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I've encountered this argument before, but also applied to other subject such as eg Latin:

> 3) math has an indirect usefulness which is a way of thinking that is transferable to a myriad of disciplines and solutions to problems in everyday life. And it is this third reason that makes math relevant for most people.

Are there actually any good studies that show this in a counterfactual setting? Like, do we actually know that spending time teaching maths (or, less plausibly, Latin) helps students aquire these abstract skills more than other subjects? Is this "transferability" of meta-skills a testable outcome?

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I’m skeptical of (3) as well, and yet I encourage students to study math through calculus, and to study Latin.

My feeling is that the utility of higher math, Latin, history and literature comes every minute of every day, as you experienced life as someone who has familiarity those things and your life will be richer and fuller.

This is decidedly not testable. And yet I still believe it.

There are plenty of ways to use this stuff in everyday life.

I took logic in college, and although the "logic as english statements" stuff was sort of confusing, the symbolic stuff like A&B = !A|!B stuff has helped with computers all my life.

It was only much later in life that I ran back into logic as english statements in a way that made sense as practical.

I read a book where they took apart the statement:

  If you loved me, you would take me to the movies.

Most people in relationships will respond to this with:

  Well, I just took you to the movies last week!  Why do you want to go again tonight, we had other plans!  etc...

But the book explained that with "If X, then Y" it was futile to address Y. You must address X:

  Wait, do you think I don't love you?  Of COURSE I love you!

...just hard to unpack this in the middle of an emotional situation unless you've studied the logic

I would highly advise against treating informal natural language statements as logical statements. It is impossible to know what someone who says "If you loved me, you would take me to the movies" actually means without far more context. The fact that it has the form of an X=>Y statement is at best a hint, but it definitely shouldn't be taken as literally as that.

I think you meant

  !(A&B)

Anyway… I made a video called “Why Think Mathematically?” as the first in a series called “Thinking Mathematically” on a YouTube channel years ago:

https://www.youtube.com/@thinkingmathematically

It might help to answer the question

An intro to formal logic class was the first thing that made me think of becoming a professional programmer. The class had a lab portion that used a program called Tarski's World that I remember as being a lot of fun.

The correct answer is

  Since when have you thought that I didn't love you?

Read The Gentle Art of Verbal Self-Defense for why.

I actually think point (3) is a good one, but am still extremely skeptical of teaching students more maths.

Basically, I believe that there's a heavy correlation between being good at maths and being good at solving every day (and not so every day) problems.

But I don't believe there's much of a correlation between being taught math at school for even more hours will make much of a difference. Most schools are terribly at teaching anything.

I feel I became much better at writing non-fiction after taking math at university (mainly calculus, linear algebra and statistics).

Going through proofs and proving things on your own really transferred to being able to better present arguments. The diversity of the math I learned has helped to reflect on things from different perspectives.

In sum this helped with everything from thinking more and better about the core issue at hand, writing argument chains in the correct order, cutting down on irrelevant stuff and more.

I've used this to significantly help the grades of both my SO and a family member, who both took non-math topics, by improving their hand-ins. I didn't know their field so was strictly improving the structure and presentation, and asking for clarifications where I felt the arguments didn't add up, and have them write down the answer.

I feel it still helps me a lot writing emails at work and similar.

That (3) is a very interesting issue. My suspicion is, it basically says "knowing logics is good for your well-being".

The skill of logical inference — even at the level of very basic syllogisms — is both very much underappreciated and underdeveloped in the American college population, at least from my personal experience. As good citizens, we all collectively should grab a couple of Martin Gardner's or Lewis Carroll's books off the shelf and give them a good read. I predict it will do much good... and if I'm wrong, it certainly won't do any harm!

Here is a study: https://journals.plos.org/plosone/article?id=10.1371/journal...

And, since LLMs are so bad at math currently, we may find that, by improving their math ability with gobs of synthetic data, we get improvements in general reasoning.

Thanks, this is a nice reference! Interesting that the abstract and introduction mention the lack of existing evidence - seems like an under-studied question?

One aspect that's quite easy to criticise about this study is that it uses existing groups of students with different levels of maths training. This means that there is possibly self-selection etc, and one may argue there might also be a causal effect in the opposite direction (e.g. folks that are good at reasoning like to do maths.)

> Are there actually any good studies that show this in a counterfactual setting? Like, do we actually know that spending time teaching maths (or, less plausibly, Latin) helps students aquire these abstract skills more than other subjects? Is this "transferability" of meta-skills a testable outcome?

We know that if you try to train someone in math (or in Latin), and they do well, then they will also do well at other things in the rest of their life. Some people would like to give the credit for that good performance to the Latin training.

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