Leonhard Euler

Record year1752–1757

M rationaleInternal pressure fields, local momentum equations, and continuity form a general nonlinear continuum framework for ideal-fluid motion; it retains the limits of a smooth ideal medium, state/external-force inputs, and no general solution, and excludes viscosity, modern computation, and accumulated industrial benefits.

attribution rationaleEuler's formation of the general framework of internal pressure fields, momentum equations, and continuity receives 0.65; d'Alembert's fluid-PDE input receives 0.14, Bernoulli's fluid method 0.16, and the remaining 0.05 is unallocated. Newtonian classical mechanics has already been accounted for in the continuing effects of the original function of the Principia and cannot claim this item again merely as foundational influence; publication support likewise did not form the equations.

overlap boundaryThis counts only Euler's general new framework for ideal continuum fluids; Newtonian mechanics, as an already-accounted-for parent function, receives no further precursor share, and viscosity, modern computation, and industrial results are excluded.

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 year1750–1765

M rationaleRotational control and orientation reconstruction for extended rigid bodies form a general foundational capability; this excludes general integration, deformable systems, modern control, and all engineering.

attribution rationaleEuler developed new rotational, axis, and inertia devices and orientation calculations; existing mechanics and unresolved contemporary dependencies remain substantive inputs, and the d'Alembert pool is not presented as verified coauthorship.

Record year1736

M rationaleA systematic differential setup for the motion of physical point particles, including tangential/normal decomposition, forms a widely reusable basic scientific capability; it excludes all physical laws, later rigid-body/continuum work, and industrial implementation.

attribution rationaleEuler created a readable analytical-mechanics scheme; existing foundations in physics and calculus, directly acknowledged Bernoulli input, and actual publication support are all retained as other inputs.

Record year1748

M rationaleA coherent public framework for the language of analysis forms a foundational mathematical capability; it does not include all results in every chapter, nor is its scope inflated through fame or interval averaging.

attribution rationaleEuler organized functions and analytical methods into a coherent, readable public system; direct construction predominates and receives 67% attribution. Shares are separately retained for Johann Bernoulli and transmitted earlier analytical work, book production, and publication channels, with an additional unresolved input retained.

overlap boundaryThis item counts the systematic organization of functions, series, exponential and logarithmic functions, and trigonometric functions. Separately identifiable evaluations, identities, and constructions in the book are scored under their own outcomes, so their particular results are not counted again here; coordinate transformations and curve normalization in Volume II are also listed separately.

Record year1744

M rationaleThe general stationary-value condition replaces guessing curves one by one with a reusable class method; it includes only the original finite condition, not later Lagrange algorithms, existence theory, all physics, or individual elasticity applications.

attribution rationaleEuler's general derivation and public systematic result predominate; earlier isoperimetric and calculus inputs are listed separately, and later work by Lagrange is not retroactively counted as coauthorship.

Record year1737–1748

M rationaleThe exact bridge between reciprocal powers of positive integers and prime factorization is a widely reusable structural method; it is limited to the original identity for n>1 and excludes modern complex analysis and the prime number theorem.

attribution rationaleEuler led both the identity and its public exposition; factorization and series methods remain functional prerequisites, while Riemann's work and results on prime distribution are not retroactively counted.

overlap boundaryThis item counts the product identity between sums of reciprocal integer powers and prime factorization, limited to integer n>1; it does not repeat the particular evaluation of even reciprocal-power sums and excludes Riemann's complex-analytic method and the later prime number theorem.

Record year1744

M rationaleA reusable stability criterion involving load, stiffness, and length forms an important foundational science-and-engineering capability; its scope is limited to ideal buckling modes and is not equivalent to all beam theory or real structural benefits.

attribution rationaleEuler derived the physical instability threshold; Daniel Bernoulli's energy input has a substantive role, while the inherited tradition and subsequent industrial benefits are not converted into personal attribution.

Record year1753

M rationaleReusable encoding and effective counting methods across classes of additive problems form an international mathematical platform; they are limited to the demonstrated finite/formal methods and exclude later asymptotic theory and the separate pentagonal-number outcome.

attribution rationaleThe constructive work is attributed chiefly to Euler, while the problem posed by Naudé is retained; later combinatorial theorists are not retroactively written in as coauthors.

overlap boundaryThis item counts the method of encoding partition problems with generating functions, extracting coefficients, and counting them; the pentagonal product identity and divisor recurrence are listed separately and not counted again here.

Record year1768

M rationaleReusable algebraic comparison for non-elementary integrals advances foundational mathematical capability; it is limited to the original even-quartic construction and excludes complete elliptic functions, periods, inversion, modular theory, and applications.

attribution rationaleEuler's public addition construction predominates; Fagnano and the early tradition of integration retain conditional shares, and no quantifiable individual contribution is asserted when only institutional search excerpts are available.

Record year1763

M rationaleIndependently usable capabilities for composite moduli and residue-class counting extend arithmetic beyond the already-accounted-for prime number theorem; group theory and modern cryptography are not retroactively included.

attribution rationaleThe composite-modulus structure was constructed primarily by Euler; the earlier prime number theorem is acknowledged as a dependency but is not again treated as an independent Euler outcome.

