John von Neumann

Record year1928

summaryProved the minimax theorem for finite two-person zero-sum games under mixed strategies.

M rationaleIt establishes the central existence/duality conclusion of a new theoretical field, slightly above Watt's mature-system M5.8; but its object is far narrower than Shannon's information theory M7, hence M6.0.

attribution rationaleAuthorship, joint research, and predecessor roles are provisionally estimated from existing sources; the complete budget retains unidentified inputs. Neither byline order nor citation count is treated as a contribution share.

overlap boundaryThe minimax conclusion for finite two-person zero-sum games under randomized strategies; it does not include all of game theory, general equilibrium, or N08B/C.

Evidence gapsThe 1928 original proof has not been read; predecessor budget and Borel's role await verification. The number of mathematical prerequisites cannot mechanically be converted into a deduction.

Record year1929

summaryExtended the study of Hilbert-space operators to unbounded cases and established related mathematical tools.

M rationaleMore abstract than ACE M5's single computer-design report and reusable across several mathematical-physics problems, hence 0.6 higher; below a complete M6 new theoretical system because the current scope is a tool family rather than operator-algebra classification or the quantum axioms as a whole.

attribution rationaleAuthorship, joint research, and predecessor roles are provisionally estimated from existing sources; the complete budget retains unidentified inputs. Neither byline order nor citation count is treated as a contribution share.

overlap boundaryN02 exclusively claims the value of general mathematical tools for unbounded/self-adjoint operators and related spectral theory; N03, N06, and N07C only use it as a consumed input.

Evidence gapsThe original works and itemized predecessor shares have not all been read; this is currently a provisional candidate with publicly missing evidence. Both M/a are revisable research judgments.

Record year1936–1943

summaryDeveloped the structural theory of operator algebras with Murray.

M rationaleRelative to N02 M5.6, N03 adds sustainable algebraic objects, structures, and a classification system, hence 0.4 higher; it remains below Shannon M7's cross-domain general theory.

attribution rationaleAuthorship, joint research, and predecessor roles are provisionally estimated from existing sources; the complete budget retains unidentified inputs. Neither byline order nor citation count is treated as a contribution share.

overlap boundaryThe numbered paper series is combined as one family of operator-ring/algebra structures and classifications; Hilbert-space and general unbounded-operator tools are consumed from N02 and do not raise M again.

Evidence gapsThe original works and itemized predecessor shares have not all been read; this is currently a provisional candidate with publicly missing evidence. Both M/a are revisable research judgments.; The location of specific independent structures in the originals still needs to be supplied, but does not block the public provisional estimate.

Record year1927–1932

summaryOrganized the mathematical expression of quantum mechanics through states and observables in Hilbert space.

M rationaleIn the same band as N02 M5.6 but from a different source of value: N02 is a general mathematical tool, N06 is a unified organization of quantum-theoretical objects; both cover more broadly than ACE M5 and remain below Shannon M7.

attribution rationaleAuthorship, joint research, and predecessor roles are provisionally estimated from existing sources; the complete budget retains unidentified inputs. Neither byline order nor citation count is treated as a contribution share.

overlap boundaryOnly the public mathematical formalization organizing quantum states, observables, and axioms is included; physical discoveries, N02's general operator tools, N07Q's statistical theorem, and universal exclusion of hidden variables are all excluded.

Evidence gapsThe original works and itemized predecessor shares have not all been read; this is currently a provisional candidate with publicly missing evidence. Both M/a are revisable research judgments.; The joint ledger must mark N02 as CONSUMED_TOOL rather than claim tool value a second time.

Record year1945

summaryOrganized the arithmetic, control, storage, and input-output logic of a stored-program computer, and produced a public design report.

