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The Math Myth

econlog.econlib.org

31–40 of 328 posts

Re: The Math Myth

#31
As a mathematician, I would like to point out that there are a lot of different areas of math, and higher math isn't just learning more calculus. Graph Theory and Stats, for example.

I have no idea what he's talking about with including Stats in up to 8th grade math. I've taken a few university classes on it, and I still don't feel like I have enough to be confident solving all but the simplest statistical problems.

There's a lot you learn in High School. Functions is a big one that comes to mind. The idea that f(x) = x^2 + 2 or something, and you can compare it to another function g(x) is pretty important, but not really covered till the end of High School. Sure, if you have studied programming too, then you know what functions are, but that's not quite a good assumption to make for the general population.

Re: The Math Myth

#32
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…

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

To be honest, I think it's unreasonable to expect anybody - even with a Ph.D in a field other than mathematics - to be able to even define the real numbers: My definition is probably very different from yours(I tend to say there's countably many real numbers).

Re: The Math Myth

#33
post #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 t…

> 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

That's the point -- the "math myth" is specifically in relation to math (and science) skills as being of particular importance as a comparative advantage over other countries (Russia, Germany, Japan, India, China) where these fields are perceived to be prioritised higher in education.

If there's low market demand for the skills, it's unlikely that countries with a higher supply of those skills can leverage them to surge ahead in comparative advantages.

That said, I don't think I agree with the conclusion. Most people who are good at something don't particularly know they are, and few can explain why they are, so just asking them is useless. Sure, math and science are probably of limited value in their distilled, pure forms, but my impression is that most successful people in computers and software do subconsciously draw on a fairly solid math/science basis on a daily basis, even if they never consciously sit down to apply science to a problem.

I took particular issue with the Accenture anecdote - we can all laugh at useless consultants all day long, but I've met more than a few who can pick inconsistencies (not validate hard math, but "why is that number so low when that is so high, and is revenue in X really only a third of Y" style things) out of a wall of numbers in what seems like an instant. You don't do that without a solid math foundation, even if you don't think you use it.

Re: The Math Myth

#35
post #22

I think the author is both right and wrong. Maths skills is a litmus test that reflects the scientific education in general among the population. Given the anti-intellectual and antiscience trends in US and Europe - where US seems to lead the way, it's at least one way of monitoring the situation. As a practical skill, anything beyond 5th grade is rarely used, except if in rather specialized professions, but learning…

I think the author is mostly attacking a straw man.

The argument that mathematics skills in the US (or many other Western countries) are inadequate usually isn't a complaint that there aren't enough graduates familiar with advanced pure mathematical theorems. It's usually a complaint that after years of compulsory education the masses struggle to do basic arithmetic and understand basic statistics, and plenty of people whose jobs do entail working with figures or making calculations from time to time lack the "eighth grade level" numeracy to spot the figures in the Excel output table are out by two orders of magnitude because someone screwed up inputting the formula.

Re: The Math Myth

#36
post #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 t…

What would you study instead to remain valuable in the next two decades? I've gotten pretty deep into engineering: worked on games, mobile, web, FP, legacy code revival, a half dozen popular languages, automated testing, and people management. I'm looking for something new to study to add flexibility and "luck surface area" to my career. I was thinking ML would be another area of valuable study. Do you have any alterative suggestions?

Re: The Math Myth

#37
post #20

Earlier quoted context omitted.

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.

Most people are happy to accept 0.33333... is the same as one third and from there it's a quick hop to 3*0.3333...

Well, that's if they accept that an infinitely repeating number is actually EQUAL to the fraction. Some people just accept that a non-infinite number will never equal the fraction, but don't understand the concept of infinite repetition as an actual number (point on the number scale), not an estimate.

Re: The Math Myth

#39
post #23
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…

What is the generalised rule/case where small sample sizes are sufficient?

Depends on what effect size or power you are looking for and/or other factors like variance in the data (standard deviation), etc. There are some different ways to calculate sample sizes here: https://en.wikipedia.org/wiki/Sample_size_determination

or google: sample size calculator

Re: The Math Myth

#40
post #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…

Yes! This! I am 30+ years post Ph.D. and work in microscopy and image analysis. I have repeatedly needed to go into areas that I never anticipated and learn what I needed to solve the problem at hand. Happily, my graduate advisor taught our group to expect this to happen and to become self-directed learners and to embrace the process.

I will also note that I found this works best when surrounded by a few like-minded individuals with complementary skills to serve one another as "a second pair of eyes" and a sounding board for hypotheses and conclusions.

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