Carl Friedrich Gauß

Record year1827

M rationaleCurvature, geodesics, and relations between curved triangles together give a coherent account of the local and global structure of surface geometry, establishing a foundation for research in that field. The scope remains limited to surface geometry. This item uses M6.1.

attribution rationaleThe author's text directly supports Gauss's completion of this theoretical construction; geometric prior work that cannot be determined item by item is retained as an unallocated share rather than invented for specific individuals.

Record year1813

M rationaleThe 1813 text gives the geometric setup and integral transformations inside and outside an ellipsoid, producing a general-method result for such gravitational problems; Newton, Maclaurin, Lagrange, and Legendre are explicit prior work, but their shares remain at the a level, and later potential-theory applications are not counted in M. This item adopts M5.7.

attribution rationaleGauss wrote the reviewed geometric setup and integral transformations; Newton, Maclaurin, Lagrange, and Legendre are prior work expressly identified in the text, but the available receipt cannot separate their specific roles, so the residual is not allocated by named person.

Record year1801

M rationaleA unified language and specialized notation for congruences, a rigorous proof of the quadratic reciprocity theorem, and auxiliary propositions jointly provide an executable procedure for determining quadratic residues. The final M places this definition-theorem-proof-procedure closed loop at 5.8; quadratic forms, regular polygons, other plans, and later applications are not combined.

attribution rationaleGauss completed and publicly delivered the framework; inherited number-theory inputs from Fermat, Euler, Lagrange, and Legendre, as well as the book-production team and publishing channel, remain in the ledger and are not absorbed by the personal share.

Record year1801

M rationaleThe basic properties of composition of quadratic forms provide a reusable operational structure for a mathematical object and are assessed at M5.4. This exceeds an isolated equation, but the item covers only limited properties and does not include all results of Section Five, the entire Disquisitiones Arithmeticae, or later applications in algebraic number theory.

attribution rationaleGauss is the named author of the treatment in Section Five and the result in Article 235. The acknowledged prior contributions of Lagrange, Euler, and Fermat cannot be apportioned individually from the available material, so a foundational share remains unallocated.

Record year1801

M rationaleThe regular seventeen-gon was reduced to four quadratic equations and given a cosine expression, combining a specific construction result with value as an algebraic method, assessed at M5.1. Only the construction for n=17 is counted; neither the general criterion for all regular polygons nor later cyclotomic theory is included.

attribution rationaleThe available original text names no co-producers of the regular seventeen-gon result. Euclid's precedents for dividing a circle into three and five equal parts are treated only as background, with no demonstrated role in producing this result; Gauss therefore receives the entire share.

Record year1823

M rationaleThe squared criterion, observation relations, elimination, and relative minimum jointly form a complete transferable method platform for general error observations; it does not yet constitute a complete probability theory or foundation of statistics. This item adopts M5.1.

attribution rationaleGauss publicly delivered the general error theory and its derivation; Legendre's prior least-squares work and unresolved prior work remain retained, so Gauss's share covers only delivery of this complete theory.

Record year1839

M rationaleA unified field representation on a global scale provides a methodological foundation for the discipline. The available evidence for the full scope of the theory is limited, so the magnitude is set only at the entry point to that level. This item uses M5.0.

attribution rationaleGauss completed and publicly delivered the theoretical construction of field components and a potential function; separate actions of Weber, observers, and teams are not evidenced, so remaining shares stay unallocated.

Record year1868

M rationale6.7 is above the general disciplinary-foundation centre because multidimensional metric, local curvature, and empirical boundaries jointly reconfigured the problem space of geometry; a complete modern axiomatic and operational system had not yet formed, and later transfer into physics is not included, so the score does not enter 8.

attribution rationaleIn the 1854 lecture, Riemann introduced multidimensional metric, local curvature, and empirical boundaries of physical measurement, taking the main share of mathematical content; posthumous editorial publication receives separate credit.

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 year1851

M rationaleThe complete 1851 framework changed the objects that could be handled and their methodological relations, reaching the global disciplinary-foundation tier; unresolved general proofs and later modern systems are not claimed. This item is assessed at M6.3.

attribution rationaleRiemann connected complex functions, branched surfaces, connectivity cuts, and conditional conformal constructions into a framework; the principal credit is for this synthesis and construction, while the specific predecessor methods used have separate shares.

Record year1809

M rationaleThe completed work combines multiple observations, a model of conic motion, corrections, and orbital elements into a reusable method of orbit determination. Its scope remains limited to inferring orbits around the Sun, so it is assessed as a complete general method within an important specialized field. This item uses M4.1.

attribution rationaleGauss publicly delivered the method, derivation, and a four-observation worked example; Piazzi's observations are explicit inputs, so Gauss receives the share for delivering the method rather than all results as personal credit.

Record year1833

M rationaleThis method established shared absolute-measurement capability for an important specialized field, exceeding a single procedure but remaining narrower than a general-method platform or complete field theory. This item adopts M4.2.

attribution rationaleGauss's public text explicitly gives the measurement method; specific actions of Weber and implementation teams in this limited result are not verified, so non-Gauss portions remain unallocated rather than being transferred to Gauss.

