Gottfried Wilhelm Leibniz

Record year1660s–early 18th century

M rationaleTake 7.3. General differential/integral calculus incorporates rates of change, accumulation, tangents, quadrature, and curve problems into a reusable method family, constituting a cross-generational global mathematical foundation, meeting M7. Lowering it to M6 would mistake it for a specialized technique; approaching M8 would double-count the entirety of later analysis, standard notation, textbooks, and scientific/engineering applications. A common origin does not lower the M of the achievement itself; the shares of Newton, Leibniz, and precursors are left to a.

attribution rationaleNewton and Leibniz independently formed the general differential/integral method, each taking 0.37; identifiable precursors like Barrow, Wallis, Descartes, Mercator, etc., collectively take 0.21, with 0.05 unallocated. Early publication and adoption demonstrate dissemination and continuous effect, not common origin formation.

overlap boundaryM counts only the general differential/integral method family and its continuous foundational function; later analysis, standard notation extensions, textbooks, and engineering applications are not double-counted. All holders share this single budget.

Evidence gapsFollowing existing sources and limited primary family assessments; not exhausting continuous use, independent alternative paths, and evidence of precursor contributions. This revision did not re-read all original works in full. Evidence of direct use across generations at high M levels must provide specific source locations, just as evidence for contributions in philosophy must and cannot be exempted by familiar conclusions from the history of science; named precursors receiving credit again must likewise be checked for duplicate attribution.

Record year1686–1714

summaryInterconnected works including Discourse on Metaphysics, New System, New Essays, Theodicy, and Monadology place sufficient reason, simple entities, classifications of truth, the mind-body relation, knowledge, and problems of evil and freedom into one network of arguments. What is recorded here is the works and their discussable arguments; their ontological claims are not treated as established facts.

M rationaleM5.9 is assigned: SEP confirms several major works and related but non-identical principles, while passages of Monadology that have been checked provide direct textual vehicles for simple entities, the principle of contradiction, sufficient reason, and classifications of truth. One broad corpus avoids repeated scoring by the concepts of monads, reason, harmony, epistemology, and theodicy; M assesses its cross-problem argumentative resources and continuing discussability, without making acceptance of its ontology a condition of the score.

attribution rationaleLeibniz 0.42; ancient, scholastic, and early modern philosophical prehistory 0.25; correspondents and opponents in debate 0.08; editing, publication, and translation 0.09; preserving institutions 0.04; unresolved textual boundaries 0.12.

overlap boundaryThe major mature philosophical texts from 1686 to 1714 are treated as one interconnected corpus: sufficient reason and the principle of contradiction, the distinction between truths of reason and truths of fact, monads and simple entities, mind-body coordination, innate ideas and perception, and questions of theodicy. The concepts are interconnected but do not each create an M by term; only the works, argumentative structure, and resources for discussable questions are counted. These propositions are not treated as established natural facts, and no claim is made to later rationalism, German idealism, or analytic philosophy.

Evidence gapsThe relevant passages on pre-established harmony in New System, the central arguments on evil and freedom in Theodicy, and the epistemological text of New Essays still require direct checking. ; The relations among manuscripts, first publications, delayed publications, and modern critical editions of the major works require bibliographical closure. ; Cross-period influence should distinguish direct reading, later reconstruction, and independently similar arguments.

Record year1686–c. 1700

summaryLeibniz used equivalence in raising and lowering and Galileo's falling-body relations to challenge Descartes's scalar quantity of motion, and used the mv² 'living force' to discuss collisions and dynamics. He directly absorbed Huygens's ideas on collisions and squared velocity; this entry is not equivalent to Newton's laws of motion, modern momentum, 1/2mv², thermodynamics, or general conservation of energy.

M rationaleM5.7 is assigned: there is a public argument from 1686, later systematizing texts, and clear objects of application in raising/lowering and collisions, while the mv² quantity captures the core squared-velocity structure of modern kinetic energy. M is not higher because the achievement's actual terminal state still mixed force, work-like ability, and metaphysical active force; universal conservation depended on ideal elasticity or a microscopic-elasticity hypothesis, and it did not deliver modern total-energy conservation. This difference follows from the achievement's own scope and error boundaries, not from a discount caused by incomplete reading of the original text.

attribution rationaleLeibniz 0.36; direct Huygens input 0.18; Galileo's falling-body and height-velocity baseline 0.09; Descartes, Wren, and mechanical prehistory of collisions 0.14; publication and correspondence team 0.07; institutions 0.04; unresolved 0.12.

overlap boundaryThe documented core scheme runs from the 1686 Brief Demonstration of a Notable Error of Descartes and Others through dynamics texts of 1689–1695 and the c. 1700 Essay on Dynamics: using the counterfactual that a body falling obtains an effect equal to that required to raise it back to the same height, together with Galileo's falling-body relations, to argue that scalar mass × speed is insufficient to measure force and that vis viva is measured by mass × speed²; distinguishing directional quantity of progress from living force; and discussing ideal elastic collisions and an account in which living force in inelastic collisions passes into minute parts. Calculus methods are consumed by the pre-existing SCI-O-SL0002-03; no claim is made to Newton's laws of motion, complete modern momentum, the 1/2mv² convention, potential energy, internal energy, heat, thermodynamics, or general conservation of energy.

