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The Math Myth

econlog.econlib.org

151–160 of 328 posts

Re: The Math Myth

#151
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…

That's one way of looking at it, but you don't just happen to have those skills. You get them from experience and practice - or doing well at the 99% that doesn't feel important.

This arguement reminds me of people who focus on a key, heroic play in sports, rather than all the good and bad that led up to it.

Re: The Math Myth

#152
the purpose of teaching math is not purely to be applied in the context of daily work. It is to be able to think through complex problems of different nature and divide into multiple steps that can be tackled more easily. Technology has allowed us to easily graph and instantaneously observe math as it unfolds in daily life. Think bell curves in statistics, regression analysis and divide and conquer algorithms.

This article misses the point. The purpose of teaching math is not to memorize equations and solving methods, but to teach to approach problems in different ways.

As a developer and now a PM I've used complex math at many different times. I'm not solving in paper, but actually using it to solve real world problems.

Re: The Math Myth

#153
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.

Property of real numbers: between distinct real numbers is at least one other number. Now try to find a decimal representation of a number bigger than 0.9999999... but less than 1.0. You clearly can't. They must be equal. No need for infinitesimals.

Okay, so it follows from completeness. Now prove that real numbers are complete (or provide a construction of the reals that uses completeness as an axiom) without using concepts foreign or confusing to someone with a middle school level exposure to math.

Re: The Math Myth

#154

Earlier quoted context omitted.

You obviously don't hang out with many statisticians, who also don't tend to believe in truth or being right or wrong; to them, they are just making models that can be tested to reliably approximate some observation. There is no pretense at truth, it's just a model.

This is a significant misunderstanding of statistics. Statisticians believe in truth, they just accept that it might not be possible to know it.

I think we have a disagreement about epistemology. I say, you can't believe in truth if you don't believe it is knowable.

In any case, statisticians are not interested in learning the truth, either, and the goal of their enterprise is not access to it.

Re: The Math Myth

#155
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…

I agree wholeheartedly! It reminds me of when I was studying music. When the teacher wanted you to perform a piece for a recital or concert, you'd always play a piece that was a level or two below where you were at because you could nail it. You didn't play the piece you were currently working on because it's already hard enough to play during practice, without the added stress of doing it in front of an audience.

Re: The Math Myth

#156
post #43

I don't buy the sports analogy with which he argues that it is "self-serving nonsense" if people state that mathematics education trains your general problem solving skills. His argument that soccer players should only play soccer seems not to be anchored in reality: Of course professional soccer players spend a lot of time in the weights room or go running to enhance their general strength and stamina [1]! They do n…

I agree.

I used to do IT work at a company where playing chess was popular among the techs and I decided to improve my skill.

The ways to improve:

   * Study tactics and strategy books
   * Study grandmaster games
   * Do two-to-mate or tactical chess problems
   * Review your own games and look for mistakes
   * Study openings (once you're more advanced)
Some of these things are straightforward, some not. If I study openings and know e5 is a good response to e4, I know my study did that. I am following an opening I memorized from a book.

If I spend months carefully studying the games of Kasparov, Fischer, Karpov etc., and my playing begins improving - how do I prove studying the greats carefully has improved my game? It might be "self-serving nonsense", as I can't draw a line between a move I do to some game I studied, like I can for an opening I memorized from a book. All I know is my general problem solving skills have somehow increased. I now see patterns I did not see before, and the correct path forward where before it was muddled, although I can't fully explain why. The only test is a sample comparison of those who do it versus a sample of those who don't.

Re: The Math Myth

#157

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…

There is more to math than just calculations, algebra, geometry, etc. Logic, and reasoning through choices & the effects of those choices are vital math skills as well, and for many people in math, they don't manifest until one takes a few rigorous proof-based classes, where one often sees new approaches to arriving at concepts they know, and how to properly get to a conclusion from a particular point. I wish these s…

For software engineers specifically -- every time you are coding formalized programmatic logic, you are using math. If you took a logics and proofs course, it would help you formalize logic better. Every time you write a "for" loop you are essentially using summations.

There is a book called Concrete Mathematics and one of the primary authors is Donald Knuth, basically it's "Programmers math" and in my opinion, would make your average developer who completes the text into an exceptional developer.

Re: The Math Myth

#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 after kindergarten.

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In the first class of calculus in the University, the teacher make us do a division between a largueish number and a small number, at hand. We was something like 50 people. I don't remember anyone was able to perform it in time and give the correct result (or if somebody was able, surely was a very small number, I don't remember it well).

At that moment I know that the whole point of learn calculus will be a disaster.

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

Like Bruce Lee say:

"I fear not the man who has practiced 10,000 kicks once, but I fear the man who has practiced one kick 10,000 times."

Re: The Math Myth

#159
post #114

I think this essay asks the wrong question, and then reaches doubtful conclusions from it. We should not be asking whether most individuals today use higher-level math in their daily lives, because the answer we get will depend on the degree of math literacy of the people with whom those individuals must interact every day. The level of discourse is often dictated by the 'lowest common denominators' -- that is, the p…

Can't we look at places where that is the case today and see? I always hear about how in places like Russia, every student learns much harder math than here in the US, and they learn it better. But I don't see other countries like Russia producing better engineered products or better science than we do here. Same with China or Japan, or whoever is supposedly the best this year.

Re: The Math Myth

#160
His conjecture is correct, but his conclusion is not.

Advanced mathematics are rarely used for any professional position (including software engineering), but that doesn't mean that technical degrees are irrelevant. In my experience, such filters (like an MIT degree in CS) are invaluable for two reasons:

1. Math does teach you to think logically, which is an invaluable skill in all careers and essential in some (software engineering, specifically). He claims that "transference of mathematical skills is unsettled," but in my experience that's totally untrue: try teaching programming to a bunch of math majors and a bunch of sociology majors, see how learns more easily. Of course, math is definitely not the only way to learn this—philosophy is also an excellent way to learn logical thinking, and I wish that more CS departments required some basic philosophy courses.

That being said, what would be a better way to teach logic skills directly? The sports analogy is pretty bogus because athletes typically spend the majority of their time practicing things besides full games of their sport.

2. For almost any professional field, having smarter employees is an advantage. Unfortunately, administering and/or requiring IQ tests is cumbersome and potentially illegal. A technical degree from a top university is a convenient proxy.

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