The Math Myth (opens in new tab)

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 those opportunities based on the skills you have that other people don't have. They will make money for the organization because of features or insights that your competitors lack. Your customers will buy it because it lets them do things that they couldn't otherwise do.

The stuff that you and everyone else spends 99% of your time doing is economically irrelevant. You probably still need to do it (though if you can program a computer to do it, you have a huge leg up on competitors), but it doesn't get you anywhere.

Ironically, this is one of those insights that a good understanding of math will give you. The common-sense understanding is that we should be teaching what the majority of people are doing; the data says that we should be teaching what the majority of people are not doing but desire the results of.

The typical career arc is to get through college, then sit down at a CAD workstation, or programming terminal, and forget all of your math and theory within a few years or even months. Time that isn't spent doing CAD, is spent on testing, troubleshooting, dealing with vendors, and so forth. A few of them start prepping for management. It's becoming increasingly common for engineers to start their MBA training as soon as the company agrees to pay for it.

Truth be told, outside of a few life-support-critical applications, most design is done by trial and error. Very little real engineering gets done.

And the products we make, are designed to provide similar benefits in another profession. We are told by management: "Our customers don't want products that require them to think. They want something where a person with an 8th grade education can push a button and get an answer."

When a math or theory problem arises, they take it to the resident "math person." That's me. I'm glad that I spent the better part of my youth learning math and theory, because I'd be as suited to the CAD workstation as I'd have been to working at a loom, or a lathe, 100 years ago. For the most part, the people who emerge as "math people" are the ones who were interested in it as an end unto itself, in the first place. I didn't study math because I expected it to be necessary for a job. I studied math (and physics, programming, electronics, etc.) because I was interested in those things. They were for me an escape from preparing for my career.

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 people with the least math literacy.

For example, freshly minted engineers who are surrounded by math-illiterate work colleagues quickly learn that they must avoid higher-level math if they want to interact successfully with others at work. Over time, the level of discourse of these engineers gradually drops toward that of the work colleagues with the least math literacy.

A type of "Gresham's Law for math literacy" is at work.[1]

The question we should be asking instead is whether society would be better off if more people had greater math training and literacy. Would our debates be more informed and higher-quality? Would our decisions be smarter? Would there be more technological innovation and wealth creation? Would society as a whole be better off if more people were trained to think creatively and critically with the rigor of higher-level mathematics?

I suspect the answer is yes.

[1] Gresham's Law -- https://en.wikipedia.org/wiki/Gresham%27s_law -- states that "bad money drives out good." In this case, unsophisticated discourse drives out high-level discourse.

Before that, I'd worked on automatic theorem proving and proof of correctness. I still like Boyer-Moore theory. I recently revived the old 1970s-1992 Boyer-Moore theorem prover and put a working version on Github. It's fun to run that again; it's a thousand times faster than it was in the early 1980s.

If you do anything serious with graphics, you need to understand 4x4 matrix transformations throughly. I have the whole shelf of Graphics Gems books, and they're mostly math. At one point I rewrote many of the C code in C++, and got rid of their start-at-one arrays. (The original was Graphics Gems in FORTRAN, and the C version used a horrible hack to make arrays start at 1.)

I didn't know enough filter theory when we were doing the DARPA Grand Challenge. We had a lot of trouble integrating the GPS and AHRS data into a good position and orientation. We had about 3 degrees of heading noise, which kept messing up the map-making function. We really need 3D SLAM, but didn't know how.

Now I need more math to understand machine learning.

I'm also looking at designing a specialized switching power supply for the antique Teletypes I restore. You can get enough energy from a USB port to drive the big selector magnet if you use and store it properly. Fortunately I can get LTSpice to do most of the number crunching.

I think I've used all the math I was ever taught. And I'm not really into math.

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 probably keep going with just examples from statistics/probability/combinatorics. But there are other examples of people misunderstanding math.

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

[1] https://medium.com/@jeremyjkun/habits-of-highly-mathematical...

I do think that learning math does help you to think more clearly and to analyze problems in a more systematic matter.

Now, he does not define well what he means by "higher mathematics": I agree that (as with almost all learning) there is diminishing marginal utility in mathematics education. While I would argue that learning how to work with percentages and also basic calculus (to get a feeling for the difference between a change in position and a change in velocity, for example) increase your general problem solving skills by a lot, if you have been through all this then learning about Ricci flow will probably not do that much to your general problem solving anymore.

