Relating natural language aptitude to differences in learning programming

Honestly the biggest benefit I can see with knowing some math beyond basic arithmetic for some types of programming is understanding code complexity and big-O notation.

If you're doing 3D graphics projections you're going to want linear algebra. If you're doing financial forecasts you'll probably want to know calculus. If you're modeling throughput of large menssage-passing systems with multiple cooperating processes you need to know ratios and proportions. If you're the one maintaining the query planner for a database or maintaining a large, high-performance data store you're going to want to understand relational algebra.

For a CRUD application or some light server automation understanding data flows, boolean logic, and some really light set theory helps but is not necessary to get started. There's an awful lot of code out there that is not actuarial, simulation, or engineering code.

People understand things numerically, sure, but also spatially, linguistically, mechanically, or logically. Mathematicians and physicists can give you more precise descriptions of many things that people don't do much math about in their daily lives. Just like people don't need to be linguists to communicate, people don't need to do a lot of heavy math just because the underlying tools are based in math and mathematical logic.

Math can definitely help one understand the system better and excel at optimizing code and solving certain programming issues. And as I said, a lot of the problem domains people write code for are themselves very heavy with math. There's a reason CS grew largely out of mathematics and physics departments at universities, but this study was about understanding the concepts of programming in a high-level language.

I don't disagree with you, but as far as I'm aware the study was talking about "numeracy", not math.

From the Wikipedia article on "numeracy":

Fundamental (or rudimentary) numeracy skills include understanding of the real number line, time, measurement, and estimation.[3] Fundamental skills include basic skills (the ability to identify and understand numbers) and computational skills (the ability to perform simple arithmetical operations and compare numerical magnitudes).

More sophisticated numeracy skills include understanding of ratio concepts (notably fractions, proportions, percentages, and probabilities), and knowing when and how to perform multistep operations.[3] Two categories of skills are included at the higher levels: the analytical skills (the ability to understand numerical information, such as required to interpret graphs and charts) and the statistical skills (the ability to apply higher probabilistic and statistical computation, such as conditional probabilities).

A variety of tests have been developed for assessing numeracy and health numeracy.

That's just basic arithmetic, not any of the heavy math that you described. I'd argue that for a lot of CRUD apps, numeracy as a skill is quite important - though that's not relevant to the topic of picking up programming languages/concepts.

From their supplementary table this looks like a general cognitive ability effect, although they don't seem to have included the range of measures that are typically included in general cognitive ability measures.

The short answer is that it's difficult to say from their results, and they don't explicitly test that, but it looks like it.

"Across outcome variables, fluid reasoning and working-memory capacity explained 34% of the variance, followed by language aptitude (17%), resting-state EEG power in beta and low-gamma bands (10%), and numeracy (2%). "

Seems fluid intelligence is twice as important.

I am missing something. This is a study with 36 triallists fitting responses to a relatively high-dimensional model with several input and explanatory variables.

I think one could reasonably expect to see a wide range of outcomes in this circumstance, but it does not seem newsworthy.