incompleteness
101Busy beaver — In computability theory, a busy beaver (from the colloquial expression for an industrious person) is a Turing machine that attains the maximum operational busyness (such as measured by the number of steps performed, or the number of nonblank… …
102Mathematical proof — In mathematics, a proof is a convincing demonstration (within the accepted standards of the field) that some mathematical statement is necessarily true.[1][2] Proofs are obtained from deductive reasoning, rather than from inductive or empirical… …
103Zermelo–Fraenkel set theory — Zermelo–Fraenkel set theory, with the axiom of choice, commonly abbreviated ZFC, is the standard form of axiomatic set theory and as such is the most common foundation of mathematics.ZFC consists of a single primitive ontological notion, that of… …
104Recursion theory — Recursion theory, also called computability theory, is a branch of mathematical logic that originated in the 1930s with the study of computable functions and Turing degrees. The field has grown to include the study of generalized computability… …
105John Boyd (military strategist) — John Boyd Nickname Forty Second Boyd, Genghis John, The Mad Major, The Ghetto Colonel …
106Foundations of mathematics — is a term sometimes used for certain fields of mathematics, such as mathematical logic, axiomatic set theory, proof theory, model theory, and recursion theory. The search for foundations of mathematics is also a central question of the philosophy …
107Proof theory — is a branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively defined data structures such as plain lists, boxed… …
108Function (mathematics) — f(x) redirects here. For the band, see f(x) (band). Graph of example function, In mathematics, a function associates one quantity, the a …
109Axiomatic system — In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A mathematical theory consists of an axiomatic system and all its derived theorems. An axiomatic… …
110The Art of Fugue — A portrait which may show Bach in 1750 The Art of Fugue (or The Art of the Fugue, original German: Die Kunst der Fuge), BWV 1080, is an incomplete work[1] by Johann Sebastian Bach (1685–1750). It was most likely started at the beginning of the… …
