Math Jokes

The AMS has a 2005 paper “Foolproof: A Sampling of Mathematical Folk Humor” which is — delightfully — filled with math jokes. Excerpts:

Q: What’s sour, yellow, and equivalent to the Axiom of Choice?
A: Zorn’s Lemon.

Q: What is a topologist?
A: Someone who cannot distinguish between a doughnut and a coffee cup.

Theorem. All positive integers are interesting.
Proof. Assume the contrary. Then there is a lowest noninteresting positive integer. But, hey, that’s pretty interesting! A contradiction.

Q: How many light bulbs does it take to change a light bulb?
A: Just one, if it knows its Gödel number.

One day a farmer called up an engineer, a physicist, and a mathematician and asked them to fence in the largest possible area with the least amount of fence. The engineer made the fence in a circle and proclaimed that he had the most efficient design. The physicist made a long, straight line and proclaimed “We can assume the length is infinite…” and pointed out that fencing off half of the Earth was certainly a more efficient way to do it. The mathematician just laughed at them. He built a tiny fence around himself and said, “I declare myself to be on the outside.”

One day the Wiener family was scheduled to move into a new house. Mrs. Wiener, mindful of her husband’s propensity for forgetting, wrote the new address on a slip of paper and handed it to him. He scoffed, saying, “I wouldn’t forget such an important thing,” but he took the slip of paper and put it in his pocket. Later that same day at the university a colleague came by his office with an interesting problem. Wiener searched for a piece of paper and took the slip from his pocket to use to write some mathematical equations. When he finished, he crumpled up the slip of paper and threw it away. That evening, he remembered there was something about a new house but he couldn’t find the slip of paper with the address on it. Without any alternative course of action, he returned to his old home, where he spotted a little girl on the sidewalk. “Say, little girl,” he said, “Do you know where the Wieners live?” The girl replied, “That’s o.k., Daddy, Mommy sent me to get you.”

The full paper is here. For still more jokes, see this MathOverflow question and this page.

Hal Abelson on Math for Programmers

Seibel: So that explains why the book is the way it is. But in general for programmers, how much math and what kinds of math are important for working programmers to know?

Abelson: I don’t even know anymore. We have these arguments at MIT all the time. People say, well, there’s math. Other people say, well, what they really need to know are algebraic structures so you understand abstract data types, how you think about axiomatizing them. And then people say what you really need to know is what a mathematical proof is so you can think rigorously. And I don’t know what to say. These arguments have been going on for thirty or forty years.

Seibel: And have you ever had a position?

Abelson: Well, the last time I had a position I tended to say that they ought to be able to like a lot of math. I’ve never been partial to the thing that says they need to be able to do proofs, but that’s just taste. And again, these days the main thing you try to understand is abstraction. Maybe that’s related to proofs. You need to be able to say look, here’s this thing and here’s the rules for how it works. And then I don’t need to look below that layer most of the time in order to get started. And there are people who really get hung up on that.

Hal is known for, among other things, co-authoring perhaps the most influential programming book of all time, Structure and Interpretation of Computer Programs. The entire interview is here.

It Probably Won A Prize

Architect Sam Sloan coordinated a project in which employees … were able to select their own office furniture and plan office layout … Since both the Seattle and Los Angeles branches of the FAA were scheduled to move into new buildings at about the same time, the client for the project, the General Services Administration, agreed with architect Sloan’s proposal to involve employees in the design process in Seattle, while leaving the Los Angeles office as a control condition where traditional methods of space planning would be followed.

Several months following the move into the new buildings, surveys by the research team were made in Los Angeles and Seattle. The Seattle workers were more satisfied with their building and work areas than were the Los Angeles employees… [T]he Los Angeles building has been given repeated awards by the American Institute of Architects while the Seattle building received no recognition. One member of the AIA jury justified his denial of an award to the Seattle building on the basis of its ‘residential quality’ and ‘lack of discipline and control of the interiors,’ which was what the employees liked most about it. … Employees in both locations rated their satisfaction with their job performance before and after the move into the new building. There was no change in the Los Angeles office and a 7 percent improvement in rated job performance in the Seattle office.
—from The Design of Everyday Things

Why Dogs Bark At Night

A reformed thief, telling of his success, put it this way, “I’m telling you, if I had a hundred dollars for every time I heard a dog owner tell their dog to ‘shut up and go lie down’ while I was right outside their window, I’d be a millionaire.”
<span id=”quote-attribute”>—from <em>The Design of Everyday Things</em></span>

Presumably, if he were any good, he’d already be a millionaire.

