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Comment by ggm | Hacker News Reader

The reversed relationship however, is strong: maths benefits programming learning immensely.

Do you have proof of this like a large participant study or it is just intuition or your personal experience? I feel like lots of people who are good at maths are good at programming but they are not actually similar structurally.

To me it was always much more similar to some combination of learning a language and learning the linguistic rules of that language in great detail to the point where you have a metalinguistic understanding of it. Then, math would be an adjunct but very separate component that could be manipulated by the programming language.

Languages are part of mathematics.

Please read this fascinating book: https://dickgrune.com/Books/PTAPG_1st_Edition/

Parsing, generating phrases, understanding (analysis), etc, are all studied in applied math.

Ah cool, that looks interesting!

My interest in the comment was whether learning programming is like learning for natural languages or mathematics. At least one study shows that both intuitions about learning programming turn out to be wrong lol:

https://boingboing.net/2020/12/30/study-finds-brain-activity...

Python is fairly distant from actual math.

Haskell, for one example, is much closer, the definitions in Haskell are very math-y: let this = that in what; f x = z where z = g x y. Even list comprehension in Haskell is much more like the actual math notation than what is implemented in Python.

I work with fairly large code base(s) with tons of legacy, as of late. In my case, I do the detective work - find alleged culprits, link them, present evidence, prove, etc.

I guess in next study one should do MRI for detectives and programmers working on legacy code base. ;)

> but they are not actually similar structurally.

The Curry-Howard isomorphism wants a word.

True, I guess as the other commenter has pointed out there is a huge difference between scripting languages and their seeming closeness to natural language compared to mathy languages like Haskell that have this isomorphism and are very structurally similar.

A less type-safe language would still be isomorphic to a mathematical proof, but it could contain a wider range of errors compared to a more type-safe language. The language could be either functional or imperative, and still be isomorphic to a proof.

A correct (error-free) computer program written in any language (even javascript) would be equivalent to a correct mathematical proof.

It's a bit mind-bogglingly profound, but that's the beauty of the Curry-Howard correspondence.

Completely agree. And also disagree with the research results to some extent. My anecdotal experience is quite the opposite. I have started grasping programming while at school specifically to be able to make games. And that helped me immensely to learn math and physics.

Absolutely, in practice, math degree is such a good indicator whether a hire will grok code.

> The reversed relationship however, is strong

Is it? How do you know?

By osmosis.

Are you seriously wrestling with the proposition that computing is a subfield of mathematics?

My intuition here is strong. I am deficient in maths and struggle with formalisms in computing. All my competent programming family & friends who program are mathematically literate. Those who program in functional languages especially so.

But your point though tersely made stands: it deserves to be demonstrated rather than just asserted. Certainly there are proponents of the theory language faculty matters more than mathematical ability.

I'm absolutely atrocious at maths and I have a PhD and successful-enough research career in CS - they seem disjoint to me.

Yes but that's anecdata against statistics, studies and theories of mind.

I am also 44 years into an uninterrupted career in CS and networks. I still believe it's a strong indicator of skill and ability to have the maths chops I don't

> Yes but that's anecdata against statistics, studies and theories of mind.

I'm using anecdata? You said your argument was just 'intuition' a second ago and then gave some anecdotes about your mates.

Can you reference the statistics, studies and the data supporting the theories of mind?

There's a bizarre adversarial quality in your engagement here. If I implied I didn't know I was speaking anecdata I apologize. However, since the searches in google to find papers which discuss the role of mathematics in computer science education are trivial as are the ones which argue language skills are more important, I really don't see why I have to do this.

If you want to disrate my responses because you feel they lack quality, go ahead. I see little signs you actually want to consider this possibility, where I am open to the question "which is more important, language or maths"

https://scholar.google.com.au/scholar?q=the+role+of+mathemat...

https://scholar.google.com.au/scholar?q=the+role+of+language...

or you could drill down in the royal society review of computer science education

https://royalsociety.org/-/media/policy/projects/computing-e...

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