The Math Myth

Suggests the article, yeah. I honestly don't buy that - citation needed. After some time STEM-educated people might not always remember exactly how what they learned works, sure. I certainly don't, for one. But I'd be hard pressed to believe they don't remember it exists - i.e. or at least remember enough to google their way into rediscovering it and finding a shortcut to solve their problem.

What is the generalised rule/case where small sample sizes are sufficient?

At my workplace, we have about 60 scientists and engineers. The author's observation is accurate, that most people never use math beyond Excel and 8th grade math. They also never use most of the theory that they learned in their science (including CS) and engineering educations.

The typical career arc is to get through college, then sit down at a CAD workstation, or programming terminal, and forget all of your math and theory within a few years or even months. Time that isn't spent doing CAD, is spent on testing, troubleshooting, dealing with vendors, and so forth. A few of them start prepping for management. It's becoming increasingly common for engineers to start their MBA training as soon as the company agrees to pay for it.

Truth be told, outside of a few life-support-critical applications, most design is done by trial and error. Very little real engineering gets done.

And the products we make, are designed to provide similar benefits in another profession. We are told by management: "Our customers don't want products that require them to think. They want something where a person with an 8th grade education can push a button and get an answer."

When a math or theory problem arises, they take it to the resident "math person." That's me. I'm glad that I spent the better part of my youth learning math and theory, because I'd be as suited to the CAD workstation as I'd have been to working at a loom, or a lathe, 100 years ago. For the most part, the people who emerge as "math people" are the ones who were interested in it as an end unto itself, in the first place. I didn't study math because I expected it to be necessary for a job. I studied math (and physics, programming, electronics, etc.) because I was interested in those things. They were for me an escape from preparing for my career.

It's also not strictly, theoretically true. More an 'for all intents and purposes' kind of thing.

At the level of individuals, this article is complete bullshit. There is a WORLD of difference between an average mathematician/physicist/engineer and an average English literature graduate solving the same problem with the same tools. Those disciplines teach and/or reinforce A) critical thinking (question assumptions, look for counter-examples), B) decomposing problems to smaller problems, C) pattern recognition. The average software engineer would be somewhere in the middle, he's probably as good as a mathematician at A) and B), but probably not C). Even amongst reasonably mathematically educated people (say physicists), you see a difference in C) depending on the depth of their math education. There is a difference between people who know eg fractions, and people who know eg fractions AND integrals, and people who know eg fractions AND integrals AND group theory, in how often these individuals look at a situation and go "I've seen something like this before". Acquiring some areas of more advanced maths isn't a quantitative increase like doing bigger sums. In terms of the patterns that you see around you, it's a qualitative jump. It's like being able to use your eyes AND having IR goggles: you will see some aspects of the world very differently.

At the level of societies, maybe. Can a poor society with lots of mathematicians "beat" a society with lots of wealth and infrastructure and comfortable niceties but whose individuals can only use Excel? Probably not, certainly not in < 1 generation. It certainly didn't turn out great for the soviets.