If you’ve spent any time learning a specialized subject along with a group of friends & peers, you’ve probably experienced Discipline-Specific Humor—that uncomfortable but oh-so-funny form of joke telling that only makes sense to you and your fellow students. Usually, they rely on a carefully-constructed pun (like this one), but occasionally they tell you something about the inner-workings of the discipline.

Since I’m a mathematician by training, math jokes are the ones I appreciate the most. I’m guessing you’ve all heard a few in your school days, and maybe you’ve even heard a few outside of the world of the math class.

What I’d like to do here is lay out some of my favorite math jokes, and spend a moment examining what exactly they tell us about mathematics and mathematicians. You may learn something new about the intellectual habits of the field, and you’ll definitely gain an appreciation for the people whose quirks give this subject some of its appeal. Here we go!

An engineer, a physicist, and a mathematician were on a train ride through Scotland. They passed by a field with a black sheep in it. The engineer said, “hmm, I guess sheep in Scotland are black.” The physicist said, “well, at least one sheep in Scotland is black.” The mathematician said, “there exists at least one sheep in Scotland, at least half of which is black.”

Mathematicians are known for being annoyingly precise. One famous case appears in Imre Lakatos’ book, *Proofs and Refutations*. In it, a professor and a group of students try to prove Euler’s formula: “The number of vertices of a polyhedron, minus the number of edges, plus the number of faces, equals 2.” The thing is, they go through a dozen proofs (and refutations of those proofs), and just as many reformulations of the theorem. After a while, you’re not sure that any mathematical statements are true at all! (Don’t stop there, though, because Lakatos brings it home eventually.) Good times. Next:

A physicist and a mathematician live in adjacent apartments. In the middle of the night, an electrical short starts fires in both of their kitchens. The physicist awakes first, sees the fire, grabs the fire extinguisher, and puts it out. The mathematician awakes later, sees the fire, then sees the fire extinguisher, and says “Aha! A solution exists!” and returns to bed.

Okay, I love this one. In mathematics, there’s a distinction between “constructive” proof and “existential” proof. Constructive proofs rely on the fact that you can find an example of something that has a desired property: for instance, you can prove the statement “there is a positive number *x* for which *x*²–*x*–2 equals zero” by pointing out that the number 2 satisfies this property. However, you can’t take this approach with the statement “there is a power of 2 that begins with the digits 50283086.” (Prove me wrong, I dare you.) Nonetheless, this is a true statement. (The general theorem is “For any positive integer *n*, there is a power of two whose first digits make up the number *n*.”) Maybe I’ll give the proof in a future post. In the meantime:

A biologist, a physicist, and a mathematician are having lunch at a sidewalk cafe. They see two people enter an apparently-empty building across the street; a few minutes later, the same two people leave with a third person. The physicist says “Our initial observation must have been incorrect.” The biologist says “They must have multiplied.” The mathematician says, “If another person enters the building, it will be empty again.”

Math gets some ridicule for being a “head in the clouds” sort of subject, where decades-long research programs could have no immediate applications to the real world. This isn’t all that fair—there are lots of applications of mathematics! More to the point, though: one of the best things about mathematics is that *it has real-world applications regardless of whether a mathematician is looking for them or not*. A famous example is Riemannian geometry, which was a paragon of “head in the clouds” mathematics, until it became the framework for general relativity theory. It’s a similar story for linear algebra and quantum mechanics. And here are some other theory/application pairings you might not know about: group theory & quarks, field theory & cryptography, and even Graeco-Latin squares & experimental design (see Klyve & Stemkoski and then go find Ronald Fisher’s book, *Design of Experiments*).

This last one’s just for fun:

Professor Wilson and his family recently moved to a new neighborhood. Since the professor was known to be absent-minded, his wife wrote down their new address on a slip of paper and gave it to him as he left the house for work that morning. At some point during the day, he needed to write down an important equation for a student, and took out the slip of paper to write it on the back, and gave it to the student. Forgetting all about the paper, and his new house, he went back to his old house. Realizing his mistake when he arrived, he said to the young girl on the front step, “Hello, little girl, do you know where the Wilsons live?” The girl said, “It’s okay, daddy, mommy sent me here to get you.”

I can be absent-minded sometimes, but I’m very glad it’s not *this *bad.

Finally, if you’re yearning for some more math geek humor, go here next.

“However, you can’t take this approach with the statement “there is a power of 2 that begins with the digits 50283086.” (Prove me wrong, I dare you.)”

I assume you speak of integer power here. First integer power of 2 that fulfills this requirement is 7891588 – decimal expansion is, of course, almost 2.4 million digits long, but nonetheless. Little play with logarithms, arbitrary-precision arithmetic and brute force is enough in this case; and brute force could be replaced with sophistication, to some extent.

http://www.wolframalpha.com/input/?i=2^7891588

Ah yes, WolframAlpha has messed up my off-the-cuff estimations yet again. But you can always choose a bigger number!

Actually this computation took couple minutes on Mathematica, Wolfram Alpha is just a “proof” of the find. Probably the problem could have been written in more clever way, requiring only fractions of a second to compute.

What is computable can indeed be sometimes hard to tell if it’s infeasible to prove through giving an positive example for an hard-looking example. Modern cryptography tends to stand on this edge all the time.