M rationaleRelative to ACE M5, the EDVAC report supplied an earlier and more widely disseminated complete stored-program logical framework, hence 1.0 higher; it remains below Shannon M7's cross-domain theory. John's 13% in the ACE row only represents an EDVAC input and does not retroactively raise all ACE value into N09A.

attribution rationaleAuthorship, joint research, and predecessor roles are provisionally estimated from existing sources; the complete budget retains unidentified inputs. Neither byline order nor citation count is treated as a contribution share.

overlap boundaryThe 1945 EDVAC stored-program logical design and public report retains multiple technical inputs; N09D claims only residual implementation for the actual IAS engineering, and the later ACE design claims only its added construction, while the existing 13% is a specific predecessor input.

Evidence gapsRead contemporaneous discussion records to verify individual technical increments and shares; 35/50/15 is a public attribution scaffold and cannot be split into unsupported fine-grained personal ratios.; The IAS working machine and cross-institution replication materials supply a downstream-adoption anchor; they only support that the architecture received engineering uptake, not each person's inventive share in N09A.

Record year1925–1929

summaryDeveloped a first-order axiomatization scheme for set theory, providing a basis for later system revisions.

M rationaleRelative to Church M5's specialized formal system, N01 covers set theory's foundational objects and first-order axiomatic organization, with broader methodological reach, hence 0.4 higher; it remains substantially below Shannon M7's cross-disciplinary foundational platform.

attribution rationaleAuthorship, joint research, and predecessor roles are provisionally estimated from existing sources; the complete budget retains unidentified inputs. Neither byline order nor citation count is treated as a contribution share.

overlap boundaryOnly the original 1925–1929 family of first-order axiomatization schemes is included; Bernays's revisions and Gödel's later results do not enter its intrinsic value.

Evidence gapsThe original works and itemized predecessor shares have not all been read; this is currently a provisional candidate with publicly missing evidence. Both M/a are revisable research judgments.; Existing uptake evidence still rests mainly on Bernays's retrospective and must retain the calibration-required marker.

Record year1931–1932

summaryProved strong convergence of time averages of unitary operators, connecting dynamical systems and operator methods.

M rationaleAs a reusable convergence tool for general dynamical systems, it belongs with Watt's condensation method M5.2 in the general-method band; it is above the more conditionally narrow N07Q M4.5 and below N02 M5.6's general unbounded-operator tool family.

attribution rationaleAuthorship, joint research, and predecessor roles are provisionally estimated from existing sources; the complete budget retains unidentified inputs. Neither byline order nor citation count is treated as a contribution share.

overlap boundaryOnly strong/L2 convergence of ergodic averages for unitary operators in Hilbert space is included; Koopman supplies the operator-theoretic predecessor. Birkhoff's pointwise theorem, 1929 quantum ergodicity, and duplicate theorem value from physical applications are excluded.

Evidence gapsThe 1932 original paper has still not been read in this round, and the modern abstract formulation comes from Halmos's retrospective; leads on Carleman and other independent proofs and Weil's suggestion await primary-source reading; the 1932 original has not been read through; Carleman's independent proof and Weil's suggestion still await primary-source reading.

Record yearLate 1940s–1966

summaryStudied how abstract automata can construct and reproduce themselves; Burks organized and completed unfinished portions.

M rationaleIn the same band as ACE M5: both are bounded, generally applicable computational constructions that were not fully physically realized; modern artificial life and biotechnology are not borrowed to raise it into the mature-system band.

attribution rationaleJohn's conception/posthumous papers 60%, Burks's technical completion 20%, Ulam's simplified-model input 10%, Turing's methodological predecessor 5%, unknown 5%; all are rough estimates.

overlap boundaryOnly the formal scheme for general construction and description copying, together with Burks's technical completion of the unfinished design, is included; probabilistic reliable logic N11A, stored-program N09A, actual self-reproducing hardware, energy closure, and every later cellular automaton are excluded.

Evidence gapsThe details of Chapter Five of the original book have not been checked page by page; Ulam's model input is cited from a research monograph's quotation of original materials; Chapter Five has not been checked page by page; part of Ulam's input comes from the monograph's quotation.

