Natural Blogarithms

One of my students in Linear Algebra reminded me of quote I had heard some time back concerning the pecking order of the sciences. The version he quoted was what he had heard from a colleague of mine here at Wayland:

All chemists want to be physicists.
All physicists want to be mathematicians.

Although, I couldn’t recall it at the time. I looked it up and found the two forms of this quote I have heard before:

Biologists answer only to Chemists.
Chemists answer only to Physicists.
Physicists answer only to Mathematicians.
Mathematicians answer only to God.

or

The biologist wants to be a chemist.
The chemist wants to be a physicist.
The physicist wants to be God.
God wants to be a mathematician.

No, I do not have a God complex. But who could blame me. I am a mathematician.

written by SplineGuy

Here are some more that I even use more frequently than in the last entry. All of these come from Dick Wood, in the November ‘98 edition of The Mathematics Teacher.  (I have to say my favorite is the Proof by Accident.)

Proof by Obviousness: “The proof is so clear that it need not be mentioned.”
Proof by General Agreement: “All in Favor?…”

Proof by Imagination: “Well, We’ll pretend its true.”
Proof by Convenience: “It would be very nice if it were true, so …”

Proof by Necessity: “It had better be true or the whole structure of mathematics would crumble to the ground.”
Proof by Plausibility: “It sounds good so it must be 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 so 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: ” For any epsilon> 0 there exists a corresponding delta > 0 s.t. f(x)-L < epsilon whenever x-a < delta”

Proof by Profanity: (example omitted)
Proof by Definition: “We’ll define it to be true.”

Proof by Tautology: “It’s true because it’s true.”
Proof by Plagiarism: “As we see on page 238 …”

Proof by Lost Reference: “I know I saw this somewhere …”
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: ” ¥ ª Ð Þ þæ”
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 just the same as the last.”
Proof by Divine Word: “And the Lord said, ‘Let it be true,’ and it came to pass.”

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 t approaches infinity.
Proof by Design: “If it’s not true in today’s math, invent a new system in which it is.”

Proof by Intuition: “I just have this gut feeling …”
Proof by Vigorous Assertion: “And I REALLY MEAN THAT!”

Proof by A.F.K.T. Theorem: “Any Fool Knows That!”
Proof by Divine Intervention: “Then a miracle occurs …”

powered by performancing firefox

written by SplineGuy

Today in my Intermediate Analysis class, I presented 14 different proof techniques that we will be using throughout the semester. While the students were surprised to see that there were that many different types of proof techniques, they realized that by this point that had seen and used every last one of them. That was reassuring. However, I neglected to mention that are a great many more (invalid) proof techniques that their professor will likely make use of. Here a few for your consideration.

Proof by vigorous handwaving: Works well in a classroom or seminar setting.
Proof by forward reference: Reference is usually to a forthcoming paper of the author, which is often not as forthcoming as at first.
Proof by funding: How could three different government agencies be wrong?
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 omission: “The reader may easily supply the details.” “The other 253 cases are analogous.“

Proof by deferral: “We’ll prove this later in the course.“
Proof by picture: A more convincing form of proof by example. Combines well with proof by omission.
Proof by intimidation: “Trivial.“
Proof by seduction: “Convince yourself that this is true!“
Proof by cumbersome notation: Best done with access to at least four alphabets and special symbols.

Proof by exhaustion: An issue or two of a journal devoted to your proof is useful.
Proof by obfuscation: A long plotless sequence of true and/or meaningless syntactically related statements.
Proof by wishful citation: The author cites the negation, converse, or generalization of a theorem from the literature to support his claims.
Proof by eminent authority: “I saw Karp in the elevator and he said it was probably NP-complete.

Proof by personal communication: “Eight-dimensional colored cycle stripping is NP-complete [Karp, personal communication].“
Proof by importance: A large body of useful consequences all follow from the proposition in question.
Proof by accumulated evidence: Long and diligent search has not revealed a counterexample.
Proof by cosmology: The negation of the proposition is unimaginable or meaningless.
Proof by vehement assertion: It is useful to have some kind of authority relation to the audience.
Proof by ghost reference: Nothing even remotely resembling the cited theorem appears in the reference given.

Proof by semantic shift: Some of the standard but inconvenient definitions are changed for the statement of the result.
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 reference to inaccessible literature: The author cites a simple corollary of a theorem to be found in a privately circulated memoir of the Slovenian Philological Society, 1883.
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 metaproof: A method is given to construct the desired proof. The correctness of the method is proved by any of these techniques.

written by SplineGuy

Try this one on for size:

Two men are sitting in the basket of a balloon. For hours, they have been drifting through a thick layer of clouds, and they have lost orientation completely. Suddenly, the clouds part, and the two men see the top of a mountain with a man standing on it.
“Hey! Can you tell us where we are?!”
The man doesn’t reply. The minutes pass as the balloon drifts past the mountain. When the balloon is about to be swallowed again by the clouds, the man on the mountain shouts: “You’re in a balloon!”
“That must have been a mathematician.”
“Why?”
“He thought long and thoroughly about what to say. What he eventually said was irrefutably correct. And it was of no use whatsoever…”

Hey! I resemble that remark.

written by SplineGuy

Well, I laughed.

See more at xkcd

written by SplineGuy

Q: What do you get when you cross an elephant with a monkey?
A: |elephant| |monkey| sin

Q: What do you get when you cross an mountain climber with a Volkswagen?
A: You can’t cross them since a mountain climber is a scaler.

[groan . . .]

written by SplineGuy

Since I am now on a roll with these “wonderful” capsules of hilarity, try a few more that tickled my funny bone. By the way, most of these are not that funny, but just plain sad. And yes, the title of this entry should probably read, “Worse Math Humor.”

written by SplineGuy

I laughed out loud for 15 minutes when I read this one.

Click here if you don’t get it.

HT: CastingOutNines

written by SplineGuy