Can a simple algebra test predict programming aptitude?

What kind of "programming"?

What "ability"?

Ability to write space-O(my_god * n) sorting algorithms? Ability to duct-tape queries to an ill-documented SOAP webservice and upsert the return into a Your-Boss-Normal-Form database schema? Ability to brutally optimize the runtime of a really hairy numerical analysis algorithm? Ability to design a centralized data pipeline architecture and lead 12 hackers during the implementation and migration? Ability to find the off-the-shelf OSS project that solves the first 50% of the problem instead?

I was watching the news the other day on TV, which is something I almost never do, and there was a segment about the educative value of tablets, smartphones and laptops for teenagers and children. The value of the freely available information on the internet was discussed, along with the quality of free and... not free educative and scientific applications, and the ill effects of such devices on people's attention span, and... That's it.

Example devices included many, many Apple products, a few off-the-shelf Android devices. A Windows machine running MS Word.

Same ideology regarding technology in education: locked-down workstations with user-friendly applications, internet access which blocks every port except for 80 and 443.

A relentless and sustained effort to erase everything but the topmost layer of the IT stack. Locked-down devices. People come to me asking me to remove viruses, to speed up their old XP machines fraught with annoyware. No Windows license, don't want to pay for one, don't want Linux. Computers run on magic, right? How can you know that programming stuff and not be able to remove all that bad magic from my computer. Computer Science students who can't find the slash on their keyboards. People who see computers as a monolithic entity rather than a brittle but transparent stack of conceptually distinct layers. The new generation of systems administrators, can't scp a tar at the other end of the lab.

A teacher spending three hours explaining red-black trees to a class scrolling down 9gag; students, diploma in hand, who aren't entirely sure what's the difference between an array and a hash, who are not sure of what happens when one puts an array in another array, in PHP, after 120 hours spent theoretically writing PHP.

Computer Science students convinced that Linux is 100% not worth learning, in any way, because nobody uses it.

This is how the knowledge economy dies.

I am REALLY terrible at algebra (to the extent that I am borderline LD in math), and I have completed a degree in CS and hold a steady job as a software engineer. And I am definitely not the only one. Ask a room full of developers how many are bad at math, and I guarantee the results will surprise you. On the other hand, I know a plenty of folks I went through school with that were math majors so good at algebra they could do full page derivations piss drunk without at hitch. And yet, they would take an intro java course and be totally lost. If they didn't get a java intro class, how do you think they would have done with something as algorithmic as an assembly language, a functional language, or understanding the nuts and bolts like Turing machines and automata?

Algorithmic thinking is definitely an important part of programming, but it is just that, only a part. And quite a few types of development don't emphasize that sort of thinking. I could perhaps see this being a PARTIAL solution for areas where one would be doing a lot of functional programming, but the vast majority of the job market these days is still OOP.

This could really quash the job prospects of programmers who are perfectly capable of writing quality code but are poor with algebra.

It’s fairly common for incoming Computer Science majors to ask the question, “Why do I have to learn all this math if I just want to learn to program?” The correlation above suggests a possible answer: The ability to understand basic mathematics is likely correlated with the ability to “think algorithmically,” which is well-known to be a foundational skill for expert programmers.

If it's just a weak (as the chart suggests) correlation, it doesn't mean learning one will make you better at the other. And if you do assume causality - it can go either way. Perhaps learning math makes you better at programming. Perhaps learning programming makes you better at math.

My 2 cents... It's more complicated because there are other things involved. Perhaps it's the nerd gene that makes people who like computers also more likely to play D&D and be in band. (I was a card carrying member) Does one of these 5 variables cause the other, or are they all part of the same thing?

It may be controversial but running this place has shown me that not everyone can program competently or is cut out to be a professional programmer. Anyone who says "everyone can code" is mistaken.