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The Math Myth

econlog.econlib.org

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Re: The Math Myth

#221

Post by doozy »

jdietrich wrote: post #80
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…

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.

Reminds me of something one of my Economics professors said once: An Economist is just a mediocre Engineer, an Engineer is a a real bad Physicist, a Physicist nothing but a bad Mathematician, and a Mathematician the lowest form of Philosopher.

Re: The Math Myth

#222

Post by quantumhobbit »

sidlls wrote: post #81
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 want everyone to read and re-read your bit about data science and machine learning. Many times. I think even people in the software industry underestimate both how accurate and how difficult it is to employ statistics to produce something truly meaningful. My current job is on a data science team. I find it amusing that the business folks are able to sell our product, and then sigh to myself and do a little crying…

To most people machine learning and data science are magic. They either believe in magic or they don't.

Once you learn it with sufficient mathematical sophistication, it stops being magic and starts being a tool that works in some situations and not in others.

You are surrounded by people who believe in the magic and will buy anything whether it works or not. Equally frustrating is being surrounded by non-believers who don't accept that simple things are actually possible.

We are still on the upswing for now so there are more believers than not. But if another AI winter happens, be prepared for the mbas to reject applications of data science that make complete sense because "we tried that data science stuff and it doesn't work".

Re: The Math Myth

#223

Post by quantumhobbit »

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…

You know I might actually take a pay cut for a more mathematical role over my current situation 'creating value'. I would love for my work to be driven more by logic and data than big personalities and office politics.

Re: The Math Myth

#225

Post by nilkn »

banach2 wrote: post #195
nilkn wrote: post #118

Earlier quoted context omitted.

This proof is more subtle than it appears. Here's a bogus rewrite, for instance: Let 10X = 9.9. Then 10X - X = 9.9 - 0.9 = 9 = 9X. Hence X = 1, but X is actually 0.99 in this case (not 0.9). You need 0.99 = 0.9 for this to work with the exact same structure as your version. Your proof only works because appending a 9 to an infinite expansion of 9s does not actually add a 9. But at this point you're forced to establis…

What? Why -0.9?

Because that's exactly what the argument above does. It simply subtracts away the decimal part of 9.999....

This is always wrong except in the case of infinitely many repeated digits, and the proof does not explain this.

More rigorously, let 9.999{n} denote an expansion with n 9s after the decimal point, where n can also be infinity. The subtlety with the argument is that it needs X to be the same as everything after the decimal point (so that the result of the subtraction is just 9). This is never true for finite values of n, and the proof does not establish that it's true for an infinite value of n -- indeed, it can't do so without supplying a meaning in the first place.

Another way of phrasing it is that it assumes that if X = 0.999..., then 10X = 9.999..., where there are the "same number" of 9s after the decimal point in 10X as there are in X. This seems intuitive for an infinite repeating sequence of 9s, because "one less than infinity" is still infinity, but it's not very rigorous, and the argument as written certainly doesn't explain this.

Re: The Math Myth

#226

Post by rohit89 »

morgante wrote: post #192
rohit89 wrote: post #189

Earlier quoted context omitted.

I believe the OP's exercise was to do the division manually not mentally. Basic mental arithmetic is probably the most used in day-to-day life. It feels weird having to whip out a calculator/phone every time you need to make a quick estimate.

> I believe the OP's exercise was to do the division manually not mentally. That's equally useless. Why would I try to figure out the result manually when I have a computer in my pocket at all times? If anything, doing things manually when we have computers seems weirder.

The point of that exercise was to show whether you knew how to do it. Things like division and multiplication etc are so basic that you should know how to do it even if you haven't done it for years.

As for mental arithmetic, its main advantage is speed. Faster to mentally solve and continue along your train of thought/flow of conversation than to pull out a calculator. Physical actions will never be faster than speed of thought.

Re: The Math Myth

#227

Post by ethan_g »

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,…

If you define "really make it" as making millions every year, yes that's rare. But if it's making 300k+ per year, there are multitudes of math-types doing that, and not much luck is involved.

Re: The Math Myth

#228

Post by losteverything »

dmfdmf wrote: post #163
losteverything wrote: post #108

Earlier quoted context omitted.

" 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?

If a math guy makes a math statement (in a forest of mom-math-understanders), does it make a sound?

Re: The Math Myth

#229

Post by raarts »

I fear that if this becomes reality it will result in even more people without respect for science or engineering, and thinking that everything is easy.

You need to have experienced that some things are complicated. And we need a lot of people to respect science and engineering, because they will be the ones taking decisions, and those decisions need to be good ones.

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