Posts tagged ‘blog’
I discovered Guillermo Bautista’s blog Proofs from the Book about a month ago, and I wrote about it last week. But just yesterday, Guillermo published a guest post showing the connection between proofs and jokes written by little ol’ me. His blog is worth checking out whether you want to read my post or not.
Paul Erdös once said, “You don’t have to believe in God, but you should believe in The Book.” He was referring to a mystical book in which the most elegant proofs of all theorems appear. The Book is the inspiration for the name of Guillermo’s new blog. Unfortunately, Martin Aigner and Günter M. Ziegler had the same inspiration when they published Proofs from THE BOOK in 1998. Some may think that this duplication is unfortunate. But I say that sometimes lightning strikes twice. After all, if Newton and Liebniz can both be credited for discovering the calculus, then Guillermo deserves as much credit as others for coming up with this awesome name.
The following are some methods of proof that are covered neither in the book Proofs from THE BOOK or at the blog Proofs from the Book.
Proof by Obviousness: “The proof is so clear that it need not be mentioned.”
Proof by Lack of Sufficient Time: “Because of the time constraint, I’ll leave the proof to you.”
Proof by Lack of Sufficient Space: “I have discovered a truly marvelous proof of this [theorem], which this margin is too narrow to contain.”
Proof by General Agreement: “All in favor?”
Proof by Imagination: “Wel, let’s pretend it’s true.”
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 we’ll assume it’s true.”
Proof by Intimidation: “Don’t be stupid; of course, it’s true.”
Proof by Accident: “Hey, what have we here?”
I replied in the only way I knew how. “Well, that’s a given.”
Of course, I was making a joke. But lots of people are like my friend and think that proofs are boring. They don’t see the beauty in proofs, probably because they’ve never been exposed to the beauty. That’s why I’m so excited that Guillermo started this blog. His proofs allows students to glimpse the beauty and elegance of mathematical theorems discussed in school mathematics, whether it’s proving that the square root of 3 is irrational, providing multiple proofs for the sum of the first n positive integers, or having a little fun and “proving” that 2 = 1.
Two of my favorite proofs follow.
Theorem. Every positive integer is interesting.
Proof. Assume that there is an uninteresting positive integer. Then there must be a smallest uninteresting positive integer. But being the smallest uninteresting positive integer is interesting by itself. Contradiction!
Theorem. A cat has nine tails.
Proof. No cat has eight tails. Since one cat has one more tail than no cat, it must have nine tails.
An excellent proof relies on mathematical insight. The most exciting moment of my mathematical life occurred while I was walking my dog. Though I had found an answer to the Three Points on a Square problem, I had no proof that it was correct, other than thousands of examples generated by Excel. With no pencil, no paper, and no agenda — just some time to think — an elegant proof came to me as I was picking up feces. (I have no idea what that says about me.)
This is my favorite part of mathematics. I can literally spend hours reworking equations, drawing figures, and thinking about a problem, and I’ll make no progress. Then later, when I least expect it, when I’m freed from the confines of pencil and paper, the solution gently alights in my mind like a butterfly coming to rest on a marigold.
My hope is that everyone has a chance to see as much beauty in mathematics as I have seen, and Proofs from the Book is a place where you can take a peek.
The following jokes, taken from Math Jokes 4 Mathy Folks, provide proof that math can be funny. Sort of.
Did you hear about the one-line proof of Fermat’s Last Theorem?
It’s the same as Andrew Wiles’ proof, but it’s written on a really long strip of paper.
At a conference, a mathematician proves a theorem.
Someone in the audience interrupts him. “But, sir, that proof must be wrong. I’ve found a counterexample.”
The speaker replies, “I don’t care — I have another proof for it.”
What’s the difference between an argument and a proof?
An argument will convince a reasonable man, but a proof is needed to convince an unreasonable one.
A meek man appeared in a court room, and the judge was incredulous when he read the charges against the man. “Sir,” said the judge, “you’re a well educated man. How did you end up here?”
“I’m a mathematical logician, dealing in the nature of proof.”
“Yes, go on,” said the judge.
“Well, I was at the library, and I found the books I wanted and went to take them out. The librarian told me I had to fill out a form to get a library card, so I filled out the forms and got back in line.”
“And?” said the judge.
“And the librarian asked, ‘Can you prove you’re from New York City?’ So I stabbed her.”
Let’s Play Math is hosting Math Teachers at Play 58, a blog carnival for math teaching and learning. This month’s issue includes two puzzles, links to at least 50 math blogs, and nine jokes that Denise borrowed from the MJ4MF blog.
What’s special about 58? Well, not much, except that it’s the minimum wind speed (in miles per hour) needed to issue a severe thunderstorm warning, it’s “the luckiest number ever” according to Patrick from SpongeBob SquarePants, and it’s an 11‑gonal number:
I highly encourage you to check out Math Teachers at Play 58, even if you’re not a teacher. But don’t go for the jokes; if you read this blog, you’ll have seen them all before. As it says at the carnival, “If you like to learn new things and play around with ideas, you are sure to find something of interest.” Sounds good to me. Enjoy!
The most popular post of the year was At 41, I’m Pretty Happy (1,640 views). It’s good to know that my old age is a topic of interest.
And when 1,796 people went searching for “ant” on October 6, they were directed to an image on Mathy Animals. (Phishers?)
No matter you’re reason for visiting, thanks for stopping by in 2012.
(Should you care, feel free to take a peek at the MJ4MF year-end report from WordPress.)
The MJ4MF blog was featured in another blog carnival, this one at Ramblings of a Math Mom.
Blog carnivals are collections of blog posts around a single theme. There are blog carnivals for all kinds of topics, including mathematics. The most recent carnival for mathematics was hosted by Maxwell’s Demon, and starting today, a new carnival will be hosted by Wild About Math. They’re fun, if for no other reason than to let you see lots of blog listings all in one place, which might introduce you to some new bloggers.
Q: How many bloggers does it take to change a lightbulb?
A: 100. One to change the lightbulb, and 99 to comment on how it should have been done.
For more blog carnival topics, check out Blog Carnival.
A man walks into a blogger’s office and sees a parrot next to the blogger’s desk.
“Does he talk?” the man asks.
“Nah,” says the parrot. “He just clicks.”