Record year1738

M rationaleA definite-integral construction extends an integer sequence to non-integer arguments, forming a reusable new object/method; it does not include later complex Gamma theory, uniqueness, notation, or the entire theory of special functions.

attribution rationaleThe integral construction is Euler's leading work; verifiable inputs from Wallis and Goldbach and the uncertainty of earlier calculus are retained, and they are not absorbed into modern uniqueness results.

Record year1750–1760

M rationaleThe proved infinite-product structure and usable divisor recurrence provide connected discrete/analytic methods; they do not include all partition theory or later asymptotic results.

attribution rationaleEuler supplied the actual public derivation, and earlier conjectures/tentative recurrences belong to the same event; Franklin and Jacobi are not retroactively made coauthors, while support and residual uncertainty are retained.

overlap boundaryThis item counts once the proof of the pentagonal-product structure and its connected divisor recurrence; it does not repeat general partition generation and coefficient counting, nor list the earlier conjecture separately as a completed outcome.

Record year1748

M rationaleAn integrated procedure for coordinate transformation and conic normalization forms an internationally reusable platform; it does not claim modern geometry as a whole, complete curve classification, or a new origin for Cartesian coordinates.

attribution rationaleThe public work of transformation and normalization is attributed to Euler; dependencies on classical conics and Cartesian coordinates are retained, and authorship of a book is not itself equivalent to receiving all geometric attribution.

overlap boundaryThis item counts the specific procedure for coordinate transformation and conic normalization, not the overall organization of the analytic-function framework in Volume I; existing knowledge of conics and Cartesian coordinates is not counted as Euler's new discovery.

Record year1744

M rationaleFinite convergent-fraction recurrences and Euclidean division provide a reusable method of arithmetic approximation; Pell proofs, universal convergence of infinite continued fractions, and later periodicity theory are excluded.

attribution rationaleEuler organized the new convergent-fraction method; the expressly acknowledged work of Brouncker and Wallis, and methods of division, remain prerequisite inputs.

Record year1735–1740

M rationaleThe surviving exact sums and the route to evaluating even powers form an internationally important mathematical method beyond isolated numerical values; they do not include the prime product, later entire-function theory, or the separately accounted-for framework of analysis.

attribution rationaleEuler receives the principal attribution for the exact values and extension route, while the Bernoulli problem, series, and trigonometric/algebraic inputs are retained; later rigorization of infinite products is not retroactively counted.

overlap boundaryThis item counts the exact evaluation of even reciprocal-power sums and its extension method; it does not count the separately listed prime-product identity or repeat the overall value of the analytic-function framework.

Record year1767

M rationaleA nontrivial class of exact configurations provides useful celestial-mechanics knowledge; it excludes general three-body integration, stability, the full rotational framework, and spaceflight benefits.

attribution rationaleEuler's new solution of the fixed-ratio collinear configuration receives 0.90, with the remaining 0.10 reserved for specific formative inputs not yet closed. Newton's gravitational framework is an already-accounted-for precursor function; no other unaccounted-for new Newtonian act has been found in this item, and publication support is excluded.

overlap boundaryOnly the exact collinear three-body configuration is counted; continued use of Newton's gravitational framework does not generate another personal share for Newton, and general three-body integration, stability, and spaceflight applications are not counted.

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 year1768

M rationaleThe exactness criterion and integrating-factor construction for the stated first-order classes form a scalable solution method; they do not include a general method for finding factors or general ODE/PDE theory.

attribution rationaleCredit attaches only to the read public explanations and constructions of exactness and integrating factors; prior solution methods remain aggregated dependencies, and no precise individual priority is claimed where the sources are insufficient.

Record year1736–1747

M rationaleThe public general proof of divisibility of powers modulo primes provides reusable arithmetic reasoning rather than a list of examples; it does not include the phi theorem for composite moduli or Gauss's reciprocity law.

attribution rationaleThe reusable proof is credited to Euler; prior Fermat statements and inherited binomial/arithmetic methods have separately listed inputs, and repeated proofs in the same material are not counted again.

Record year1749

M rationaleThe stability/instability criterion for the stated floating-body geometry and density parameters provides a reusable technical method; it does not include an entire fleet, general ship dynamics, or actual deployment.

attribution rationaleThe public derivation is credited to Euler; prior statics foundations remain substantive but unspecified dependencies, with no conjecture about named coauthors or shares in realized vessels.

Record year1859

M rationaleAnalytic continuation, the functional equation, the xi function, and explicit inversion form a systematic connection across generations and thus belong to the disciplinary-foundation tier; the original text's incomplete proofs, the qualification of summing zeros, and the RH, prime number theorem, and successor L-function results are all excluded.

attribution rationaleRiemann connected analytic continuation, the functional equation, the xi function, zeros, and prime-counting inversion into a method, taking the principal synthesis and derivation share; unfinished conjectures and successor theorems are not included.

