Isn’t it great? The picture shows a farmer neglecting his fields while trying in vain to solve the famous sliding block puzzle (also known as the 15-puzzle). In this case, the puzzle is set to Loyd’s starting configuration—with the 14 and 15 switched. Loyd offered $1000 for the first correct solution of this puzzle. He wrote:

People became infatuated with the puzzle and ludicrous tales are told of shopkeepers who neglected to open their stores; of a distinguished clergyman who stood under a street lamp all through a wintry night trying to recall the way he had performed the feat… Pilots are said to have wrecked their ships, engineers rush their trains past stations and businessmen became demoralized… Farmers are known to have deserted their plows and I have taken one of such instances as an illustration for the sketch.

Unfortunately mathematical research is often too much like this picture—Loyd never paid out the $1000 because his 15-puzzle is impossible to solve. The proof of impossibility is a nice application of group theory. Johnson and Story gave the first proof in 1879 (you can find their article here, although it may require a password; see this article for a more modern treatment).

Incidentally, Sam Loyd insisted until his death in 1911 that he invented the puzzle. However, in a recent book (that has a whopping 3 subtitles!), The 15 Puzzle: How It Drove the World Crazy; The Puzzle That Started the Craze of 1880; How America’s Greatest Puzzle Designer, Sam Loyd, Fooled Everyone for 115 Years, Jerry Slocum and Dic Sonneveld show that this was another instance of Loyd’s trickery and deception. They investigated the the origin of the puzzle and discovered that Loyd was not the inventor. The puzzle was invented around 1874 by Noyes Palmer Chapman, a postmaster from Canastota, New York.

1. Finite Simple Group (of Order 2) by the Klein Four Group (lyrics). This excellent song was written and performed by graduate students at Northwestern University, where I did my graduate work. I think it is funny that I noticed the familiar stairwell before I noticed the familiar professors (in the background).

2. Nonagon by They Might be Giants (which I posted in this blog post). Of course, they have a full CD/DVD of math songs: Here Come the 123′s.

3. A Song About Pi by Irving Kaplansky, sung by Lucy Kaplansky (my blog post about the song)

4. Pi by Kate Bush (lyrics). This is a surprisingly nice song in which Kate Bush sings the digits of pi (too bad she made some mistakes—artistic license wins over mathematical rigor?)

5. One Geometry (rapped to the tune of Snoop Dogg and Pharrell William’s “Drop it Like it’s Hot”) by Steve Sawin (AKA Slim Dorky) (lyrics). I posted this video about the Poincare conjecture on the day that Perelman was chosen as a Clay Millennium prize winner—an award that he famously turned down.

6. Down With That (Bolzano Weierstrauss Rap) by Steve Sawin (AKA Slim Dorky) (a previous blog post has links to the lyrics)

7. Lobachevsky by Tom Lehrer (I gave links to other math songs by Tom Lehrer in a previous blog post)

8. I Will Derive (to the tune of Gloria Gaynor’s “I Will Survive”) (lyrics)

9. Mathematical Pi (sung to the tune of Don McLean’s “American Pie”) by Ken Ferrier and Antoni Chan (lyrics)

10. Calculus Rhapsody (to the tune of Queen’s “Bohemian Rhapsody”) by Mike Gospel and Phil Kirk (lyrics)

[Edit] OK, I said 10, but I forgot to add this one when I made the post live. Thanks to Blair for reminding me…

11. The twelve days of Christmath by Vi Hart (be sure to check out all of Vi Hart’s videos)

Bonus video. This isn’t a song, and it isn’t really about math. It is just a hilarious video about numbers.

24 is the highest number from Mr. Show

Irving “Kap” Kaplansky (1917–2006), the mathematician and former head of MSRI, was also a pianist and songwriter. In 1973 he brought all of these interests together to pen a song called “A Song about Pi.” The tune is was inspired by the digits of pi (C~1, D~2, etc.). You can read more about how he chose the structure for the song on Ivars Peterson’s MathTrek page. That page is also where I obtained the lyrics:

In all the bygone ages,
Philosophers and sages
Have meditated on the circle’s mysteries.
From Euclid to Pythagoras,
From Gauss to Anaxag’ras,
Their thoughts have filled the libr’ies bulging histories.
And yet there was elation
Throughout the whole Greek nation
When Archimedes made his mighty computation!
He said:

CHORUS

3 1 41 Oh (5) my (9), here’s (2) a (6) song (5) to (3) sing (5) about (8,9) pi (7).
Not a sigma or mu but a well-known Greek letter too.
You can have your alphas and the great phi-bates, and omega for a friend,
But that’s just what a circle doesn’t have–a beginning or an end.
3 1 4 1 5 9 is a ratio we don’t define;
Two pi times radii gives circumf’rence you can rely;
If you square the radius times the pi, you will get the circle’s space.
Here’s a song about pi, fit for a mathematician’s embrace.

