The PhD of Comedy

It's practically a tradition for math teachers to subject their students to hackneyed old jokes. Such math jokes are part of the cultural heritage of mathematics handed down from teacher to student for generations: What's purple and commutes? An Abelian grape. Did you hear about the dog in the Complex plane? He left a residue at every pole. Sometimes they can even be funny. Students in Dr. Lew Lefton's mathematics classes at the University of New Orleans, however, can be sure that not only will they learn some beautiful math, but also that the man can tell a joke. After all, he's a professional.

Legislating Pi

Everyone knows that the legislature of the state of Indiana once passed a law setting the value of pi. Well, perhaps not everyone knows it, but many people with only a passing acquaintance with mathematics have it firmly in their heads that one of our sovereign states once tried to impose its will on a constant of nature. Everyone may not remember all of the details precisely: the date is often recalled only vaguely, and it might have been the legislature of Iowa, or Idaho, or maybe Illinois but no one has any doubt that pi was the subject of legislation.

The Ultimate Flat Tire

How flat can a tire be and still roll? Can something as straight as a straight line be used as a wheel? Sure, if, as explained below, one uses some care in defining its center. The insight is due to G. B. Robison in 1960 [1]; he also realized that by suitably truncating a doubly infinite straight line one could form a square wheel, which would indeed roll on a properly shaped road.

The Roots of the Branches of Mathematics

Mathematics is justifiably called the Queen of the Sciences. Our word mathematics comes from the ancient Greek term mathematikos. Ask a friend sometime to guess what the word meant originally: you are likely to get some narrow response like "numbers", "calculation", "equation." Actually, the root meant "mental discipline" or "learning." Plato, the Greek philosopher who flourished around 380 BCE, believed that no one could be considered educationed who was not trained in such mental discipline, such mathematikos. He went so far as to say, "He is unworthy of the name of man who is ignorant of the fact that the diagonal of a square is incommensurable with its side." The etymology of the word "mathematics" is a concentrated residue of the sweeping way in which this activity was conceptualized in the ancient world.

A Dozen Reasons Why 1=2

Guidobaldo del Monte (1545-1607), a patron and friend of Galileo for twenty years, believed he had witnessed the creation of something out of nothing. In athematically proving that 0=1 he thought he had clearly established the existence of God! I daren't be so bold with my claims, but I am willing to suggest instead that 1=2.

Irrationality Dominates Pi

I never should have asked my in-laws to go with me to see the movie Pi. Luckily, they didn't accept. But that just meant I had to tell them about it later.

A Student Visits Mathfest

As a freshman, I knew very little about the life of a professional mathematician. I only saw professors in my department teach and research. I did not know who was in the math community or the areas of current research outside the department either. Fortunately, my advisor knew the benefits of attending professional meetings and convinced me to attend Mathfest, the joint summer meeting of the Mathematical Association of America, MAA, and Pi Mu Epsilon, PME, in Burlington, Vermont in 1995.

Fighting Tuberculosis with Mathematics As a freshman at St. Olaf College, I was entirely undecided about choosing a major. Taking full advantage of the breadth of opportunity at a liberal arts school, I registered for a smorgasbord of classes. Each semester, however, I took one math class. Amidst the changing array of other classes in my schedule, I looked forward to my math class as a source of order and clarity. The math classes became progressively more difficult, but I continued to do well, often surprising myself. I gravitated toward activities that utilized my math skills, including tutoring other students in mathematics. I chose a favorite professor in the Mathematics Department as my advisor. When the time came for me to declare a major, I chose mathematics -- not because I envisioned how I would use the major after graduation, but because I enjoyed the classes (and already had completed half of the necessary course work at that point!).

Problem Section:

S-23.

Proposed by Allen G. Fuller, Gordon College. A number is a palindrome if it reads the same backwards as forwards, e.g., 1846481. Prove that a palindrome with an even number of digits (in base 10) is divisible by 11. Generalize.

S-24.

The "size" of a rectangular box is defined as the sum of its length, width, and height. Is it possible for a rectangular box to contain another one of greater size?

S-25.

Proposed by E. M. Kaye, Vancouver, B.C. A given polynomial P(x) takes on real values for real values of x and non-real values for values of x. Prove that P(x) is linear.

S-26.

Proposed by Emilia Simeonova, student, Macalester College. Show how to construct a perpendicular to a line L through a point P lying on L using only an unmarked straightedge and a pair of dividers. Note that the dividers can only be used to transfer distances from one line onto another.

The Final Exam: Who Said It?

Karl Weierstrass, the nineteenth-century German mathematician, once said, "A mathematician who is not also something of a poet will never be a complete mathematician." Most of the people quoted below were decidedly complete mathematicians, and their words have become part of the history or folklore of mathematics. We have selected some famous (and some not-so-famous) musings, aphorisms, quips, and quotes about mathematics, and we want you to identify the speaker (who is usually, but not always, a mathematician).