Emmy Noether

Record year1918

summaryIn 'Invariant Variational Problems', two interconnected theorems and their converses are presented, establishing a systematic connection between continuous symmetries and conservation laws. Here they are presented as a theorem family; later applications such as energy and momentum are not counted repeatedly.

M rationaleM7.0 is on par with Maxwell's electromagnetic field-light unification: both compress broad physical phenomena into reusable mathematical structures. The Noether method spans classical field theory, relativity, and subsequent physical formalisms, but currently does not include all later applications, so it is not further upgraded due to the number of applications. It is higher than Maxwell's transport M6 and the bounded method anchor of ACE M5.

attribution rationaleNoether receives 0.65 for core authorship responsibility for the theorems, converses, and general proof; Hilbert's problems and relativistic background 0.10, Klein's problem organization 0.05; prior development in calculus of variations, invariants, and group theory 0.15; unknown 0.05. Problem posing and prior development are visible in a, but M is not repeatedly deducted.

overlap boundaryThe two interconnected theorems and their converses in the 1918 'Invariante Variationsprobleme' are treated as one method family: conservation laws and identities in variational problems under continuous transformation groups; distinguishing continuous symmetries described by independent parameters from local symmetries dependent on arbitrary functions. M is not accumulated separately by the names of the two theorems, energy, momentum, gauge, or each category of later application. Excludes the problem backgrounds of Hilbert and Klein, Weyl's later developments, and independent increments from quantum field theory and gauge theory.

Evidence gapsThis revision did not obtain the 1918 original text that can be parsed page by page; The shares for the specific problem exchanges between Hilbert, Klein, and Noether are still normative estimates. Evidence for direct cross-generational use of high-tier M must be shown with source positioning similarly to philosophy, and cannot be exempted from verification by familiar conclusions from the history of science; named precursors receiving credit again are also subject to reuse review.

Record year1921

summaryStarting from ideal theory, advancing abstract ring methods satisfying chain conditions, and developing structural results such as primary decomposition; this is a continuous body of algebraic work, not isolated results.

M rationaleM6.5 is higher than Maxwell transport M6 because this method family established the general objects and long-term structural language of modern abstract algebra; it is lower than or does not exceed Maxwell field—light and Noether symmetry—conservation M7, because the current scope is primarily concentrated on commutative rings and ideal theory.

attribution rationaleNoether as the core paper and abstract method author receives 0.70; Lasker special case 0.10; Dedekind, Hilbert, and the antecedents of ideal algebra combined 0.15; unknown 0.05. van der Waerden's subsequent textbook does not enter this body's budget.

overlap boundaryThe period from 1921 to 1924, advancing from specific objects to abstract commutative rings satisfying chain conditions, primary decomposition of ideals, and related structural conditions, is considered a continuous algebraic method family. Excluded are Lasker's polynomial ring special case, the expression and global dissemination of van der Waerden's textbook, all subsequent Noetherian theory, and the 1927–1933 non-commutative collaboration family.

Evidence gapsThe existing basis is mathematical history biographies and bibliographies; the original texts from 1921–24 have not been individually verified and read; the internal distribution within the antecedent pool has not yet been subdivided.

Record year1927

summaryResearch conducted at the intersection of non-commutative algebra, representation, and number theory since 1927; the 1932 co-authored results with Richard Brauer and Helmut Hasse are considered a joint delivery by the three.

M rationaleM5.8 is slightly lower than Maxwell transport M6: this collaboration family contains a fundamental structural theorem and cross-domain connections, but its applicable objects are narrower than general physical transport or commutative ring methods. It is higher than ACE M5's single architectural report because it forms a sustainable mathematical research structure.

attribution rationaleNoether has a continuous conceptual and research role in the collaboration family, provisionally receiving 0.35; Brauer and Hasse, as co-authors of the 1932 core theorem, each receive 0.25; the antecedents of representation and number theory 0.10; unknown 0.05. In the absence of division-of-labor archives, Noether is not given sole credit based on author order or reputation.

overlap boundaryCombine the continuous research at the intersection of non-commutative algebra, representation theory, and number theory from 1927 to 1933 into a single collaborative family. The core anchor is the 1932 joint proof by Brauer, Hasse, and Noether that every simple algebra over an algebraic number field is a cyclic algebra. Exclude the abstract foundations already claimed by earlier commutative ideal/ring methods, the cumulative addition of individual papers, unverified increments from other co-authors like Schmeidler, and all subsequent works by the three authors.

Evidence gapsArchives documenting the division of labor among the three authors in the proof, conceptualization, and writing are missing; The limited materials are insufficient to incorporate every relevant paper from 1927–33.

Record year1916

summaryDisseminating the concepts and methods of abstract algebra through courses, seminars, and weekly lectures at Göttingen, Bryn Mawr, and Princeton; the related textbook was written by van der Waerden, incorporating lectures by Artin and Noether.

M rationaleM3.5 is higher than a single lecture or general tool M3, due to multi-year, cross-institutional, and specific course and seminar service; lacking complete class hours, rosters, and teaching effectiveness, it is far below the core mathematical method M5 and above.

attribution rationaleNoether as the primary teacher 0.65; Hilbert's early course bearing 0.05; Göttingen 0.05, Bryn Mawr 0.10, Princeton 0.05; Artin and algebra teaching input 0.05; unknown 0.05. Students as beneficiaries do not receive or transfer back shares in this point due to future achievements.

overlap boundaryCount only verifiable course assistance from 1916–1935, Göttingen ideal theory teaching, a 1933 home student gathering, a seminar with three students and one faculty member at Bryn Mawr, and weekly lectures at Princeton in 1934. Exclude future research results of students and colleagues, the full value of van der Waerden's sole-authored textbook, all academic history of exile, and the core theorems of abstract algebra.

Evidence gapsLacking complete class rosters, class hours, and student learning outcomes; The 1935 colleague's obituary in this revision has only been verified to metadata.