I’m a theoretical mathematician, which, for those who may not know, means that I love math because it’s math (as opposed to practical mathematicians who are interested in math for its applications). So, my complaint might surprise you, because I’m annoyed that math education doesn’t provide any motivation for what I’m doing.

What you say?! Clearly I must be confuse and can’t be a theoretical mathematician! Hang in there – I’ll explain:

Most people I’ve talked to are practical mathematicians, which is really why math gets more and more hated as you learn more and more: because it becomes less and less useful in the average person’s life. But this is already well covered in Lockhart’s Lament, which I completely agree with.^{[1]}

What I didn’t expect was that if you keep studying math, you get past calculus and on to the proof of calculus. Which is all very theoretical and wonderful. And then, you go on to this thing called “complex variables”. What is this, you ask? Well, it’s calculus, but with complex variables. Well, I think so.

We talk about algebra with complex variables, and powers, roots, logs, trig functions, and all that fun stuff. Then we talk about complex series, and limits and integration and differentiation of series. This is all quite interesting from a theoretical standpoint, as you might expect. But then we started talking about “residues and poles”. Someone came up to me while I was working on the homework:

Them: “What are you working on?”

Me: “Complex variables.”

Them: “What is that?”

Me: “Well, right now we’re studying… residues and poles.”

Them: “What does that mean?”

Me: “It’s… Um… I don’t know…”

So, I thought about that, and I realized that I really don’t understand what I’m doing. I mean, I can find a residue and tell you what type of pole it is, but what have I done? M=1 and B=1/2, but what does that mean? And therein lies the problem. I’m sure there’s some wonderful question that arises out of the math I know for which the answer is “residues and poles”. But I don’t know what it is. So, if someday I saw a problem for which this method was the answer, even though I could solve it, I would have no idea what to do.

For those of you who went to college with me and remember Dr. Fast, that was half of why he was so awesome – because he explained to us the problem BEFORE we learned the solution, so we knew why we were learning whatever theory we were learning that day. Sadly, Dr. Fast was unjustly let go, and I am, for the first time in my life, stuck in a math class I don’t understand and don’t really care about. Which is really sad for a theoretical mathematician majoring in math.^{[2]}

Lockhart is even more right than I feared. We can’t just teach people how to solve equations anymore – We do need to help people discover solutions for themselves, but the first step is to explain to them what they’re doing in the first place. In the meantime, I’ll just keep being unmotivated to find new algebraic tricks for obtaining these meaningless residues and poles.

^{[1]}Also, I’m going to have to acknowledge Vi Hart for providing the alternative motivations of art and fun. Not sure this is sustainable in upper level math, but she certainly makes an admirable effort.

^{[2]}Disclaimer: My professor, Dr. Anderson, is a great prof, and he’s really good at teaching how to solve equations. I just wish I knew why I’m solving these equations…

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Very interesting, thank you for sharing!

Just stumbled on your post while googling about FreeNAS.

That’s a bit unfortunate to just give up like this (maybe you haven’t over the last 2 years?). There are dozens of applications for complex calculus in many fields of electrical engineering. Control theory uses this as a foundation, but you also find it when having to perform integrals in quantum mechanics, electromagnetics, and DSP. Often times you are integrating over periodic cosines, but it is much easier to do this over complex variables and then take the real part. For DSP and controls you typically see it in feedback systems through the Laplace transform.

I started in EE and was just drawn to math as I kept seeing these parallels coming up. I wanted to understand the commonality between methods in electromagnetics and methods in say, fluid dynamics. Math is the bridge between fields, but it takes time in all of them to see through the fog.