Irving Kaplansky’s daughter Lucy is a folk singer. Here she is performing “A Song about Pi.” (If you want to skip straight to the song, go to 2:58.)

I decided to ask my Twitter followers if they knew where I could find this mystery logo. I haven’t gotten a reply about that, but Blair Miller pointed me to a fantastic Wikipedia edit from April 15, 2009. It was a section on the Edmonton Oiler’s page that read:

Edmonton Eulers

During the month of February 1972, the Oilers temporarily changed the franchise name to the Edmonton Eulers as a tribute to mathematician Leonhard Euler (Euler’s number ~ 2.72, thus corresponding with the month 2/72). The team introduced jerseys with lowercase “e”s in place of the usual capital “E”s at the beginning of both city and team name, first wearing them during a home game on February 1. For the entire month, the team utilized a pricing scheme for individual tickets akin to Euler’s formula to approximate e, using n as the day of the month:

Ticket prices started out at $1.50 on February 1, topping out at $2.67 on February 29. Fan reaction to the temporary change was mixed: in general, casual fans were deeply confounded and upset by the change, while more mathematically-oriented fans welcomed the change with open arms, some going even so far as to suggest that it be permanent. The tension and confusion were relieved on March 3, when the Oilers reverted to their old jerseys for an away game against the Winnipeg Jets.

The edit lasted for about 2 hours.

While of course it would be really cool if this were a true story, it is easy to debunk. No, I didn’t go to Snopes, I just looked at the Edmonton Oiler’s schedule. It turns out that they were founding members of the World Hockey Association and this league’s first season was 1972-3. The Oiler’s first game was October 30, 1972 (as the Alberta Oilers), several months after the supposed name change.

Were you ever looking up papers in MathSciNet and you found one that especially made you smile or laugh? And were you ever wishing that MathReviews were sorted by amusement factor? Well, we did. In fact, it is a long-standing game among many mathematicians to find the most amusing or worst MathReviews they can.

As a gesture of humanitarianism, I’ve compiled a list of what I take to be, for one reason or another, exceptional MathReviews of which I have been made aware. A review may merit listing by being unexpected, witty, scathing, humorous or otherwise deviating considerably from the run-of-the-mill reviews. It may be either good or bad, called for or uncalled for, but it should be in some way exceptional.

Here are a few of the reviews (or snippets of reviews) that I found while browsing the list.

Spike Milligan wrote of a certain poet that he tortured the English language, yet had still not managed to get it to reveal its meaning. Trying to fathom the paper under review is similarly frustrating.

It is hard to imagine in a single paper such an accumulation of garbled English, unfinished sentences, undefined notions and notations, and mathematical nonsense. The author has apparently read a large number of books and papers on the subject, if one looks at his bibliography; but it is doubtful that he has understood any of them… What is amazing to the reviewer is that such a thing was ever printed.

Not every text containing mathematical formulae or terminology may be considered as a scientific work. Sometimes it is a mere imitation. My impression is that this is exactly the case of the paper under review.

The author adds three introductory sentences to a paper of G. P. Whittle [Discrete Math. 54 (1985), no. 2, 239; MR0791665 (86j:05047)] and changes the word “principal” to “fundamental”. He also adds an acknowledgement to the referee but fails to add an acknowledgement to Whittle for writing the original paper.

This paper seems to the reviewer to contain no mathematics.

The author asserts that “this book is written by an amateur for other amateurs, but we amateurs won’t mind having the professionals reading over our shoulders”. The reviewer, a professional, would like to benefit from whatever insights the author may have. However, he has not been able to see through the blizzard of unusual (and largely unexplained) notations and formulas that fill the 274 hand-written pages of this book. If the author has a message for professional mathematicians, he will have to try again, using a language that is not a personal secret.