[1]: http://well.blogs.nytimes.com/2014/07/16/train-like-a-german...

The market of people who are genuinely passionate about complex subjects in math and science is saturated relative to available opportunities. 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) than waste time competing against the countless PhDs vacating academia.

I use a similar argument for avoiding the ML/Deep Learning hype train. At a large corp, that job should be left to people who've spent a lot of time mastering the subject. And if you're using ML heavily in an early stage company and don't have a PhD, you may very well be out of your depth competitively or wasting your time optimizing prematurely.

But even ignoring all of that: anyone who's either spent time on or interacted with a data science team understands how difficult it is to create value with ML as well as how intangible the value that's created can often be. I worked at a fairly well known company that told clients we have a data science team and could use ML, knowing full well that the team rarely if at all manages to generate meaningful insights, because dropping buzzwords is an essential branding tool.

Here's a better approach and the crux of why higher math is often superfluous: the best way to create value is to specialize in problem-solving first principles and remain amenable to either adopting new skills ad hoc or hiring to fill any skill deficiencies.

The caveat: if you're passionate about STEM and that's a higher priority than 'creating value' in a deterministic and practical way (and maybe it is and that's perfectly fine and even reasonable), then by all means indulge in it. But it's important to align your expectations about what you want to do with yourself with the way in which you spend your time. A lot of pain arises in misconceptions around the question of what we want and the reality of what we're doing.

3D rendering and animation and 2D browser transforms are math.

AI and ML have large math components.

Speech recognition is math.

Industrial electrical power distribution engineering is math.

Bridge and other kinds of structural engineering are math.

Analog circuit design is math. Once you get past the op-amp cookbook stage it can get quite complicated, especially if you need to handle RF issues.

Rocket science and aerospace design is math.

Supply chain process optimisation is math.

Traffic modelling is math.

Quant fintech is math.

Encryption and security are math.

At the absolute minimum these need geometry and trig/complex numbers. Many are impossible without differential equations/calc.

So this is one of the most idiotic comment pieces I've ever read. But unfortunately it proves that many people don't understand professional engineering at all, which makes it very hard for them to value it.

Even if the math is packaged and hidden (CAD etc) someone still has to write and check the software. If math isn't taught properly at school, the number of people capable of that shrinks.

Because these people are disproportionately valuable, that's a very bad policy indeed.

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 "rote learning" in the past couple decades. I believe that our minds need repetition in order to learn patterns and understand abstractions properly. Yes, you forget most of it, but without it, you won't learn it properly. I don't think you can be any good in any field without lot of time spent on boring and repetitive things (AKA "work").

The article asserts that most modern professional jobs requires only "Excel" and 8th grade programming. In my experience, over-reliance on software like Excel rather than a basic competency in numerical programming is a hindrance to economic growth. Spreadsheet-based numerical programming is opaque and ill-suited to interoperation. This leads to subtle errors, duplication of work, difficulty of replication and silo-ing of meaningful results in the private sector, the public sector and academia.

I take the second point that the transferability of critical thinking skills developed by learning mathematics is unproven. Nonetheless, history is flush with anecdotal evidence of this hypothesis, and in the absence of empirical evidence, it seems unwise to reject that hypothesis out of hand.

EDIT: removed an assertion that the article was poorly argued.

Linear algebra, computational complexity, type theory, Newtonian physics, circuit design (it's weird being a computer scientist a room full of electrical engineers and being the only person who knows Ohm's law off the top of his head and what it means for the project we're dealing with right now) all of it has been a constant companion for the last 15 years of my career. The more I can get my hands on, the better.

I know my colleagues in the past [0] haven't employed knowledge to the same degree that I have, but they have also typically given up and come to me to solve even fairly trivial problems in trigonometry or object oriented design. They don't "need" math because they don't care if the only work they work on is solved problems with easy copypasta solutions on StackOverflow.

My take away from this is not that math isn't "necessary" for work. To me, it is necessary because I could not be happy living the kind of mediocre, under achieving lifestyle that it takes to willfully ignore math. My takeaway from this is that most people are just bad at their jobs. If you want to be any good (and being this site is focused on startups, I think that is a fair assumption), you necessarily have to avoid doing what most everyone else does.

[0] I'm finally out of those sorts of environments.

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.

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 very obvious application. Cryptography is another. The "tricks" in CS or crypto are not taught in school for everyone, yet having the background in math will undoubtably help getting into CS and crypto.

