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The Math Myth

econlog.econlib.org

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Re: The Math Myth

#101

Post by iopq »

dredmorbius wrote: post #54
iopq wrote: post #42

Earlier quoted context omitted.

If the difference between samples is VERY large, you don't need a very large sample size. In other words, we're trying to find the chance that the result we got was due to chance. Let's say you have numbers like these: A: 11, 11, 12, 12, 13, 13, 13, 13, 13, 13, 14, 15 B: 90, 92, 93, 94, 94, 95, 95, 96, 97, 99, 99, 101, 101 What is the chance that those two samples come from the same distribution? On the other hand, i…

That sounds intuitively reasonable. Is there a cononical reference argument that you're aware of?

I'm really talking about https://en.wikipedia.org/wiki/P-value

Most people just look at the number of subjects in a study, but not the p-values

Re: The Math Myth

#102

Post by alejohausner »

stesch wrote: post #2

Last week I needed an arctangent at work. Looked it up on Wikipedia and let Wolfram Alpha compute the result. It was partly my fault because I was using Blender instead of a CAD system. Had to rotate something to align it to the base plane for 3D printing. But hey, I'm no engineer and it worked. And all for a door stopper with the company logo.

Perhaps the biggest skill I got from university was knowing enough context to know which references (books, Wikipedia) I should consult, to solve a technical problem.

Re: The Math Myth

#103

Post by wrong_variable »

Davidp00 wrote: post #89
yodsanklai wrote: post #67

Earlier quoted context omitted.

> 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) I would say that the surest way to make money for a mathematicaly-inclined person is to graduate in maths from a prestigious school and work in finance. At least, that's how I feel when I look at alumni from my school.…

>Those that went into finance make consistently much more than the others Hm, I would never have guessed that. Does anyone have any data on this? The top 1% sure, but the average and median also?

Finance is fairly broad. People in middle management whose job is basically to deal with paper work many times say they are "Working in Finance".

Just like people working at helpdesk say they are working in "IT".

Higher finance is filled with crazy maths, if you are interested in statistics and probability then finance is the best way to make a lot of money.

Its also not "gambling,etc" - its educated decision making. People in higher management need to make a lot of very important decisions all the time. 90% of the time they just use their "gut feeling". This is where people with strong technical knowledge in finance comes in.

Where to allocate money is a very hard question to answer, you can throw a random dart at your options or bring in complex ML models. The sky is the limit.

Re: The Math Myth

#104

Post by visarga »

mseebach wrote: post #33
sp527 wrote: 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) wh…

> 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

Isn't that math pre-level 8? It's just simple algebra or arithmetic. Interesting how little use trigonometry and calculus have.

Re: The Math Myth

#105

Post by yodsanklai »

kozikow wrote: post #97
yodsanklai wrote: post #67

Earlier quoted context omitted.

> 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) I would say that the surest way to make money for a mathematicaly-inclined person is to graduate in maths from a prestigious school and work in finance. At least, that's how I feel when I look at alumni from my school.…

Only few people in finance really "make it" - and it mostly consists of portfolio managers (quantitative or else). "Superstar economy" analogy discussed in this thread have very strong effect in finance. Luck is also a huge factor. I know cases of International Olympiad gold Medalists, who didn't make it as portfolio managers. Do you really think you are smarter? If you are mathematically inclined software engineer,…

> To even get considered for the good quant position you need a good phd in applied mathematics or statistics.

Are you sure about that? again, it's only anecdotal but I know at least 3 quants that didn't do a PhD (just a MS from reputable schools), including one that worked at GS as a new graduate. But there may very well be the exceptions.

Re: The Math Myth

#106

Post by randcraw »

Davidp00 wrote: post #91
js8 wrote: post #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…

>I can tell from personal experience that I only properly understood simpler mathematics when I started learning more complicated one. That's interesting, I have similar experience. Maybe that just means we didn't learn the original material well enough?

But the only way to maaster new material is to apply it to something more advanced, rather than just practice it. Rote takes you only so far; you can solve only problems you understand already. But learning new kinds of problems expands your understanding of the limits of the concepts and techniques you already know.

Re: The Math Myth

#107

Post by visarga »

skybrian wrote: post #100

This is probably true for many programmers today, but machine learning is hot and that definitely requires heavy math, so I wouldn't bet on it remaining true.

Maybe, but not necessarily. There is a lot of space for hacking on neural network frameworks, and even people who don't understand 100% the math involved can use them to make cool projects. When you understand a powerful idea, new connections pop up and you see potential applications in your domain.

Re: The Math Myth

#108

Post by losteverything »

majos wrote: 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

Re: The Math Myth

#109

Post by Ologn »

__s wrote: post #38

Relevant Carmack tweet: https://twitter.com/ID_AA_Carmack/status/767911253763170304

But Carmack didn't finish college. He's using what he has. This tweet is him defending his math ignorance in a particular case.

I consider him a better programmer than me, and he is honest about his shortcomings (like in this tweet), but I am often very surprised about what things he says he just learned - things any CS undergrad would know.

It's kind of like stories of programmers who were allowed to feed punchcards to the mainframe once a week - it's amazing what they accomplished with that limitation, but one thinks how much more productive they would have been with a more robust interaction.

Re: The Math Myth

#110

Post by yummyfajitas »

astazangasta wrote: post #82
jdietrich wrote: post #80

Earlier quoted context omitted.

In my experience, a surprising number of people with a humanities education simply don't believe in "wrongness", but merely differences of opinion. They regard truth as peculiar abstraction used by mathematicians and hard scientists, not a phenomenon that actually exists. It's hard for someone to admit to being wrong if they don't even believe in the concept.

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.
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