Methods of Mathematical Proof

Proof by inspection

"Well, as anyone can see from this four-board proof, you can see by inspection that this is the case."

Proof by exhaustion

Prove that for 1 it's true. Then prove for 2 it's true... and keep proving it until the class is alseep.

Proof by class exhaustion

"And, since all of you are basically asleep, I'll just say that it's true and you can all believe me."

Proof by example

"We can see from this example that this must be the case for all n."

Proof by consensus
"Does anyone disagree with this proof?"

Proof by majority rule
Only to be used if consensus is impossible

Proof by assertion

"This is true."

Proof by omission

"I don't really need to show you this on the board. It's obviously true!"

Proof by divine intervention

"Then, a miracle occurs..."

Proof by devaluation

"The proof of this problem is trivial."

Proof by imagination
"Well, we'll pretend it's true."

Proof by convenience
"It would be very nice if it were true, so..."

Proof by necessity
"It had better be true, or the entire structure of mathematics would crumble to the ground."

Proof by plausibility
"It sounds good, so it must be true."

Proof by intimidation
"Don't be stupid; of course it's true."

Proof by terror
"If you don't believe it, prove it yourself as an exercise!"

Proof by lack of time
"And because we're running out of time, I'll leave the proof to you as an exercise."

Proof by postponement
"The proof for this is long and arduous, so it is given in the appendix."

Proof by accident
"Uh... wait a second, what do we have here?"

Proof by insignificance
"Who really cares, anyway?"

Proof by Greek Letter Confusion
"So pi-alpha-gamma multiplied by nu-tau-epsilon is identical to beta-delta-omega."

Proof by definition
"We define it to be true."

Proof by toutology
'It's true because it's true."

Proof by plagiarism
"As we see on page 289......"

Proof by lost reference
"I know I saw it somewhere......"

Proof by Calculus
"This proof requires calculus, so we'll skip it."

Proof by lack of interest
"Does anyone really want to see this?"

Proof by illegibility
(scribble, scribble) QED

Proof by logic
"If it is on the problem sheet, then it must be true!"

Proof by clever variable choice
"Let A be the number such that this proof works. . "

Proof by tessellation
"This proof is the same as the last."

Proof by divine word
"And the Lord said, 'Let it be true,' and it was true."

Proof by simplification
"This proof reduces to the statement 1 + 1 = 2."

Proof by generalization
"Well, it works for 17, so it works for all reals."

Proof by poor analogy
"Well, it's just like... "

Proof by design
If it's not true in today's math, invent a new system in which it is.

Proof by authority
"Well, Newton said it's true, so it must be!"

Proof by gloss-over

"Well, this isn't the proof I was looking for, let's get onto the exercises."

Proof by mistake cover-up

"Well, I don't know what happened here, so let's just say take the equation as is."

Proof by intuition
"I just have this gut feeling..."

Proof by contradicting statements

"Well, what you're saying obviously ISN'T true, so therefore THIS must be true."

Proof by hope

"Would someone like to prove #3 on the board?"

Proof by delay

"That would be a good exercise to do over the weekend."

Proof by coercion

"That would be a good exam question."

Proof by bribe

"If you can prove it, you get bonus marks!"

Proof by inability

"The proof is beyond the scope of this course, so we'll accept it to be true."

Proof by Piggy Back

"The proof follows from..."

Proof by appreciation

"Let's discuss the last professor left on the board."

Proof by accidental erasure

"And so, we can see from... whoops, looks like I accidentally erased it. But you can see that it's true."

Proof by historic example

"Somebody has proven this already, so I don't need to do it again."

Proof by Obfuscation

(A long list of lemmas is helpful in this case)

Proof by Confusion

Arrange the lemmas into a circular argument.

Proof by reference to inaccessible literature

The author cites a simple corollary of a theorem to be found in a privately circulated memoir
from 1883.

Proof by accumulated evidence

"We've been trying for a long time and we have not revealed a counterexample."

Proof by prosterior extraction

Enough said, you figure out what it means

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