Proofs

Some articles on proofs, proof:

Shmuel Safra
... NP-hard even for weak factors of approximation--- and the theory of probabilistically checkable proofs (PCP) and the PCP theorem, which gives stronger characterizations of the ... Gödel Prize in theoretical computer science for his papers "Interactive Proofs and the Hardness of Approximating Cliques" and "Probabilistic Checking of Proofs A ...
Mathematical Beauty - Beauty in Method
... Mathematicians describe an especially pleasing method of proof as elegant ... Depending on context, this may mean A proof that uses a minimum of additional assumptions or previous results ... A proof that is unusually succinct ...
Stars And Bars (combinatorics) - Proofs - Theorem Two
... The case n = 0 (no bins at all) allows 0 configurations, unless k = 0 as well (no objects to place), in which there is one configuration (since an empty sum is defined to be 0) ... In fact the binomial coefficient takes these values for n = 0 (since by convention (unlike, which by convention takes value 0 when, which is why the former expression is the one used in the statement of the theorem) ...
Tarski's High School Algebra Problem - Example of A Provable Identity
... innocuous statements can require long proofs using only the above eleven axioms ... Consider the following proof that (x + 1)2 = x2 + 2 · x + 1 (x + 1)2 = (x + 1)1 + 1 = (x + 1)1 · (x + 1)1 by 9 ... The length of proofs is not an issue proofs of similar identities to that above for things like (x + y)100 would take a lot of lines, but would really involve ...
Circle Packing Theorem - Proofs of The Theorem
... There are many known proofs of the circle packing theorem ... Paul Koebe's original proof is based on his conformal uniformization theorem saying that a finitely connected planar domain is conformally equivalent to a ... There are several different topological proofs that are known ...

Famous quotes containing the word proofs:

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    —H.L. (Henry Lewis)

    Would you convey my compliments to the purist who reads your proofs and tell him or her that I write in a sort of broken-down patois which is something like the way a Swiss waiter talks, and that when I split an infinitive, God damn it, I split it so it will stay split, and when I interrupt the velvety smoothness of my more or less literate syntax with a few sudden words of bar- room vernacular, that is done with the eyes wide open and the mind relaxed but attentive.
    Raymond Chandler (1888–1959)

    To invent without scruple a new principle to every new phenomenon, instead of adapting it to the old; to overload our hypothesis with a variety of this kind, are certain proofs that none of these principles is the just one, and that we only desire, by a number of falsehoods, to cover our ignorance of the truth.
    David Hume (1711–1776)