Aristotle prove what is obvious by what is not is the mark of a man who is unable to distinguish what is self-evident from what is not.


Cabell, James Branch

"But I can prove it by mathematics, quite irrefutably. I can prove anything you require of me by whatever means you may prefer," said Jurgen, modestly, "for the simple reason that I am a monstrous clever fellow."


Davis, Philip Hersh, Reuben

He rests his faith on rigorous proof; he believes that the difference between a correct proof and an incorrect one is an unmistakable and decisive difference. He can think of no condemnation more damning than to say of a student, "He doesn't even know what a proof is." Yet he is able to give no coherent explanation of what is meant by rigor, or what is required to make a proof rigorous. In his own work, the line between complete and incomplete proof is always somewhat fuzzy, and often controversial.

The Mathematical Experience The Ideal Mathematician (p. 34)

Gleason, Andrew

...proofs really aren't there to convince you that something is true— they're there to show why it is true.

In D. Albers, G. Alexanderson and C. Reid (eds) More Mathematical People (p. 86)


Proof by obviousness

"The proof is so clear that it need not be mentioned."

Proof by general agreement "All in favor?..."

Proof by imagination

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 lack of sufficient time

"Because of the time constraint, I'll leave the proof to you." Proof by postponement

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

Proof by accident

"Hey, what have we here?"

Proof by insignificance "Who really cares, anyway?"

Proof by mumbo-jumbo

Proof by profanity (example omitted)

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

Proof by tautology

"It's true because it's true."

Proof by plagiarism

Proof by lost reference

"I know I saw it somewhere..."




Proof by intimidation

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

Proof by calculus

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

"When intimidation fails..."

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 majority rule

Only to be used if general agreement is impossible 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 stubbornness

"I don't care what you say—it is true!"

Proof by simplification

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

Proof by hasty generalization

"Well, it works for 17, so it works for all reals."

Proof by deception

"Now everyone turn their backs..."

Proof by supplication "Oh please, let it be true."

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

Proof by avoidance

Limit of proof by postponement as it approaches infinity. Proof by design

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

"Well, Don Knuth says it's true, so it must be!"

Proof by intuition

"I just have this gut feeling..."

Source unknown

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