### Some articles on *proofs, proof*:

... 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 ...

... 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 ...

**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) ...

... 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 ...

**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:

“A man’s women folk, whatever their outward show of respect for his merit and authority, always regard him secretly as an ass, and with something akin to pity. His most gaudy sayings and doings seldom deceive them; they see the actual man within, and know him for a shallow and pathetic fellow. In this fact, perhaps, lies one of the best *proofs* of feminine intelligence, or, as the common phrase makes it, feminine intuition.”

—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)