Zach Weinersmith On The Importance Of Reading Books

Zach Weinersmith writes Saturday Morning Breakfast Cereal, my current favorite webcomic. I wanted to know: Where’s this creativity spring from?

Turns out, he reads. A lot.

I try to read 3-5 books a week in many different subjects. Whenever I stop that, I run out of ideas reaaallll fast.

When asked about his writing process:

Usually I just read a lot (at LEAST 4-6 hours a day) then sit myself in front of a blank google doc and try to write.

Or how to overcome writer’s block:

If you can’t write, read more. In my experience, writer’s block is not a condition, but a result. Lots of people seem to think they can play video games 12 hours a day, then one day happen upon a great idea. It doesn’t work that way. You’ve got to put in time on input if you want good output.

When someone asked how he manages to publish everyday:

I try very hard to read a lot and write a lot.

And when asked about his inspiration:

I really just try to read a lot, think a lot, then write for an hour a day. I also schedule my life a lot. So far that seems to be working all right.

On what to read:

It’s very liberating to read a book on a subject you think is boring. You might end up surprised.

I read pretttty much anything.

His broader philosophy here:

Most people tend to like what they like. I try to like things I dislike.

Why does he read so much?

Also, in general, if you’re an entertainer, you have precisely one job – be more interesting than the people you are entertaining. Otherwise why should they listen to you. That’s why if you want to improve at your work, self-cultivation is the best route.

Remember, you get paid to be more insightful than people who don’t write. That means you have to read more and think more.

He’s not the first to push the virtues of reading. Warren Buffet says his secret is “reading 500 pages a day.” Alan Kay reportedly attempts to read a book a day. Who knows how much Chomsky reads? Stephen King says, “If you want to be a writer, you must do two things above all others: read a lot and write a lot.” And so on.

You Could Have Discovered Quantum Mechanics

Quantum mechanics is what you would inevitably come up with if you started from probability theory, and then said, let’s try to generalize it so that the numbers we used to call “probabilities” can be negative numbers. As such, the theory could have been invented by mathematicians in the nineteenth century without any input from experiment. It wasn’t, but it could have been… And yet, with all the structures mathematicians studied, none of them came up with quantum mechanics until experiment forced it on them. And that’s a perfect illustration of why experiments are relevant in the first place! More often than not, the only reason we need experiments is that we’re not smart enough.
Quantum Computing Since Democritus

The chapter itself goes into more details. You should buy a copy. The author blogs.

Statistician on a Plane Joke

Speaking of probability and statistics, there is the story of a statistician who told a friend that he never took airplanes: “I have computed the probability that there will be a bomb on the plane,” he explained, “and although this probability is low, it is still too high for my comfort. ” Two weeks later, the friend met the statistician on a plane. “How come you changed your theory?” he asked. “Oh, I didn’t change my theory; it’s just that I subsequently computed the probability that there would simultaneously be two bombs on a plane. This probability is low enough for my comfort. So now I simply carry my own bomb.”
—from To Mock a Mockingbird

Bill Thurston on Reading Hard Things

I was really amazed by my first encounters with serious mathematics textbooks. I was very interested and impressed by the quality of the reasoning, but it was quite hard to stay alert and focused. After a few experiences of reading a few pages only to discover that I really had no idea what I’d just read, I learned to drink lots of coffee, slow way down, and accept that I needed to read these books at 1/10th or 1/50th standard reading speed, pay attention to every single word and backtrack to look up all the obscure numbers of equations and theorems in order to follow the arguments.
—Bill Thurston, from the foreword to Teichmüller Theory and Applications to Geometry, Topology, and Dynamics

He goes on to talk about the importance of using one’s whole mind in understanding mathematics. You might want to check it out.

Two Cultures of Number Theorists

There is a famous distinction in prime number theory between the number theorists who like to multiply primes, and the number theorists who like to add primes. As the primes are very heavily multiplicatively structured, the mathematics of multiplying primes is very algebraic in nature, in particular involving field extensions, Galois representations, etc. But the primes are very additively unstructured, and so for adding primes we see the tools of analysis used instead (circle method, sieve theory, etc.).

Mentioned by Terry Tao in a comment at n-category cafe.

Feynman on Reading Difficult Things

Well, I asked him, “How can I read it? It’s so hard.” He said, “You start at the beginning and you read as far as you can get, until you are lost. Then you start at the beginning again, and you keep working through until you can understand the whole book.”
—Joan Feynman, Richard Feynman’s sister, recalling a discussion with her brother

Taken from No Ordinary Genius.