Record year1944

summaryJointly organized with Morgenstern the framework of game information structures, allocations, and cooperative solutions.

M rationaleThis framework adds formal organization of multiple game structures beyond ACE M5, but its current terminal and adoption chain is less clear than that of a single theorem; reduced from 5.5 to 5.3, below N08A M6.

attribution rationaleAuthorship, joint research, and predecessor roles are provisionally estimated from existing sources; the complete budget retains unidentified inputs. Neither byline order nor citation count is treated as a contribution share.

overlap boundaryAs one book-level joint-framework episode in the 1944 coauthored work, it claims the combined increment of information-set/extensive-form organization and cooperative-game formalization; its two internal content classes may no longer be separately counted toward M. N08A's minimax proof, N08C's utility representation, and later specific cooperative-solution concepts are explicitly excluded.

Evidence gapsChapter-level differences in the original book have not been fully read; symmetric shares are provisional rather than proven divisions of labor; it does not claim that all cooperative games have solutions.; 40/40 is a symmetric provisional estimate under joint authorship and does not claim measured division of labor.

Record year1934–1935

summaryExtended the study of almost-periodic functions to groups and continued developing this method with Bochner.

M rationaleThe residual theory remains a reusable framework for group analysis, in the same band as ACE M5; because the key equivalence is explicitly excluded, the former broader scope no longer supports the 5.2 band of Watt's condensation method.

attribution rationaleAuthorship, joint research, and predecessor roles are provisionally estimated from existing sources; the complete budget retains unidentified inputs. Neither byline order nor citation count is treated as a contribution share.

overlap boundaryOnly the increment in the 1934 extension to groups and the 1935 coauthored sequel apart from the left/right almost-periodicity equivalence is included. The adopted Turing shared row continues to exclusively claim the intrinsic value of that equivalence.

Evidence gapsThe original works and itemized predecessor shares have not all been read; this is currently a provisional candidate with publicly missing evidence. Both M/a are revisable research judgments.; A machine-checkable EXCLUDES relation must be retained; restoring vague value for the whole paper is prohibited.

Record year1937

summaryArgued for the existence of an expansion equilibrium in a specified linear economic model.

M rationaleSlightly broader than N10A M4.5's specialized error analysis because it reaches economic-equilibrium structure, but narrower than N08C M5's general representation of risk and N08A M6's core theorem.

attribution rationaleAuthorship, joint research, and predecessor roles are provisionally estimated from existing sources; the complete budget retains unidentified inputs. Neither byline order nor citation count is treated as a contribution share.

overlap boundaryLimited to equilibrium existence in a specified linear-activity expansion model; the 1932 report, 1937 publication, and later English translation are one results chain and do not duplicate M.

Evidence gapsThe original paper and comparison with Wald's work have not been read; proof-tool duplicate value and conditions of application need checking.

Record year1946–1949

summaryAdvanced computer-based random-sampling methods jointly with Ulam, Metropolis, Klára, and others.

M rationaleIt adds a computational-sampling paradigm transferable across problems beyond ACE M5, hence 5.5; it remains below mature engineering systems M5.8 and more complete theoretical systems.

attribution rationaleParticipant accounts distinguish conception, planning, and implementation: Ulam 30%, John 25%, Metropolis 20%, Klára 10% are rough estimates rather than measurements; the other pool totals 15%.

overlap boundaryOnly the 1946–1949 organization of existing statistical sampling into an electronically executable scheme and its early implementation is included; the invention of statistical sampling, the 1953 Metropolis algorithm, ENIAC hardware, all later simulation, and wartime consequences are excluded.

Evidence gapsParticipants' late-life recollections have not been cross-verified against all contemporaneous documents; full wartime consequences remain independently unquantified, and no net lifetime score is claimed; role breakdown mainly comes from Metropolis's late-life recollections and has not been cross-checked against all contemporaneous documents.

Record year1944–1947

summaryStudied with Morgenstern the representation of choices under risk by expected utility under preference axioms.