Record year1814–1816

M rationaleNon-equidistant nodes, weights, guarantees of exactness, and error handling form a reusable numerical-integration method, rated M4.0. This entry is limited to the original unweighted, fixed-interval construction; it does not include later general weights, software, or the whole field of numerical analysis.

attribution rationaleGauss was responsible for constructing and publicly delivering the method; this assessment still retains undifferentiated shares for prior history and support.

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 year1857

M rationaleAfter stripping away the shared 1851 apparatus, the 1857 inversion and theta increment remains an internationally important methodological system; the available facts are insufficient to treat this increment alone as equivalent to the foundation of an entire discipline. 5.8 is adopted.

attribution rationaleRiemann extended inversion from special cases such as elliptic ones and constructed the 1857 Abelian and theta methods, bearing the principal share for the generalization and methodological construction; Abel supplied the starting point of elliptic inversion, Jacobi supplied materials on elliptic inversion and theta functions and the technical comparison in the original work, Dirichlet supplied the proof route via the variational principle explicitly used in the original work, and Gauss corresponds only to input on local complex representation. The residual account retains only inputs or responsibility gaps not yet resolved through item-by-item verification and full-text review; prior-work special cases or proof routes are not equated with Riemann's delivered general inversion.

Record year1876

M rationale4.1 reflects a field-level increment formed jointly by a new concept and restricted relations; defective notation, editorial corrections, and incomplete general theory keep it below the middle of band 5.

attribution rationaleRiemann's manuscript proposed dimension-distinguished closed cycles that are not boundaries, connectivity, and restricted relations of variation, bearing the principal share for the concepts and relations; editorial corrections and publication are counted separately.

Record year1836–1841

M rationaleYears of coordinated observations, cross-site data, and atlases formed an ongoing professional service, rated M3.0. Stations, issues, tables, and plates are not scored separately; existing measurement methods and geomagnetic-field theory are not counted again in this entry.

attribution rationaleGauss had attributable theoretical and organizational roles in the magnetic network; Weber, Goldschmidt, the atlas authors, Humboldt, and unresolved work retain their respective or unallocated shares.

Record year1821–1823

M rationaleInstruments were used at multiple stations, with adjustment completed for 76 directions and 26 triangles, creating practical surveying capability, rated M2.5. Surveying uncertainty remained; later maps, nationwide surveying systems, and ideal precision are not included in this entry.

attribution rationaleGauss undertook leadership and methodological work in the adopted survey deployment; shares remain separately reserved for instrument manufacture, survey implementation, and collaborating personnel.

Record year1861

M rationale3.4 reflects that six conditions and their relations of independence form a reusable criterion, with independent confirmation of historical effect; the scope does not extend to general dimensions or all heat problems, keeping it far from band 5.

attribution rationaleRiemann completed sufficient conditions and a concrete criterion for constant-coefficient transformations of the three-dimensional heat equation, bearing the principal share; the early geometrical framework is not duplicated.

Record year1863

M rationale3.0 falls at the start of specialist-subfield-important results because the matching principle and application of hypergeometric quotients form a reusable method; the original manuscript is incomplete and convergence theory was completed by successors, limiting further elevation.

attribution rationaleRiemann's manuscript gives a matching method for finite asymptotic continued fractions and an application to hypergeometric quotients, bearing the principal share; subsequent convergence theory is not assigned to the manuscript.

Record year1833

M rationaleA line exceeding one kilometre actually transmitted complete words and short sentences, constituting an operational technical demonstration, rated M1.5. The present assessment scope confirms only a limited experiment and does not count sustained communication service or later telegraph networks.

attribution rationaleGauss and Weber each had identifiable joint production actions; Gauss therefore receives only a symmetric joint share with Weber, while the remainder stays unallocated.

Record year1858

M rationale2.9 approaches 3 because the preserved equation and fundamental potential are themselves complete and usable; the connected physical derivation contains major errors and lacks empirical closure, limiting the depth and coverage of the complete result.

attribution rationaleRiemann proposed the inhomogeneous wave equation and a retarded fundamental potential; the principal credit is limited to the valid mathematical structure, and the connected but erroneous physical derivation is not credited as a complete achievement.

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 year1854

M rationale1.6 reflects that equations and comparison with phenomena form a reusable model; it makes only qualitative comparisons and lacks apparatus parameters, keeping the center below the middle of band 2.

attribution rationaleRiemann organized equations for charge relaxation and made qualitative comparisons, constituting the principal delivery; adopted electrical relations, observations, and corrections retain shares separately.

Record year1854

M rationaleMeasures of bending for inextensible surfaces, limiting quadrilaterals, and conjugate directions provide a clear usable local geometrical explanation; an independent obituary confirms its specialist value. On this basis, the review treats it as a systematic explanation rather than an isolated definition, but no long-term structural change is established, nor is a general proof of convex-surface rigidity included. This item adopts M0.30.

attribution rationaleMaxwell organized the geometrical explanation and method for surface bending; explicitly adopted predecessor methods, including Gauss's, retain their respective credit.

Record year1877

M rationaleThe multidimensional construction and an independent formal paper on numerical integration confirm an early technical position, constituting local numerical-method help; the limitation that 27 points fall outside the integration domain remains. It does not claim one-dimensional predecessors, subsequent general quadrature, or the practical utility of sampling within the domain. This item adopts M0.30.

attribution rationaleMaxwell constructed the multidimensional quadrature method; the explicitly adopted quadrature results of Cotes and Gauss each retain a share, while unnamed general methods retain an unallocated part.