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The Math Myth

econlog.econlib.org

11–20 of 328 posts

Re: The Math Myth

#11

Good, now replace "Math" with "liberal arts." Secondary education for most fields is a waste.

I learned more useful things from my liberal arts class than my CS or Math classes. Granted, I had been programming for years at that point so a single public speaking class was more useful than my first 1-2 years of computer classes. The problem is not the material, the problem is 4 years is just not a lot of time vs 13 years of prior education.

Re: The Math Myth

#12

Reading someone call for in-depth study in one sentence and saying they're already convinced of their own pet theory in the next because of anecdata (anecdatum?) has me puzzled - I can't decide if it's an indictment of the author or merely ironic evidence for his thesis.

I lean towards indictment

Re: The Math Myth

#13
I can tell from personal experience that I only properly understood simpler mathematics when I started learning more complicated one. For instance, in linear algebra, finite dimensional (euclidean) vector spaces became a cakewalk once we started talking about functional analysis.

So, I think, even if you don't need that particular stuff in your work, it's still a good training.

Also, there has been a pushback against "rote learning" in the past couple decades. I believe that our minds need repetition in order to learn patterns and understand abstractions properly. Yes, you forget most of it, but without it, you won't learn it properly. I don't think you can be any good in any field without lot of time spent on boring and repetitive things (AKA "work").

Re: The Math Myth

#14

Reading someone call for in-depth study in one sentence and saying they're already convinced of their own pet theory in the next because of anecdata (anecdatum?) has me puzzled - I can't decide if it's an indictment of the author or merely ironic evidence for his thesis.

I lean towards indictment

little from column A, little from column B

Re: The Math Myth

#15
> I find it difficult to find anyone who uses more than Excel and eighth grade level mathematics (=arithmetic, and a little bit of algebra, statistics and programming)

Statistics and programming is way way higher than eighth grade from what I've seen.

But taking his premise above, then I think no one is arguing for the general public to learn more than the aforementioned eighth-grade maths. It's just that the majority of the population isn't any where near that. Specifically in statistics, programming, and a bit of logical reasoning, I might add (around modus tollens).

I might be mistaken here, but I've always thought that when someone talks about "higher maths" the public should learn, it is capped around calculus I, or some basic linear algebra. Which is like half a year more study over the list of the author.

Re: The Math Myth

#16
I think this gets it all wrong by considering mathematics to be a set of discrete tricks, like 8th grade arithmetic, algebra and statistics.

Mathematical thinking and problem solving are skills that need to be honed and kept up to date. You do that by learning new methods and tricks constantly. There are disciplines that require similar skills and have a positive cross-over to other skills. Computer science theory is very obvious application. Cryptography is another. The "tricks" in CS or crypto are not taught in school for everyone, yet having the background in math will undoubtably help getting into CS and crypto.

What I wish that mathematics education would get through to students is a better understanding on how mathematical methods are used in a lot of domains. I see too much of a divide between "math guys" and "non-math guys", with the latter group sometimes getting quite anti-intellectual when it comes to math (even if they seem smart otherwise). Even the author of this article has a very dismissive tone, if we just teach people how to apply 8th grade math and Excel, who will be the guys developing Excel and other tools?

Even if math education is learning new methods and tricks, they are not the skill that should be learned. It's the methodology of what it takes to master a new method - learning how to learn.

Just to give a counter point: I regularly use math skills, advanced calculus, arcane series formulations and spherical and hyperbolic trigonometry. A lot of these methods were not taught to me in formal education, but my education gave me the tools to tackle these advanced subjects on my own by reading text books and old research papers.

Re: The Math Myth

#18
I think society would be a lot better if BASIC math and statistics would be better understood.

How many times do you see a study posted here with N=23 and people say "the sample size is too small" when it's clearly not? How many people ask for a card deck change to change their luck? How many times do people read a poll like 49% +/- 3% vs. 43% +/- 3% and conclude the two candidates are statistically tied?

I could probably keep going with just examples from statistics/probability/combinatorics. But there are other examples of people misunderstanding math.

I mean I wonder how many people even understand that 0.999... = 1?

Re: The Math Myth

#19
This has so much more to do with the lack of easily monetizable applications of complex mathematics. I'm sure a significant number of engineers and STEM professionals feel (as I do) that they're deliberately eschewing those subjects not for a lack of interest, but rather as a response to market demand.

The market of people who are genuinely passionate about complex subjects in math and science is saturated relative to available opportunities. It makes more sense for an intelligent person to take the lower overhead and more achievable approach to becoming a value creator (e.g. full stack engineer with a strong focus on product development) than waste time competing against the countless PhDs vacating academia.

I use a similar argument for avoiding the ML/Deep Learning hype train. At a large corp, that job should be left to people who've spent a lot of time mastering the subject. And if you're using ML heavily in an early stage company and don't have a PhD, you may very well be out of your depth competitively or wasting your time optimizing prematurely.

But even ignoring all of that: anyone who's either spent time on or interacted with a data science team understands how difficult it is to create value with ML as well as how intangible the value that's created can often be. I worked at a fairly well known company that told clients we have a data science team and could use ML, knowing full well that the team rarely if at all manages to generate meaningful insights, because dropping buzzwords is an essential branding tool.

Here's a better approach and the crux of why higher math is often superfluous: the best way to create value is to specialize in problem-solving first principles and remain amenable to either adopting new skills ad hoc or hiring to fill any skill deficiencies.

The caveat: if you're passionate about STEM and that's a higher priority than 'creating value' in a deterministic and practical way (and maybe it is and that's perfectly fine and even reasonable), then by all means indulge in it. But it's important to align your expectations about what you want to do with yourself with the way in which you spend your time. A lot of pain arises in misconceptions around the question of what we want and the reality of what we're doing.

Re: The Math Myth

#20
post #18

I think society would be a lot better if BASIC math and statistics would be better understood. How many times do you see a study posted here with N=23 and people say "the sample size is too small" when it's clearly not? How many people ask for a card deck change to change their luck? How many times do people read a poll like 49% +/- 3% vs. 43% +/- 3% and conclude the two candidates are statistically tied? I could pro…

To be fair, 0.9999... = 1 is not quite basic. You need to know things like infinitesimals, the distinction between value and representation of numbers etc.
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