Near Matches
Ignore Exact
Everything
2
Methods of mathematical proof
(
idea
)
by
noaseboar
Thu Mar 01 2001 at 13:51:50
Proof by example
The author gives only the case n = 2 and suggests that it contains most of the ideas of the general proof.
Proof by intimidation
"
Trivial
" or "
obvious
."
Proof by exhaustion
"There is an issue or two of (insert
archaic
, completely
byzantine
title
of
mathematical journal
here) devoted to this
proof
.
Proof by omission
"The reader may easily supply the details", "The other 253 cases are
analogous
"
Proof by obfuscation
"By virtue of the fact that the
boxer rebellion
occured in
China
and all
metric spaces
have a
metric
space assigned to them, we know that 1 + 1 = 3."
Proof by wishful citation
"According to
Rudin
p. 215, wherein he states that
compact spaces
are
closed
. Thus 1 + 1 = 3."
Proof by funding
"The government has given us 6 grants totalling $2,500,000 to
prove
this."
mathematicians
believe this to be true."
Proof by market economics
Mine is the only
theory
on the
market
that will handle the data.
Proof by eminent authority
"I saw
Marty Fischler
in the elevator and he said that was tried in the 70's and doesn't work."
Proof by cosmology
"The
negation
of the proposition is unimaginable or meaningless."
Proof by personal communication
"Karp told me last week about a new
proof
he has to show that
eight-dimensional
colored cycle stripping is
NP-complete
"
Proof by reduction to the wrong problem
"To see that infinite-dimensional colored cycle stripping is
decidable
, we reduce it to the
halting problem
."
Proof by reference to inaccessible literature
"According to Slajk's
corollary
, which can be found in a privately circulated memoir of the
Icelandic
Philological Society, 1883..." Note:This works even better if the paper has never been translated from the original
Icelandic
.
Proof by forward reference
"As I have shown in a paper to be
published
early next year..."
Proof by importance
"A large body of incredibly useful
consequences
all follow from this
proposition
."
Proof by accumulated evidence
"Long and diligent search has not revealed a counterexample."
Proof by mutual reference
"In
reference
A,
Theorem
5 is said to follow from
Theorem
3 in
reference
B, which is shown to follow from
Corollary
6.2 in
reference
C, which is an easy
consequence
of
Theorem
5 in
reference
A."
Proof by metaproof
"A method is given to construct the desired proof. The correctness of the method is proved by any of these
techniques
. A strong background in
programming language
semantics
will help here."
Proof by picture
A more convincing form of proof by example. Combines well with proof by omission.
Proof by flashy graphics
A moving sequence of shaded, 3D color
models
will convince anyone that your object recognition
algorithm
works. An
SGI
workstation is helpful here.
Proof by vehement assertion
"This is completely obvious to even the stupidest man alive."
Proof by repetition
See
Bellman's corollary
: "What I say three times is true."
Proof by vigorous handwaving
Works well in a
classroom
,
seminar
, or workshop setting.
Proof by cumbersome notation
Best done with access to at least four
alphabets
, special symbols, and the newest release of
LaTeX
.
Proof by lack of space
"The
proof
is not detailed due to lack of space in this proceedings..." works well in conjunction with proof by forward reference.
Proof by delegation
"You will proof this in exercise 31 a)."
Proof by blackmail
"We have now reached the end of this lecture. Of course, if you don't believe this theorem, I can give you the proof in only 30 minutes."
Proof by threatening
"If this theorem would be wrong, mathematics would be wrong altogether."
Anti-authoritarian proof
"XY claims that the negation of this theorem is true, and he can't be right."
What do theorems look like?
1+2+3+ ... +n : Proof by Picture
To crush your enemies, see them driven before you, and to hear the lamentations of the women
base 60
Proof by contradiction
Proof by oddity
exercise for the reader
Proof by intimidation
Technology is not the remedy for problems caused by technology
Semantic Tableaux proof method for predicate logic
inductive proof
Infinite Descent
Mathematical Induction
Degenerate Case
The History of Numbers
Technology is the remedy for problems caused by technology
Bellman
the smallest number that looks prime but isn't
Monstrous Moonshine Conjecture
Logical fallacy
NP-complete
Byzantine
A Mathematical Adventure, or, How I Spent an Afternoon Proving Nothing
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