First, I came across this interesting blog post that asks how many times you would have to fold a piece of paper so that its thickness would be the same as the distance from the earth to the moon. It is a really nice illustration of exponential growth.

Speaking of 42…

I also received a nice email from David Freeman, whom I’ve gotten to know (electronically speaking) since he first contacted me after I wrote a blog post that mentioned him (in my 13th Division by Zero blog post). David’s email contained three of his favorite mathematical quotes from The Hitchhiker’s Guide to the Galaxy. (I especially like the second one. The first is funny because it so true.)

The startling truth finally became apparent, and it was this: Numbers written on restaurant checks within the confines of restaurants do not follow the same mathematical laws as numbers written on any other pieces of paper in any other parts of the Universe.

“The Hitchhiker’s Guide to the Galaxy” offers this definition of the word “Infinite.” INFINITE: Bigger than the biggest thing ever and then some. Much bigger than that in fact, really amazingly immense, a totally stunning size, real “wow, that’s big,” time. Infinity is just so big that by comparison, bigness itself looks real titchy. Gigantic multiplied by colossal multiplied by staggeringly huge is the sort of concept we’re trying to get across here.”

And finally this humorous quote that contains some shady mathematical reasoning:

It is known that there is an infinite number of worlds, simply because there is an infinite amount of space for them to be in. However, not every one of them is inhabited. Therefore, there must be a finite number of inhabited worlds. Any finite number divided by infinity is as near to nothing as makes no odds, so the average population of all the planets in the Universe can be said to be zero. From this it follows that the population of the whole Universe is also zero, and that any people you meet from time to time are merely the products of a deranged imagination.

Today I read a short blog post by John D. Cook called There isn’t a googol of anything, which is a nice discussion a very large number. I think it interesting to put it up against the second of the Hitchhiker quotes.

Finally, here’s a quote that one of my colleagues sent to me the other day—it is also related to the infinite and the infinitesimally small. It is St. Thomas Aquinas’ solution to Zeno’s arrow paradox:

Instants are not parts of time, for time is not made up of instants any more than a magnitude is made of points, as we have already proved. Hence it does not follow that a thing is not in motion in a given time, just because it is not in motion in any instant of that time.

There is a puddle…

…on an island…

…in a lake (Crater Lake)…

…on an island (Volcano Island)…

…in a lake (Taal Lake)…

…on an island (Luzon, Philipines)…

…in the ocean.

1. Klein bottle house
2. Come in/Go away ambigram doormat
3. Klein bottle bottle opener
4. Chair made of Voronoi cells
5. Tiling a floor with irregular pentagons
6. A Möbius bridge
7. The Pittsburg Steelers logo (and my blog post about it)
8. Nesting Fibonacci kitchen knives
9. Mathematical clocks and spiral clocks
10. Fibonacci sequence rings
11. Mathematical holiday cookies
12. Fractal jewelry
13. Shiny fractal cow

I’m sure there are many more. Add your own discoveries in the comments…

Usually @TeXtip posts are useful tips or factual tidbits about the typesetting program. I decided to send him a humorous suggestion instead. He posted the tip on Twitter yesterday. I sent him a link to Hanno Rein’s coffee.sty package which adds a coffee stain to any LaTeX document.

Today I remembered another fun LaTeX package that I’d encountered years ago. The Simpsons package allows you to insert Bart, Homer, Maggie, Mr. Burns, Lisa, Marge, or the Springfield Nuclear Power Plant into your LaTeX document. (The screenshot below is from the Comprehensive LaTeX Symbol List.)

To use this on your own, go to this web page and download the simpsons.sty file. Put it somewhere that LaTeX can find it (putting it in the same directory as your tex file is fine) and put \usepackage{simpsons} at the start of your document. Then you can get your favorite character to appear using the commands \Bart, \Homer, etc. (no dollar signs needed, by the way). You can make the character turn to the left using \Left. Also, you can specify the location of the characters’ two pupils by using the \Goofy command (the coordinates for the normal pupil locations are (0,0) and (0,0)). For example, \Left\Goofy\Bart(1,1.6)(.85,1.6) produces an image of the left-facing Bart rolling his eyes at his sister Lisa (below).