People often ask why they should learn maths, what is it good for, or what is its practical purpose. Many seem to think of literature, film, or history differently. People see these things enhancing their lives everyday when they get a reference, or can recite an interesting fact to friends. They get a bit of delight when they understand the phrase tilting at windmills, when they can recite some shakespeare to a loved one, or when they make friends laugh at an anecdote about Emperor Norton I. They don’t realize that knowledge about maths can enrich their lives in similar ways. Maths can be enjoyed in many aspects of life, such as understanding the jokes in the simpsons, understanding the origins of some idioms, recognizing absurd laws, and enjoying different kinds of puzzles and games.

The Simpsons is chock-full of maths jokes and references. In the episode “The Wizard of Evergreen Terrace” Homer Simpson models himself after Thomas Edison. On a blackboard seen in the episode is the equation 39871^{2} + 43651^{2} = 44721^{2} (“The Wizard of Evergreen Terrace”). This is a joke about Fermat’s Last Theorem. Fermat’s Last Theorem says that there are no integer solutions to the equation a^{n} + b^{n} = c^{n} when n is an integer greater than 2. The equation on the board seems to contradict this if you plug it into a calculator. This is because your calculator may not remember all the digits of the numbers as it calculates them. The numbers on the board were picked by the writers as a joke to look like Homer had found a counterexample to FLT. In the episode “Treehouse of Horrors VI”, Homer is pulled into the third dimension and runs into several maths references. These include another false counterexample to Fermat’s Last Theorem, the statement P=NP, and euler’s identity, e^{πi}= -1 (“Treehouse of Horrors VI”). There are many other references in The Simpsons and its sister show Futurama. These jokes and references come from the mathematicians who are working as writers on these shows. The writers enjoy maths, and they can see that it can also be funny.

Mathematics sometimes even enters everyday speech. If you have ever heard someone say something like “Your expectations do not square with reality” or “That is as hard as squaring the circle” you know some idioms based on mathematics. These phrases come from the ancient problem of squaring the circle. The problem is trying to construct a square with the same area of a circle using only a straightedge and compass. The first reference of the problem is from plutarch. He claimed that when Anaxagoras was imprisoned he spent his time trying to construct a square with the same area as a circle (Boyer 57). This problem persisted for thousands of years until, in 1882, it was proved to be impossible.

The impossibility to square the circle was not known to Edwin J. Goodwin, a physician from a small Indiana town. Goodwin thought that he came up with a proof that he could square the circle, but it depended on the ratio of the circumference of a circle to its diameter to be 3.2 (Singh 24). You might be aware (and if you are reading this blog you probably are aware) that the ratio of the circumference of a circle to its diameter is equal to π, an incommensurable number. In 1897, Goodwin proposed a bill to the Indiana General Assembly to legislate the value of π. He offered to let the schools in Indiana use his “Discovery” for free, and he offered to split the royalties from it with the state. Sadly, the Indiana House of Representatives members did not understand the mathematics in the bill and passed it (Singh 25). Luckily, when it got to the state senate there was a mathematician in the building. The head of the Purdue University Mathematics Department, C. A. Waldo, saw the bill and explained the absurdity of it to the legislators. After their brief lesson from Waldo, the state senators mocked the bill and did not pass it (Singh 25).

Mathematics can also provide a great deal of casual fun in the form of games and puzzles. Martin Gardner’s column, Mathematical Games, in Scientific American introduced people to interesting things based on mathematics. The column contained information about a variety of topics, including Graham’s Number, Hexaflexagons, and on April Fools in 1975 it contained a false counterexample to the Four Color Theorem. Today, many people play video and board games that are complicated enough that knowing some mathematics will allow you to enjoy the game on more levels. Minecraft is well known for allowing players to express their creativity and build whatever they would like. In the game, the item redstone works like a circuit. Redstone has 2 states, on and off, and can be used to make logic gates. This lets players learn about boolean logic while they are trying to construct their crazy contraptions. In strategy games, like Twilight Imperium or Risk, understanding the basics of probability is vital. You need to understand how the dice are going to behave to know when you have the advantage or your opponent has it. Should you attack twice with each attack having a low chance to succeed, or should you attack only once with a much better chance to succeed? Should you buy the technology that increases damage with each hit or the one that gives a better chance to hit? These kinds of questions come up all the time and can be answered by analyzing them mathematically.

Everyone knows that mathematics is useful for practical purposes. We know that the sciences rely heavily on mathematics, that we should understand how interest works if we take out a loan, and that there are many other places that require maths in a practical way. However, many people do not see that a little understanding of mathematics can expand their world in countless ways. Mathematics is far more than just playing with numbers or a tool to help physicists. Mathematics can be a way to understand a joke, it can help you play a game, or it can help you understand those around you.

Sources

Boyer, Carl B., and Uta C. Merzbach. *A History of Mathematics*. 3rd ed. Hoboken, NJ: Jon Wiley and Sons, 2010. Print.

Singh, Simon. *The Simpsons and Their Mathematical Secrets. *New York: Bloomsbury Publishing Plc, 2013. Print.

“The Wizard of Evergreen Terrace” *The Simpsons*. Fox. KVVU-TV, Henderson. 20 Sep. 1998. Television.

““Treehouse of Horrors VI”” *The Simpsons*. Fox. KVVU-TV, Henderson. 29 Oct. 1995. Television**.**