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The Math Myth

econlog.econlib.org

161–170 of 328 posts

Re: The Math Myth

#161
post #158

I think that in the pursuit of higher levels of understanding, some people miss what is even more important to know. Is better to have strong basic skills, than high-level skills. I was (supposedly) of the bests student of my college. However, terrible at math? Of course. My grandmother was able to do arithmetic in his head like nothing , yet I even have trouble with sum and rest. She only have 3 years of education a…

> They need to have strong, fluent understanding of the very basic (imagine if a developer can't perform without look basic list manipulations).

Why? Basic arithmetic is almost entirely useless as a skill.

Why should I spend my time learning something which computers will always be able to do more reliably and faster than me?

Re: The Math Myth

#162
While I agree with some observations: a) most only use basic maths at their daily jobs)

b) math and computer science degrees are used as a filtering criteria, by recruiters hiring for actuary/stats/finance and programming jobs

I disagree with what appear to be a conjecture, and the subsequent conclusion:

  > Acceptance of the conjecture should have revolutionary 
  > educational implications . 
  > In particular, it undermines the legitimacy of requiring higher mathematics of all students. 
  > Such mathematics is actually needed by only a 
  > minute fraction of the workforce
Being able to abstract business-specific/domain specific problems into something that already has well-researched, validated and implement solution -- is critical, and gives a business an edge.

This is the type of capability (together with knowing a broad universe of solved topics), that the graduates with CS and Math degrees should bring in into the workforce.

I do agree with the author's implication, that there is a 'placebo-style' filtering that's going on by most of the recruiter.

And it is unfortunate, because it brings into Computer Science, especially, a huge number of people who have neither the passion, no life-long perseverance to be current in the subject.

Re: The Math Myth

#163
post #53

I think one non-obvious benefit of a good mathematics education is that you have little choice but to develop a tolerance for and understanding of being wrong. See Jeremy Kun's blog post [1] for more, but my own experience has been that in e.g. discussing different ways to solve a problem or prove something almost every person eventually has an "oh, no, I see, I'm wrong and you're right" moment. Not that every mathem…

" develop a tolerance for and understanding of being wrong. " With others. Mathwise I am always right but others can't see it. So I have a deacartes moment with others

Descartes?

Re: The Math Myth

#164
post #158

I think that in the pursuit of higher levels of understanding, some people miss what is even more important to know. Is better to have strong basic skills, than high-level skills. I was (supposedly) of the bests student of my college. However, terrible at math? Of course. My grandmother was able to do arithmetic in his head like nothing , yet I even have trouble with sum and rest. She only have 3 years of education a…

[deleted]

Re: The Math Myth

#165
post #126

The value of studying more advanced mathematics is not tied strictly to what will be used on a day-to-day basis in one's job. I studied math well beyond what I use in my day-to-day work as a software engineer, but I've found it valuable for at least two different reasons. First, it exposed me to ideas and concepts beyond what is right in front of me every day. If I happen upon the occasional question about computatio…

It's kind of a running joke at my school that you learn Calc I in Calc II and Calc II in Calc III, etc., etc.

Re: The Math Myth

#166
the percent of such individuals holding engineering as opposed to management, financial or other positions, and using more than Excel and eighth grade level mathematics (arithmetic, a little bit of algebra, a little bit of statistics, and a little bit of programming) is less than 25% and possibly less than 10%.

I would state this differently. Borrowing from the Pareto principle, one could conjecture that 80% of mathematically advanced work in the economy is performed by less than 20% of STEM graduates. The remaining 80% of STEM graduates do not get the economic opportunity to apply the skills which they trained for and end up doing less prominent work (e.g. middle management).

As the OP and others have pointed out, there is a lot of anecdotal evidence to support this conjecture.

But it is hardly surprising, and it is not limited to mathematical talent.

Take management, for example. Just because you studied business in school, does not mean that you will be an executive. I would guess that less than 20% of MBA graduates manage 80% of economic resources (senior executives, bankers, consultants, traders, etc) , while the remaining 80% of MBA graduates are left managing relatively small and inconsequential activities.

Similarly, I would bet that less than 20% of design school graduates do 80% of the design work in the economy. I bet that less than 20% of classical musicians perform 80% of orchestral music. Less than 20% of programmers implement 80% of software used. Less than 20% of athletes win 80% of medals. Less than 20% of science graduates produce 80% of scientific research. And so on.

