What’s in a name? that which we call a rose

By any other name would smell as sweet. – Shakespeare

A name is just a name. We, as mathematicians, are happy to define something to be whatever you want it to be. You want to call that function** f**? Go for it! Maybe you are in a Γ mood. That’s okay too. We’ll accept a function to have whatever name you want it to have. …up to a point. I mean, you can call it whatever you want. But, you can bet you me that if you name the darn thing π or O (pronouced “Big O”) we will all complain to the end of time. And Yes, for all you non-mathematical folks out there, there really is a function, or more accurately a notation, called Big O. Ask Wikipedia. Didn’t the folks who first started using Big O notation realize it looks exactly like a zero??

What was I saying? Oh, yes. Freedom of naming. If you want to name your child Jake then people might assume the child is white. Freaknomics famously wrote about this in 2005. But then, they may be wrong? Regardless, what I really want to talk about is **the nomenclature of mathematics**.

Secretly, every mathematician has strong opinions on the subject. Let’s start with something simple.

The lower case a seems fairly innocuous. *Little a* has many great qualities. He is the **first** letter that comes to mind (hehe, it’s a terrible joke but I can’t help myself!).* Little a* looks great with a bar, prime or hat!

Now here comes the picky part. *Little a* is for constants. In fact, the first 3 or 4 letters are reserved for constant values. Variables come from the end of the alphabet. Do no vary from this unspoken mandate. To stray is verboten! Thus, a polynomial might be written as:

## ax² + bx + c

But what if you need more than four constants? Then, I’m happy to say that *little a* looks great with indices and subscripts! Just look:

## a2x² + a1x + a0

## b2x² + b1x + b0

Looks really great! Indices look great with the second equation of *little b*s as well! But sometimes we need a random constant. Then there’s trouble. We need an arbitrary index. Mathematicians like to use i, j, and k for this. So, as an innocent mathematician, you pick the first:This is all well and good until you need another arbitrary constant for a different equation…

And anyone who doesn’t see a problem with using the term “bj” in a classroom full of mostly male teenagers is awesome and I appreciate your innocence. But, rude jokes aside, mathematics get very passionate about their nomenclature. Suffice to say, to a mathematician, a rose by any other name is acceptable, but it would **not** smell as sweet.

Maybe I can tell you more about this later. Maybe I need to do some social research on the topic…

The difference between, a, b, c …, i, j, k …, and x, y, z … has been around for a while. In 1957 it was so entrenched that when one of the first computer programming languages was defined (for mathematically-trained programmers and called Fortran [FORmula TRANslator]), the variables a, b, c …, and x, y, z … were automatically real numbers (also called floating point in those days), and i, j, k … were for automatically integers. The idea that “you can call it whatever you want” didn’t get introduced until later.