Evidence gapsThe version differences among the 1686 Brief Demonstration, the 1695 Specimen Dynamicum, and the c. 1700 Essay of Dynamics require direct passage-by-passage checking. ; Specific experiments, later validation by 's Gravesande, du Châtelet, and others, and the transmission of terminology have not been checked; the present assessment does not infer personal M from later acceptance. ; The relation between the supposed transfer into minute parts in inelastic collisions and later accounts of internal energy or heat must avoid teleological retrospective validation.

Record year1703 (including the 1679 mechanical conception)

summaryThe 1703 text explains place-value representation using only 0 and 1 and demonstrates the four arithmetic operations and uses in number theory; the binary mechanical representation of 1679 is retained only as a related conception. Available materials do not show that a binary machine was built in Leibniz's time, and this entry does not include the modern computing industry.

M rationaleM5.5 is assigned: the original text gives place-value decomposition and the four operations, rather than merely an abstract binary metaphor; institutional records also document the 1679 mechanical-representation conception. The scope remains a published mathematical method plus an unbuilt machine concept, below the anchor of a mature general computing device or system; this difference results from the difference in terminal delivery, not from prizes, dates, or failure to inspect every page of the original journal.

attribution rationaleLeibniz 0.43; prehistory of place value, binary systems, and arithmetic 0.22; academy publication and dissemination 0.09; later editors 0.05; preserving institutions 0.04; unresolved 0.17.

overlap boundaryThe 1703 public text is limited to place-value representation using 0 and 1, numerical decomposition, examples of addition, subtraction, multiplication, and division, uses in number theory, and the explicit boundary that it does not replace everyday decimal notation; the 1679 mechanical conception of using open and closed holes and spheres or cubes to represent 0 and 1 remains only a residual implementation of the same family. Functional replicas from 2003/04 show only that the conception can be visualized; they do not claim that a binary machine was made in Leibniz's time. Modern bits, electronic computers, software, and industry are excluded.

Evidence gapsThe 1703 original journal and the Gerhardt transcription require direct page-by-page collation. ; The 1679 binary-machine manuscript requires checking; it cannot currently be asserted to contain complete manufacturing drawings, contemporary construction, or reliable operation. ; The prehistory of binary arithmetic and the chain of actual later adoption have not been closed.

Record year1666–1716 (the dates of individual manuscripts still require confirmation)

summaryBeginning with the combinatorial problems of the 1666 Dissertatio de Arte Combinatoria, related manuscripts also address partitions of numbers, symmetric expressions, indexed organization of determinant terms, and elimination of linear equations. This entry treats only these non-calculus mathematical constructions; subsequent publication, complete determinant theory, probability, and the shared calculus ledger are not included.

M rationaleM5.4 is assigned: this family contains a locatable published combinatorial entry point and several technically distinct non-calculus results connected by one combinatorial-indexing method, covering the reusable problem types of partitions and elimination. M is not accumulated from more than 900 determinant drafts or the number of problems, and it does not claim later complete combinatorics or linear algebra; unpublished status and transmission limits enter the actual benefit in scope, while the fact that materials have not yet been read item by item enters only as a gap.

attribution rationaleLeibniz 0.38; prehistory of combinatorics, algebra, and number theory 0.24; early printing and preservation 0.07; critical editorial work 0.08; preserving institutions 0.05; unresolved 0.18.

overlap boundaryFrom the technical combinatorial entry in the 1666 Dissertatio de Arte Combinatoria through basic combinatorial operations, recurrences and special formulas for partitions of natural numbers, symmetric functions, double-indexed expression of determinant sums, and elimination of linear equations clearly supported by scholarly summaries of later manuscripts. Combinatorial aims and the ideal of a logical language count only their formal-reasoning value in the logic entry; this entry claims only the specific mathematical constructions. Probability, interest and annuities, complete determinant theory, Cramer's rule, Euler, Stirling, later publications, and existing calculus results are excluded.

Evidence gapsThe dates, propositions, proofs, and revision layers of key partition and determinant manuscripts require item-by-item checking; the results listed in summaries cannot currently all be treated as equally mature. ; Remaining materials on probability, games, annuities and interest, symmetric functions, and number theory have not yet formed independently bounded terminal states. ; Relations to independent routes such as Seki's, subsequent public publication, and actual transmission require dedicated checking.

