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He held her gaze steady while he summarized her promises. “She will honor me, protect me, obey me only when she believes I’m being reasonable—but I shouldn’t hold out hope that that day will ever come—try to love me before she’s an old woman, and I’d better get it straight in my mind that she will respect me until or unless I do something to prove I’m not worthy, and God save me then. Have I left anything out, Brenna?

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David Hilbert

The arithmetical symbols are written diagrams and the geometrical figures are graphic formulas.

Diagrams, Figures, Formulas, Geometrical, Graphic, Math
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In mathematics. . . we find two tendencies present. On the one hand, the tendency towards abstraction seeks to crystallise the logical relations inherent in the maze of materials. . . being studied, and to correlate the material in a systematic and orderly manner. On the other hand, the tendency towards intuitive understanding fosters a more immediate grasp of the objects one studies, a live rapport with them, so to speak, which stresses the concrete meaning of their relations.

Concrete, Hands, Logical, Seeks, Stress, Two

Every mathematical discipline goes through three periods of development: the naive, the formal, and the critical.

Critical, Development, Discipline, Formal, Mathematical, Three

As long as a branch of science offers an abundance of problems, so long it is alive; a lack of problems foreshadows extinction or the cessation of independent development.

Development, Independent, Long, Offers, Science

Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.

Connections, Indivisible, Ontology, Organism, Science, Vitality

Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. These fundamental principles are called the axioms of geometry.

Like, Logical, Principles, Simple, Small Numbers
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