M rationaleLike ACE M5, it is a formal framework reusable across specific applications; its scope is narrower than N08A's disciplinary-foundation reach as a minimax core theorem, hence 1.0 lower.

attribution rationaleAuthorship, joint research, and predecessor roles are provisionally estimated from existing sources; the complete budget retains unidentified inputs. Neither byline order nor citation count is treated as a contribution share.

overlap boundaryOnly expected-utility representation under preference axioms and later proof additions are included; all real choices and behavioral economics are not included.

Evidence gapsThe original book's axioms and version page numbers are needed; Ramsey, Bernoulli, Menger, and other dependencies remain only in a predecessor pool and are not presented as settled named percentages.

Record year1929

summaryProved that closed groups of linear transformations in finite-dimensional space have Lie-group structure.

M rationaleIt is a clear reusable structural theorem, in the same band as N10A's numerical-error method M4.5; its scope is narrower than N02's general operator tools M5.6.

attribution rationaleAuthorship, joint research, and predecessor roles are provisionally estimated from existing sources; the complete budget retains unidentified inputs. Neither byline order nor citation count is treated as a contribution share.

overlap boundaryThe 1929 conclusion is limited to closed finite-dimensional linear groups being Lie groups; it does not include Cartan's later general closed-subgroup result, 1933 compact locally Euclidean groups, or the full Hilbert fifth problem.

Evidence gapsThe original works and itemized predecessor shares have not all been read; this is currently a provisional candidate with publicly missing evidence. Both M/a are revisable research judgments.

Record year1929

summaryUnder explicit conditions on energy levels and macroscopic partitions, proved ergodic and entropy results for quantum systems.

M rationaleIt depends more on specified quantum-statistical conditions and has narrower general-tool coverage than N07C M5.2, hence 0.7 lower; like N10A M4.5, it is a specialized mathematical method with explicit conditions.

attribution rationaleThe named paper author provisionally bears 65% for this proof work; foundational dependencies remain a combined pool of 25% and unknown 10%. Literature citations are not mechanically converted into named percentages. Attribution standards must be symmetrically rechecked against other original theories.

overlap boundaryLimited to the 1929 family of quantum-ergodic/H-theorem proofs under conditions of energy levels, energy gaps, and macroscopic partitioning; it does not claim unconditional thermalization or monotonic entropy everywhere, and does not consume the 1932 classical mean ergodic theorem.

Evidence gapsThe introduction, theorem conditions, and discussion in the English translation of the original have been read, but the whole proof has not been checked formula by formula; shares and applicability impact remain revisable.

Record year1952–1956

summaryStudied how reliable computation can be constructed through redundant organization when components may fail.

M rationaleThe original gives multilayer error control and multiplexing constructions, which Moore–Shannon later explicitly adopted and improved. It provisionally takes 4.5 using Church's bounded synthesis method M4.5 as a neighboring anchor, distinguished from the later specialized relay result M3.7; it does not count device practicalization, the entire field of reliable computation, or unfinished thermodynamic theory.

attribution rationaleThe theoretical-results budget retains only the person's candidate share and a predecessor/history-to-check/unknown pool; acknowledgments, records, and institutional support remain in the role list but have no separate share for this item.

overlap boundaryThe 1952 lecture and 1956 publication form one results chain; majority voting, multiplexing, lecture, and publication are not each separately given full credit. It is distinguished from Shannon's reliable-relay result; the existing 16% predecessor budget still needs joint-ledger review for duplicate value with this item.

Evidence gapsKey formulas in the original scan and retypeset text have not yet been checked character by character.; Full error-independence and random-wiring conditions have not been formally reverified.

Record year1933

summaryUsed methods including group-invariant measures to address the analytic structure of locally Euclidean groups in the compact case.