Record year1758

M rationaleThe class constraint linking combinatorial quantities provides reusable mathematical knowledge; it includes only valid discovery/exemplification knowledge, excluding gaps in general proof and later topology, and is separate from the parity/path conditions for bridges.

attribution rationaleThe public relation and exemplary constructions are chiefly credited to Euler; earlier independent records by Descartes/Maurolico do not prove a transmission relationship, so no named contribution is invented, and only conditional prior-geometry shares are retained.

Record year1755

M rationaleThe public finite-step operators, iterated differences, and rules of operation constitute a method of discrete calculation; the scope is limited to the read first chapter and does not include all interpolation, summation formulas, or modern numerical analysis.

attribution rationaleEuler led the systematic construction; the earlier difference/calculus traditions that he explicitly acknowledged remain substantive inputs, and he did not claim to have invented subtraction or numerical tables.

Record year1770

M rationaleA valid alternative general quartic representation obtained through a cubic resolvent is a reusable specialized algebraic capability; only this method is assessed, excluding all quartic solvability, general polynomial solving, and modern software.

attribution rationaleThis three-radical route is chiefly credited to Euler; existing quartic/resolvent traditions remain substantive inputs, and the production of the work is also retained, without converting them into invented named copying shares.

Record year1859–1860

M rationaleCharacteristic invariants, hodograph linearization, and a judgment of compressive steepening changed the field's capacity to handle finite plane gas waves, exceeding a local model; the scope remains limited to smooth, nondissipative plane waves, so it is only slightly above the center of band 5.

attribution rationaleRiemann gave the characteristic invariants, linearization, and judgment of compressive steepening for smooth plane gas waves; the Euler equations and other adopted gas relations retain input shares.

Record year1741

M rationaleThe reusable position/parity abstraction goes beyond a single recreational problem to form an enduring specialized method; the original bounded text does not provide the full modern sufficiency condition for Euler paths or applications of graph theory.

attribution rationaleEuler transformed the bridge problem into position and parity conditions and completed the public argument; the direct construction of the method receives 80% credit. The remaining 20% is reserved for unresolved supporting inputs, with no coauthors assigned without basis.

Record year1816

M rationaleIt completely proves the general factorization result for real polynomials, delivering mathematical knowledge that can be used repeatedly, rated M4.5. Its objects of application are broader than a single specialized procedure, but this one proof family is still insufficient to represent an entire methodological system or disciplinary reconstruction.

attribution rationaleGauss transformed preceding algebraic methods into an argument concerning indeterminates and completed a correct proof, receiving 75% credit; Euler's explicit methodological input of 20% and unresolved scholarly and publication support of 5% are retained.

Record year1857

M rationaleThe characterization of singularities, series, transformations, and conditional integral representations formed a unified interface for the second-order hypergeometric equation, hence slightly above the center of internationally important methods; general continuation and surface apparatus have already been claimed by the preceding item, and subsequent general existence theory is also excluded.

attribution rationaleRiemann organized the P-function, second-order equations, series, and integral representations through singularities, branches, and exponents; the principal credit is for this unified construction, while the prior results used are accounted for separately.

Record year1942

M rationaleM3.5: durable professional-subfield enumeration and complexity method with concrete independent later use; broader than one teaching example or alternative proof alone, narrower than international foundational computing capability. 3.0/3.7 vary this scope-weight judgment; not inferred from target score.

attribution rationaleJoint delivery and independent technical attribution support symmetric research responsibility. A .62 joint pool is retained after explicitly allocating credit to MacMahon’s starting problem/identity, Euler and Gupta’s methods, Goeltz computation and narrower formula/asymptotic inputs; each author gets .31 by source-symmetric judgment, not by author-count alone. There is no proof of an internal lead; .44/.24 mirrors are uncertainty alternatives, not assertions. Shannon’s 1938 application setup is within his personal row, not a new external charge or a duplicated 1938 outcome.

overlap boundaryOne 1942 joint knowledge family: proof of the MacMahon generating identity; enumeration and numerical recurrence schemes/table; rigorously derived comparison bounds and an almost-all switching-function series-parallel-realization lower bound. Their semi-empirical approximation is labelled as such; no exact asymptotic formula was found.

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 yearBy 1876

M rationaleCoordinates, equations, and boundary selection form a continuously reusable method and are deeper than a single worked example; but it reuses potential-theory and hypergeometric tools, treats only toroidal geometry, and has neither experimental, industrial, nor general-potential-theory coverage, so it lies near band 3.

attribution rationaleRiemann completed the coordinates, equation transformation, separation, and selection of boundary solutions for toroidal geometry, bearing the principal share for the specific method; general potential-theory and hypergeometric inputs retain credit separately.

Record year1849

M rationaleThe relations among fixed curves, roulette curves, and pole trajectories, together with the catenary example, form connected usable constructions richer than a single hint, adopting the local-method scale M0.30. Although modern demonstrations reproduce similar mathematics, they cannot yet establish sustained adoption of this original achievement.

attribution rationaleMaxwell completed the specific construction of the roulette curve; the Willis–Euler method chain explicitly adopted in the original text retains a share, while comparisons based only on historical priority are not counted as actual inputs.