Thank you all for your comments on my previous post, I appreciate the time you all took in sharing your perspectives very much.  Many of you have brought up great analogies to demonstrate how you feel and in reading these responses I realized I must not have been very clear.

There are some musical geniuses who have composed great works without having been taught even the basics of music theory. However, this doesn’t mean they’re not doing math. The human brain excels at building approximate mathematical models and a rare few minds are capable of building exceedingly complex ones. Still, formal knowledge of the patterns of music allow a musician to both play the same song in new and interesting ways and see the underlying connections between different pieces. As a composer it informs how rhythms and melody can be juxtaposed or fitted together to create a desired effect in a way much more profound than trial and error. It expands the musician’s mind and makes them better at what they do. 

Another great example is that of the wrench wielding mechanic. There are a great many mechanics who went to trade school and learned the high level basics of engines and a long list of procedures. They might not understand the details of combustion or material science but they can replace brake pads or swap in a new timing belt without too much difficulty. After many years of experience some may have even built a mental model so superb that they can take you for a spin around the block and tell you exactly what’s wrong.

And still, as the mechanic reaches for their bolts and wrench they might not think of the underlying mathematics of what they are about to perform. Yet, you can be sure the people who made those tools worried over it greatly. If they didn’t the wrench would not fit the head or worse, the bolt might shear under the stress applied. While they surely tested many bolts before shipping their product, they certainly didn’t before creating a formal model of how the tools were shaped or how they would perform. Even if the tools might happen to work without testing, they probably wouldn’t work very well and to sell tools made in this way would be grossly negligent.

Yet, I can’t be the only one who has suffered many near catastrophes at the hands of inept mechanics over the years. From the time a post-brake change air bubble in my brake line made my car roll out into traffic or the punctured gas tank that almost left me stranded at the side of the road. One might wonder if they even bothered testing their work.

Some might think programmers shouldn’t be beholden the same strictness as our creations aren’t usually capable of quite so much damage. Instead, the worst things most are liable to do are destroying important information, providing incorrect data to critical systems, leaking private information, sharing unsalted (or worse, unencrypted) passwords or causing people to become unable to access their bank or medical records. No big deal really, just shoveling data.

I’d love to see every programmer taking the time to learn deeply about the mathematical modeling of data and programs, but I know that’s not reasonable. However, it takes just a little bit of learning to leverage tools with very complex underlying mathematics made by others. You don’t need to be an expert in category theory to use Haskell any more than you need to be an expert in set theory to use SQL. F# and Scala are even more accessible as they have access to all of the libraries and patterns you would be familiar with as a programmer who works in .NET or Java.

So, I’m not asking that you go out and spend years studying your way to the equivalent of a PhD. Instead what I ask is that you just take a little time to understand what’s possible and then use tools made by people who do have that kind of deep understanding.

I know I wouldn’t want to drive a car with parts made by someone who didn’t use models, would you?

Huge thanks to @danfinch and @TheColonial for proof reading.