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BBD decomposition theorem (algebraic geometry) BEST theorem (graph theory) Babuška–Lax–Milgram theorem (partial differential equations) Baily–Borel theorem (algebraic geometry) Baire category theorem (topology, metric spaces) Baker's theorem (number theory) Balian–Low theorem (Fourier analysis) Balinski's theorem (combinatorics)
Euler's theorem; Five color theorem; Five lemma; Fundamental theorem of arithmetic; Gauss–Markov theorem (brief pointer to proof) Gödel's incompleteness theorem. Gödel's first incompleteness theorem; Gödel's second incompleteness theorem; Goodstein's theorem; Green's theorem (to do) Green's theorem when D is a simple region; Heine–Borel ...
The length of unusually long proofs has increased with time. As a rough rule of thumb, 100 pages in 1900, or 200 pages in 1950, or 500 pages in 2000 is unusually long for a proof. 1799 The Abel–Ruffini theorem was nearly proved by Paolo Ruffini , but his proof, spanning 500 pages, was mostly ignored and later, in 1824, Niels Henrik Abel ...
The best bound, ℵ ω 4, was obtained by Shelah using his PCF theory. The problem of finding the ultimate core model, one that contains all large cardinals. Woodin's Ω-conjecture: if there is a proper class of Woodin cardinals, then Ω-logic satisfies an analogue of Gödel's completeness theorem.
In mathematics, a fundamental theorem is a theorem which is considered to be central and conceptually important for some topic. For example, the fundamental theorem of calculus gives the relationship between differential calculus and integral calculus . [ 1 ]
Pages in category "Theorems in number theory" The following 106 pages are in this category, out of 106 total. This list may not reflect recent changes. 0–9.
This following is a list of lemmas (or, "lemmata", i.e. minor theorems, or sometimes intermediate technical results factored out of proofs). See also list of axioms , list of theorems and list of conjectures .
The BEST theorem is due to van Aardenne-Ehrenfest and de Bruijn (1951), [4] §6, Theorem 6. Their proof is bijective and generalizes the de Bruijn sequences.In a "note added in proof", they refer to an earlier result by Smith and Tutte (1941) which proves the formula for graphs with deg(v)=2 at every vertex.