both results, which never appeared. Von Neumann acknowledged Gödel's priority in his next letter. However, von Neumann's method of proof differed from Gödel's, and he
12376-433: The widest coverage of any mathematician of his time, integrating pure and applied sciences and making major contributions to many fields, including mathematics , physics , economics , computing , and statistics . He was a pioneer in building the mathematical framework of quantum physics , in the development of functional analysis , and in game theory , introducing or codifying concepts including cellular automata ,
12495-422: The world. Many considered him an excellent chairman of committees, deferring rather easily on personal or organizational matters but pressing on technical ones. Herbert York described the many "Von Neumann Committees" that he 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
12614-507: The year he published another influential paper that began the systematic study of ergodicity. He gave and proved a decomposition theorem showing that the ergodic measure preserving actions of the real line are the fundamental building blocks from which all measure preserving actions can be built. Several other key theorems are given and proven. The results in this paper and another in conjunction with Paul Halmos have significant applications in other areas of mathematics. In measure theory ,
12733-564: Was a banker and held a doctorate in law . He had moved to Budapest from Pécs at the end of the 1880s. Miksa's father and grandfather were born in Ond (now part of Szerencs ), Zemplén County , northern Hungary. John's mother was Kann Margit (Margaret Kann); her parents were Kann Jákab and Meisels Katalin of the Meisels family . Three generations of the Kann family lived in spacious apartments above
12852-507: Was also approached for assistance, as was Maurice Wilkes at the University of Cambridge Mathematical Laboratory. The government department responsible for the NPL decided that, of all the work being carried out by the TRE on its behalf, ACE was to be given the top priority. NPL's decision led to a visit by the superintendent of the TRE's Physics Division on 22 November 1946, accompanied by Frederic C. Williams and A. M. Uttley, also from
12971-482: Was also of the opinion that the second incompleteness theorem had dealt a much stronger blow to Hilbert's program than Gödel thought it did. With this discovery, which drastically changed his views on mathematical rigor, von Neumann ceased research in the foundations of mathematics and metamathematics and instead spent time on problems connected with applications. In a series of papers published in 1932, von Neumann made foundational contributions to ergodic theory ,
13090-437: Was approximately a subset of the twelve operation instruction set proposed in 1947 by Jack Good, in the first known document to use the term "Baby" for this machine. Good did not include a "halt" instruction, and his proposed conditional jump instruction was more complicated than what the Baby implemented. Although Newman played no engineering role in the development of the Baby, or any of the subsequent Manchester computers , he
13209-618: Was built to celebrate the 50th anniversary of the running of its first program. Demonstrations of the machine in operation are held regularly at the museum. In 2008, an original panoramic photograph of the entire machine was discovered at the University of Manchester. The photograph, taken on 15 December 1948 by a research student, Alec Robinson, had been reproduced in The Illustrated London News in June 1949. Stored-program computer A stored-program computer
13328-474: Was committed to the development of a computer incorporating both Alan Turing 's mathematical concepts and the stored-program concept that had been described by John von Neumann . In 1945, he was appointed to the Fielden Chair of Pure Mathematics at Manchester University; he took his Colossus-project colleagues Jack Good and David Rees to Manchester with him, and there they recruited F. C. Williams to be
13447-423: Was discovered several years earlier when von Neumann published a paper on the analytic properties of groups of linear transformations and found that closed subgroups of a general linear group are Lie groups . This was later extended by Cartan to arbitrary Lie groups in the form of the closed-subgroup theorem . Von Neumann was the first to axiomatically define an abstract Hilbert space . He defined it as
13566-419: Was electromechanical rather than electronic. The earliest electronic computing devices were the Atanasoff–Berry computer (ABC), which was successfully tested in 1942, and the Colossus of 1943, but neither was a stored-program machine. The ENIAC (1946) was the first automatic computer that was both electronic and general-purpose. It was Turing complete , with conditional branching, and programmable to solve
13685-611: Was essential, so the children were tutored in English , French , German and Italian . By age eight, von Neumann was familiar with differential and integral calculus , and by twelve he had read Borel's La Théorie des Fonctions . He was also interested in history, reading Wilhelm Oncken 's 46-volume world history series Allgemeine Geschichte in Einzeldarstellungen ( General History in Monographs ). One of
13804-625: Was generally supportive and enthusiastic about the project, and arranged for the acquisition of war-surplus supplies for its construction, including GPO metal racks and "…the material of two complete Colossi" from Bletchley. Racks and Colossi parts were modified and assembled into chassis by Norman Stanley Hammond and others. By June 1948 the Baby had been built and was working. It was 17 feet (5.2 m) in length, 7 feet 4 inches (2.24 m) tall, and weighed almost 1 long ton (1.0 t). The machine contained 550 valves (vacuum tubes) —300 diodes and 250 pentodes —and had
13923-671: Was instrumental in his mean ergodic theorem . The theorem is about arbitrary one-parameter unitary groups t → V t {\displaystyle {\mathit {t}}\to {\mathit {V_{t}}}} and states that for every vector ϕ {\displaystyle \phi } in the Hilbert space , lim T → ∞ 1 T ∫ 0 T V t ( ϕ ) d t {\textstyle \lim _{T\to \infty }{\frac {1}{T}}\int _{0}^{T}V_{t}(\phi )\,dt} exists in
14042-565: Was passed through a transmission line, delaying it by exactly the time between transmitted pulses. Turing joined the National Physical Laboratory (NPL) in October 1945, by which time scientists within the Ministry of Supply had concluded that Britain needed a National Mathematical Laboratory to co-ordinate machine-aided computation. A Mathematics Division was set up at the NPL, and on 19 February 1946 Turing presented
14161-540: Was the MESM , completed in the Soviet Union in 1950. Several computers could be considered the first stored-program computer, depending on the criteria. The concept of using a stored-program computer for switching of telecommunication circuits is called stored program control (SPC). It was instrumental to the development of the first electronic switching systems by American Telephone and Telegraph (AT&T) in
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