OP's conclusion is that, in light of this dismal reality, students should not bother learning mathematics after the 8th-grade level (except for "those who need it"). Well, if we apply the same logic across all disciplines, then the OP should conclude that all forms of education should stop after the 8th-grade level for the vast majority of students (and only a minute fraction should need to pursue higher education). That is exactly what the state of education looks like in undeveloped feudal economies, and this was also the state of Western education until relatively recently. I don't think I need to expend a lot of effort convincing anyone that this a socially, economically and ethically terrible idea.

I'll also point out that there there are a couple false assumptions implicit in the OP's original, imprecisely worded conjecture. Firstly, advanced industrial mathematics is not the exclusive preserve of traditional engineering. The generalization that "engineering positions" use advanced math and "management/financial positions" use 8th-grade math, is obviously false. Many areas in finance require advanced mathematics (derivatives, trading, fixed income, etc). Much of actuarial science also depends on advanced mathematics. Marketing, management sciences and operations research are also steadily moving towards advanced analytics. Secondly, it is a false assumption that use of Excel implies that the underlying mathematics is limited to an 8th-grade level. For example, in finance, it is easy to find Excel add-ins for performing highly advanced mathematics (e.g. stochastic differential equation solvers for derivatives pricing).

Re: The Math Myth

#167
post #141

Earlier quoted context omitted.

0.999... is equal to 1 only if we assign a particular semantics to the "..." notation. Namely if "..." means "the limit of the decimal number to the left, as the repetitions of the last digit grow ever larger", then 0.999... is an alternative notation for 1 since that limit is 1. The actual number formed by repeating 9's an infinite number of times is not constructable. Whereas 1 is constructable. So they cannot be t…

You might be interested in reading about transfinite induction, which is an interesting and legitimate mathematical proof technique. However your 'induction' does not succeed in doing this. Transfinite induction requires two induction steps, you've only provided one of them. Not that you would actually use transfinite induction for anything resembling this, that's what calculus and analysis is for. For example your s…

I'm not surprised that something called "induction" doesn't succeed in achieving what "transfinite induction" can do, otherwise the latter couldn't exist as a separate technique with its own name. :)

> For example your strategy would show that the sequence of positive integers 1, 2, 3... has a finite limit!

How so? Induction is in fact the basis for the common proof that there is no highest integer: for any integer k, we can add 1 to find a larger integer. Every integer k has the property P(k) := "k is not the highest integer".

Re: The Math Myth

#169
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…

0.999... is equal to 1 only if we assign a particular semantics to the "..." notation. Namely if "..." means "the limit of the decimal number to the left, as the repetitions of the last digit grow ever larger", then 0.999... is an alternative notation for 1 since that limit is 1. The actual number formed by repeating 9's an infinite number of times is not constructable. Whereas 1 is constructable. So they cannot be t…

Cassius Clay differs from Mohamed Ali on the name property therefore they are not identical?

Re: The Math Myth

#170
post #129

This largely matches my experience - as a software engineer, I spend probably In a market economy, basically all returns come from marginal gains. The vast majority of your lifetime income will come from a dozen or fewer opportunities that you happen to be in a position to take advantage of, whether it's a new job offer or a high-profile project you volunteer for or a startup that takes off. You will qualify for thos…

Wah. >The vast majority of your lifetime income will come from a dozen or fewer opportunities that you happen to be in a position to take advantage of, whether it's a new job offer or a high-profile project you volunteer for or a startup that takes off Is this really true? I'm still way too early in my career to know. But I'd have thought if you stick with the more "traditional" route, your income would be fairly con…

Even if you stick with the traditional route, having a tiny initial advantage for your first job will have compounding results over your lifetime. This is significant enough that people who graduate college during a recession on average have a 9% lower salary during the first 10 years of working [0].

Many people can tell you about their "big break". That one success that seemed to cascade into other successes. Whether this is a real phenomenon or simply an illusion of memory, I don't know. It's quite possible that if that big event hadn't taken place, there'd have been a similar one just a little later, taking the person on a different, but equally pleasant path. I suggest you not trust individual narratives, only systematic analysis.

[0] http://www.nber.org/digest/nov06/w12159.html

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