M rationaleLike N05A, it advances bounded Lie structure, but abstracts to compact locally Euclidean groups without a presupposed linear representation and relies on Haar measure; applicability remains limited by compactness, hence M4.4, near but slightly below N05A.

attribution rationaleAuthorship, joint research, and predecessor roles are provisionally estimated from existing sources; the complete budget retains unidentified inputs. Neither byline order nor citation count is treated as a contribution share.

overlap boundaryThe 1933 result is limited to compact locally Euclidean topological groups having analytic parameters, and explicitly uses Haar measure. It is neither a duplicate of N05A's linear-group special case nor the complete Hilbert fifth problem.

Evidence gapsThe original works and itemized predecessor shares have not all been read; this is currently a provisional candidate with publicly missing evidence. Both M/a are revisable research judgments.

Record year1946–1960

summaryTogether with Bigelow and other engineers, implemented the logical design as the IAS computer and spread engineering experience through reports and personnel exchange.

M rationaleRelative to the ACE design report M5, this item adds an operating general research machine and public engineering replication, hence 5.2; but the stored-program principle has already been claimed by N09A and cannot be raised to M6 as a complete computing architecture or all applications.

attribution rationaleJohn was responsible for project initiation, logical direction, and organization; Bigelow for core engineering realization; Goldstine's and Burks's organizational/logical inputs are listed separately; other engineering, programming, and maintenance staff form a combined pool. The proportions are coarse research valuations, not measurements of personnel workload. The institution claims only its role in providing project conditions and does not duplicate individual engineering labor.

overlap boundaryOnly the residual implementation increment that realized already existing stored-program logic as an operating IAS machine and produced engineering reports and cross-institution replication is included. N09B's logical report and N09C's programming report enter this delivery chain and do not establish separate M; N09A exclusively claims the stored-program logic itself. N10B weather and N10C sampling methods are likewise not claimed by the machine-implementation item.

Evidence gapsProject funding, operating costs, each member's specific share, and net consequences of all uses have not been adjudicated; wartime and nuclear-weapons-related uses are documented, so completing a computing task cannot automatically be interpreted as a net positive civilizational consequence; Bigelow's core engineering role has direct support, while other engineers, programmers, and maintainers must remain in a team pool.; Military funding and wartime and nuclear-weapons uses are unknown net consequences and cannot be inferred from contracts or task completion to be positive civilizational-safety benefits.

Record year1950

summaryTogether with Charney and Fjørtoft, combined a simplified weather model with real data and completed four conditional numerical forecasting trials.

M rationaleLike ACE M5, it is a bounded method system closing model, computation, and actual trials; no evidence supports claiming all later weather-forecasting benefits to raise it to the general-system M5.8.

attribution rationaleWithout fine-grained evidence of divisions of labor, the coauthors are symmetrically provisionally estimated at 25% each, not shares measured from authorship. The text separately identifies actual work in coding instruction/verification, data preparation, and operation; these form a 15% combined pool rather than being split by acknowledgment headcount. The 5% predecessor history and 5% unknown are revisable estimates.

overlap boundaryOnly the closed loop of the 1950 barotropic-vorticity model, boundary-stability treatment, and four trials using observed 500mb data for 24 hours is included; the four trials are not split into four pieces, and ENIAC hardware or later operational forecasting systems are not counted.

Evidence gapsThe three authors' internal workloads and proportions of technical contribution have not been confirmed by contemporaneous divisions of labor; all experimental figures and stability derivations have not been checked page by page; these trials are not used to prove the benefit scale of long-term operational forecasting; the three authors lack a fine-grained contemporaneous division of labor, and 25/25/25 is a symmetric provisional estimate.

Record year1947–1951

summaryStudied rounding errors and conditioning limits in numerical matrix computation with Goldstine.

M rationaleIn the same band as the adopted Turing 1948 conditional-error method M4.5; its scope is narrower than ACE M5's computing architecture. The Turing row should count only his independent extension and cannot again fully claim the positive-definite conclusion already counted by this item.

attribution rationaleThe coauthored analysis is provisionally symmetric at 40% each, retaining an existing-method and unknown pool; the figures are normative judgments.

overlap boundaryThe 1947/1951 series is combined as finite-precision matrix-inversion error analysis; it does not claim Gaussian elimination, Turing's 1948 independent extension, complete backward-error theory, or all scientific computing.

