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Although the study by Prat et al. (2020) suggests that linguistic aptitude is a better predictor than numeracy for learning programming in Python, it should be

Although the study by Prat et al. (2020) suggests that linguistic aptitude is a better predictor than numeracy for learning programming in Python, it should be read carefully, as it can easily be oversimplified. To begin with, the study measures functional numeracy: the ability to solve everyday numerical problems. This is quite different from the kind of advanced mathematics often associated with programming, such as formal logic, symbolic abstraction, or the use of formal languages (as found in denotational semantics or type theory). These more abstract skills—not basic arithmetic—are essential for understanding recursion, type inference, or algorithm design. That functional numeracy has low predictive power in this study does not imply that deep mathematical reasoning is irrelevant to programming. Moreover, the language used in the study is Python, which was explicitly designed to be readable and semantically close to natural language. This may give an advantage to individuals with strong verbal skills, but the results don’t necessarily generalize to languages like C, Lisp, or Haskell, where symbolic and logical density is much higher. Finally, language and mathematics are not opposing domains. They share cognitive underpinnings, such as working memory, executive attention, and hierarchical structure processing. The key is not which one "wins," but how they interact and complement each other in different programming contexts.

mmaunder 1y ago
> These more abstract skills—not basic arithmetic—are essential for understanding recursion, type inference, or algorithm design. No they're not. Academia has spent decades trying to formalize many aspects of programming and continues to be confused by the lack of correlation between comp sci grads and innovative programmers. Why is it that the drop-outs are succeeding so wildly? Recursion, for example, is learned by most of us real world achievers when we hit a brick wall in programming that other methods won't solve, and we have that aha moment of "this is why this exists". Not because we studied advanced math with symbolic abstraction, denotational semantics and type theory. The uncomfortable truth is that almost all of professional programming and innovative programming (creating useful stuff never before seen) never uses any of the advanced math skills that are prerequisites in every degree program. I think much of the sadism around teaching this is perpetuated by "I did it so you have to" and academic gatekeeping. When you get really really good at programming and hit the most productive zone in your life, it feels like language. That you have the ability to just say it.
- ndriscoll 1y ago
  When you get good at math, it also feels like language. Mathematicians see expressions like `|x-y|` and the read it as synonymous with "distance" just as they would "distancia". Physicists pick out fragments of large equations and say "this term acts sort of like an 'effective' mass", etc. There is a sort of vocabulary to mathematical patterns. Picking up a skill without intentional study is great, but you still learned the skill. Programming languages are formal languages. Most mathematicians don't study foundations either. Professional programming doesn't often make use of specific advanced mathematical knowledge, but I find it makes everyday use of the skills.
- TheOtherHobbes 1y ago
  The drop-outs are "succeeding wildly" because people like Turing, Church, and Hilbert invented the sand pit they're playing in. Knuth created LaTeX. Pandoc is written in Haskell, famous for being a completely useless academic language with no real purpose beyond torturing undergraduates (it says here.) Efficient search and data compression algorithms aren't hacked together in late night hobby coding sessions. Cryptography, digital signal processing for images, sound, and video, and ML core algorithms are all mathematical inventions. The digital world literally runs on them. "Real world achievers" might want to try being a little less parochial and a little more educated about the originators of the concepts and environments they take for granted. Vibe coding "Social AI chatbot network with ads = $$profit$$" or "Cat videos as a service" is only possible because the entire field stands on the shoulders of mathematical giants.
  - grumpyprole 1y ago
    Well said. I guess such ignorance is not that surprising given that most "programming" today is glueing code together with scripting languages. This is really just a form of configuration. It certainly requires domain knowledge and a tolerance for digital bureaucracy, but not always maths. I do wish schools would do a better job of teaching that the entire fabric of western civilization rests upon mathematics.
  - pdntspa 1y ago
    It sounds like these advanced skills might be needed to build the platforms that the dropouts build on top of. But I agree that, as a professional programmer of 20 years with a 4-year business degree from a state school with a weak math background (and also as someone with a talent for writing and language), I have very little need for advanced math in my day-to-day.
bitzun 1y ago
This reads like an LLM wrote it.
- deleted 1y ago
  [deleted]
- nurettin 1y ago
  It does! Who structures their posts like a platonic rhetorical piece??
- CjHuber 1y ago
  There is even the em dash in it

mmaunder 1y ago

> These more abstract skills—not basic arithmetic—are essential for understanding recursion, type inference, or algorithm design. No they're not. Academia has spent decades trying to formalize many aspects of programming and continues to be confused by the lack of correlation between comp sci grads and innovative programmers. Why is it that the drop-outs are succeeding so wildly? Recursion, for example, is learned by most of us real world achievers when we hit a brick wall in programming that other methods won't solve, and we have that aha moment of "this is why this exists". Not because we studied advanced math with symbolic abstraction, denotational semantics and type theory. The uncomfortable truth is that almost all of professional programming and innovative programming (creating useful stuff never before seen) never uses any of the advanced math skills that are prerequisites in every degree program. I think much of the sadism around teaching this is perpetuated by "I did it so you have to" and academic gatekeeping. When you get really really good at programming and hit the most productive zone in your life, it feels like language. That you have the ability to just say it.

ndriscoll 1y ago
When you get good at math, it also feels like language. Mathematicians see expressions like `|x-y|` and the read it as synonymous with "distance" just as they would "distancia". Physicists pick out fragments of large equations and say "this term acts sort of like an 'effective' mass", etc. There is a sort of vocabulary to mathematical patterns. Picking up a skill without intentional study is great, but you still learned the skill. Programming languages are formal languages. Most mathematicians don't study foundations either. Professional programming doesn't often make use of specific advanced mathematical knowledge, but I find it makes everyday use of the skills.
TheOtherHobbes 1y ago
The drop-outs are "succeeding wildly" because people like Turing, Church, and Hilbert invented the sand pit they're playing in. Knuth created LaTeX. Pandoc is written in Haskell, famous for being a completely useless academic language with no real purpose beyond torturing undergraduates (it says here.) Efficient search and data compression algorithms aren't hacked together in late night hobby coding sessions. Cryptography, digital signal processing for images, sound, and video, and ML core algorithms are all mathematical inventions. The digital world literally runs on them. "Real world achievers" might want to try being a little less parochial and a little more educated about the originators of the concepts and environments they take for granted. Vibe coding "Social AI chatbot network with ads = $$profit$$" or "Cat videos as a service" is only possible because the entire field stands on the shoulders of mathematical giants.
- grumpyprole 1y ago
  Well said. I guess such ignorance is not that surprising given that most "programming" today is glueing code together with scripting languages. This is really just a form of configuration. It certainly requires domain knowledge and a tolerance for digital bureaucracy, but not always maths. I do wish schools would do a better job of teaching that the entire fabric of western civilization rests upon mathematics.
- pdntspa 1y ago
  It sounds like these advanced skills might be needed to build the platforms that the dropouts build on top of. But I agree that, as a professional programmer of 20 years with a 4-year business degree from a state school with a weak math background (and also as someone with a talent for writing and language), I have very little need for advanced math in my day-to-day.

bitzun 1y ago

This reads like an LLM wrote it.

deleted 1y ago
[deleted]
nurettin 1y ago
It does! Who structures their posts like a platonic rhetorical piece??
CjHuber 1y ago
There is even the em dash in it