On Useless Knowledge

Where do you fall on the following spectrum?

1. I need to feel like what I’m learning will be obviously helpful to me (like, soon!); otherwise, I’m not interested.
2. I crave learning things, even when there’s no apparent use for what I’m studying.

I don’t know what causes people to slot into one category or another. In high school, I felt like most people were in the first one. I was in the second.

I think I liked it better when I couldn’t see a connection between what I was learning and what I’d need to know later. I’d like to claim it was faith, but I think it was a form of rebellion. Most of the kids I went to high school with rebelled against their parents and our teachers; I rebelled against the other kids.

Here’s how bad it got. By the time I was in college, most of my homework looked like this:

Prove that if $p$ is a prime and $G$ is a group of order $p$, then $G$ is isomorphic to $\mathbb{Z}_p$.

Or this:

Let $A=\{x:P(x)\}$ and $B=\{x:Q(x)\}$.
Prove that if $(\forall x)(P(x)\implies Q(x))$, then $A\subseteq B$.

Alien, right? I mean, c’mon—one of the letters isn’t even right-side up.

But I liked proving theorems so much that I made it my major. It had to have looked impractical at the time. What would I do with a math degree? I had no intention of becoming a math professor, and that’s the only possible use for proving theorems all day, right? But it felt right doing it, so that’s what I did.

My parents, by the way, never objected.

It ended up being a fantastic choice. It turns out, proving things is a marketable skill. One of the first times I noticed it was in a business law setting. My assignment was to prosecute a case. It didn’t take long to realize, hey, a case is just a proof! The underlying axioms were different (legal vs. mathematical), but the proving part was the same.

Proving things became my life’s work. It’s the foundational skill for two of the valuable jobs that I do:

1. Constructing sound recommendations; for example, “If you do $x$, then your users’ experiences will improve by $y$.”
2. Convincing people to follow those recommendations.

Proving is essentially a form of strict, formal communication. It’s a tool for convincing yourself and others. In school, I learned about mathematics and communicated my knowledge to my professors in exchange for good grades. At work, I learn about how to make things faster and communicate my knowledge to my customers in exchange for cash.

Proving theorems at work requires me to understand axioms from computer science, information technology, finance, various branches of mathematics, psychology, sociology, and more. But still, proving is just proving, and proving is my thing, no matter where my axioms come from.

In school, I couldn’t have imagined what practical use would come of all those hours spent alone with a pencil and paper. But when I look back in time, I see connections everywhere. Off the top of my head, I can say that getting good at proving theorems has made me better at:

• writing proposals
• negotiating contracts
• writing ad copy
• serving customers
• designing and building software
• teaching courses
• retaining employees
• recruiting partners
• bookkeeping
• defending my company

For me, what started out seeming to be useless knowledge ended up being the basis for my whole career.

There’s more than one lesson at work here. Here are a few:

1. Proving theorems might have looked like a waste of time, but it turned out to be a marketable skill.
2. It is a good habit to welcome knowledge, even when you can’t see what its tangible benefits will be.
3. Indulge your curiosity. It might be your mind trying to take you somewhere important.
4. Luck favors the well-prepared.

Good… luck.