Evidence gapsThe full 1947/1951 originals have not been checked, and the series' internal theorems are not yet separated; Turing's existing combined-pool 7% cannot be transferred wholesale to John; the 1947/1951 originals have not been read through; current grounds include the introduction to Turing's original, Wilkinson's abstract, and the IAS attribution directory.

Record year1946

M rationaleA specific stored-program machine design organized computation, storage, and control as realizable architectural capabilities; it does not include actual construction, other machine paths, or the modern computing industry.

attribution rationaleTuring completed ACE's architectural design; von Neumann's pre-existing stored-program work and unallocated engineering inputs are retained and not erased by report authorship.

Record year1950

summaryCharacterize bargaining solutions using comparable feasible utility sets and several axiomatic constraints, making fairness/efficiency claims an explicitly debatable model.

M rationaleThe 1950 original explicitly defines the scope of mutually beneficial two-person cooperation and thanks von Neumann and Morgenstern for their review; the academic introduction notes that independence of irrelevant alternatives has long been controversial. It is assigned M6.0 for its independent axiomatic method and sustained analytical use.

attribution rationaleNash .47; von Neumann .04; Morgenstern .04; prior history .25; institutions .05; unresolved .15.

overlap boundaryThe 1950 'The Bargaining Problem' provides an axiomatic model and unique solution characterization for situations of mutually beneficial two-person cooperation; it does not count union, monopoly, diplomacy, or real-world policy outcomes as delivered, nor does it merge with non-cooperative equilibrium.

Evidence gapsThe direct intellectual prehistory of each axiom and the content of review suggestions remain unresolved/not verified; empirical applicability and power asymmetry boundaries have not been systematically evaluated.

Record year1956

M rationaleThe specific reliability construction and scale bounds exceed a single technique and define a clear problem class, but are insufficient to establish a broader international methodological platform; central M = 3.7.

attribution rationaleMoore and Shannon each receive 37%; prior work on the von Neumann problem 16%, the McCulloch/Pitts model pool 3%, and unknown 7%. The individual division of proof work is unknown; the shares are normative judgments.

Evidence gapsExisting sources and a limited set of principal families are retained for the assessment; evidence of continued use, independent alternative paths, and predecessor contributions is not exhaustive. This revision did not reread the full texts of all original works.

Record year1937–1938

M rationaleThe finite-approximation conclusion within connected Lie groups is a reusable specialized group-theory method; the original proposition cannot unconditionally extend to disconnected groups, so no broader disciplinary-foundation claim is made.

attribution rationaleTuring completed the proof subject to the connectedness condition; Jordan's and von Neumann's predecessor tools and publication support are retained, and finite-group counterexamples are not ignored.

Record year1935

M rationaleA finite, verifiable equivalence proof provides specialized mathematical knowledge, but shows neither a cross-domain platform nor broad application and is therefore limited to the scale of a specialist method.

attribution rationaleTuring proved the equivalence of two definitions of almost periodicity; Bohr's almost-periodic theory remains a prerequisite, and the definitional tradition is not rewritten as Turing's sole invention.

Record year1935–1936

summaryCo-chaired a mathematics seminar with Veblen in 1935–1936.

M rationaleOnly one ongoing collaborative seminar service in 1935–1936 is assessed, below long-term teaching and cultivation service; it does not inherit participants' later achievements, and session counts and attendance still need to be supplied.

attribution rationaleAuthorship, joint research, and predecessor roles are provisionally estimated from existing sources; the complete budget retains unidentified inputs. Neither byline order nor citation count is treated as a contribution share.

Evidence gapsSpecific sessions, attendance, and lecture notes have not been obtained; the provisional estimate is retained.