Record year1666–1716 (some materials unpublished)

summaryLeibniz proposed a universal characteristic and calculus scheme that would assist reasoning through conceptual decomposition, symbolization, and combination. It is not a completed modern predicate logic, automated theorem proving, or computer program, and its technical content is separate from binary arithmetic and combinatorial mathematics.

M rationaleM5.2 is assigned: the achievement is more than a single vision, with an early public vehicle and operational schemes in continuing manuscripts; its bounded terminal state, however, is an incompletely unified logical project with limited transmission, rather than a mature modern logical system. M reflects the method range formed and actual delivery, is not discounted because all manuscripts have not been read, and is not raised retrospectively by similar later techniques.

attribution rationaleLeibniz 0.39; prehistory of logic and symbols 0.26; early publication and correspondence 0.07; later editing and translation 0.07; preserving institutions 0.04; unresolved completeness and influence 0.17.

overlap boundaryThe public text of the 1666 Dissertatio de Arte Combinatoria is used as an early vehicle, together with documented schemes of symbolized conceptual decomposition, combination, and calculative reasoning in later characteristica universalis and calculus ratiocinator manuscripts. Mathematical partitions and determinants count technical value only in the preceding mathematics entry; binary place-value operations count only in the binary entry. No claim is made to completed modern predicate logic, computer programs, or automated theorem proving, nor to later independent routes of Boole, De Morgan, Frege, and others.

Evidence gapsSpecific original logic manuscripts must be selected to distinguish concept symbols, truth or inclusion relations, and actual rules of derivation. ; Published and unpublished materials, the version timeline, and the range of contemporary readers have not been closed. ; The actual transmission chain to nineteenth-century logic must be separated from parallel development of similar ideas.

Record year1672–c. 1700

summaryThe stepped-drum mechanical-calculation route includes the 1672 conception, model demonstrations in 1673/1675, and a surviving decimal four-function original machine from c. 1690 to 1700. It is a bounded chain of design, model, and original machine, and does not demonstrate generally reliable use.

M rationaleM5.2 is assigned: the chain has a specific mechanical mechanism, public models, and a surviving original machine from c. 1700, exceeding a paper concept; but available institutional records do not support widespread reliable use or deployment at scale, so M assesses limited prototype or device delivery rather than a mature computing platform.

attribution rationaleLeibniz 0.34; prehistory of mechanical calculation and clockwork 0.20; manufacturing craftspeople 0.23; demonstration and workshop institutions 0.07; later preservation and replication 0.05; unresolved 0.11.

overlap boundaryThe 1672 stepped-drum conception, wooden-model demonstrations of 1673/1675, the surviving decimal four-function original machine from c. 1690 to 1700, and continuing improvements. Only the locatable design-model-original-machine chain is counted; it does not claim generally reliable deployment, does not treat replicas from 1923 or the modern period as original-machine delivery, and does not mix in the 1679 binary-machine concept.

Evidence gapsTechnical reports on the original machine, craftspeople's accounts, and restoration records are needed to identify the division of manufacturing work. ; Records of failures, accuracy, speed, and actual operation are needed to distinguish successful demonstration from reliable use. ; The version relations among the 1673 and 1675 models and the original machines of the 1690s have not been closed.

Record year1700–1711 (founding and initial period)

summaryThe founding documents and initial organizational design of the Berlin Society of Sciences in 1700 concerned an interdisciplinary society and the exchange, examination, preservation, and archival arrangement of research documents. Frederick III's authorization, Sophie Charlotte's support, and the administrative work of early organizers each had independent roles; later academies are not included.

M rationaleM4.8 is assigned: BBAW archives directly confirm that Leibniz's General Instruction and foundation documents were core founding records, and record Jablonski's early archival administration; official history also makes political authorization and multiple promoters explicit. This entry is a specific institutional design and founding service, above a job title but below treating centuries of academy outcomes as one person's broad knowledge platform.

attribution rationaleLeibniz 0.30; Frederick III 0.17; Sophie Charlotte 0.10; Jablonski, Chuno, Rabener, and early organizers 0.17; prehistory of learned-society institutions 0.10; court and society institutions 0.08; unresolved 0.08.

overlap boundaryThe 1700 founding scheme for the Electoral Society of Sciences at Berlin, Leibniz-drafted foundation documents and General Instruction, one organizational design for natural sciences and humanities, and early archival arrangements for preserving and reviewing research documents. Only founding and initial institutional residues are counted; the formal opening after 1711, later Prussian, East German, and present-day academies, members' research, and three centuries of output are excluded.

Evidence gapsThe complete original texts of the foundation documents, General Instruction, and founding correspondence require checking to distinguish specific provisions by Leibniz and joint promoters. ; The actual operation of calendar privileges, funds, an observatory, and the first members still requires archives from 1700 to 1711. ; The current M does not claim later academy research outcomes and cannot infer an individual share from the duration of institutional continuation.