What I wish that mathematics education would get through to students is a better understanding on how mathematical methods are used in a lot of domains. I see too much of a divide between "math guys" and "non-math guys", with the latter group sometimes getting quite anti-intellectual when it comes to math (even if they seem smart otherwise). Even the author of this article has a very dismissive tone, if we just teach people how to apply 8th grade math and Excel, who will be the guys developing Excel and other tools?

Even if math education is learning new methods and tricks, they are not the skill that should be learned. It's the methodology of what it takes to master a new method - learning how to learn.

Just to give a counter point: I regularly use math skills, advanced calculus, arcane series formulations and spherical and hyperbolic trigonometry. A lot of these methods were not taught to me in formal education, but my education gave me the tools to tackle these advanced subjects on my own by reading text books and old research papers.

You can go even further and say that the whole thing would be even better if I understood more about stochastic processes and could potentially model the spot market and make predictions ahead of time to simplify the control problem and get ahead of the price fluctuations. Saying all you need is Excel and 8th grade is in the words of one famous physicist "not even wrong".

If you're in an engineering discipline then the more math you know the better.

I've also been in analytics jobs where college educated people mistake correlation for causality. (It seemed so profound when I learned the concept only in how often it's abused)

I've seen people in customer support management make enormous judgment errors because they think don't comprehend the difference between a 500K account and a 1K account.

Requiring calculus of everyone may not solve this, but requiring a couple years of hard (beyond 8th grade) stats could help.

As for the CS/engineering/Math requirement for jobs - I think that's just a reaction to the weak rigor (on average) of so many other majors.

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.

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.

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

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.

How much of any advanced learning do most people use in their day to day lives? All of it in the periphery would be my counter-conjecture.

I was always taught trade schools were for learning a particular skill. College was to equip you with the knowledge and ability to think logically required to have a better life.

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 math most probably gives you tools for abstract reasoning, and probably changes how you look at the world.

Most people will spend very little time giving first aid, controlling a vehicle in dangerous weather, resolving serious relationship discussions, negotiating important deals, or doing cost/benefit analysis of large purchases.

However, in each of those cases, the tiny fraction of time where they do those is so important, it's still worth preparing for them. It may be that most people rarely use math, but when they do, they use it on important enough things to still warrant teaching them.

Need some examples? Public key cryptography, machine learning, physics simulations of the aerodynamic properties of an airplane. I could go on and on. Just because a vast majority of the population never has to think about how this stuff works does not imply that it is somehow useless. We would not be where we are today without all this mathematics.

If you look at the requirements to be a software engineer for a company that makes video games these days, the mathematics needed is rigorous in the geometry aspect.

I'm not sure what kind of actuary this guy was interviewing but all the actuaries I know in the industry that are respected have used a significant amount of math in their career before reaching management.

I myself am no expert. I have a MS in applied Mathematics from a regular school and make over $150k in the Reinsurance industry.... I only have 4 years of experience. My superiors are definitely making 7 figures.

These days with emergence of predictive analytics which definitely using above 8th grade math, shows the relevance of advanced mathematics.

Because we can program computers, Of course you don't have to write these formulas/equations etc... Everyday but to initially design these systems, implement, revise, research and innovate, the skills are needed.

That's why at these top companies at the forefront of the industry have a very diverse international makeup of countries that excel in mathematics

In most projects, there are minority extra-brilliant people, whose talent/knowledge reflect on the entire outcome/product. So you always need people to handle more complexity. And as some others in the discussion have pointed out, often concepts at a level, become clearer when you grapple the next level of complexity.

Soviet society did not fail because they were better at Maths. It may have happened despite it. The right point to infer about that would be, brilliance in Maths is not a sufficient condition for society as a whole to excel. And that's a moot point, as there are so many other necessary conditions - food/shelter/being-alive/etc - leave aside politics.

Also the article ignores probability as a core life concept, by which you can understand so many things. I use it with my kids all the time.

Another thing which frustrates me recently is my inability to grasp modern physics. Without the relevant understanding of the complex maths, one can only get the vaguest idea, of what they(the physicists) are saying. This creates a huge intellectual gap in society.

Also the knowledge gap has another problem. If it gets too wide, then there will be a very-very few ultra elites who all know what they are saying (perhaps that's already the case, unfortunately). And the rest of us, only take their word on face value. I know one person can't know everything and this is an era of specialization. But still, I think Maths is a fundamental thing. And society would only gain when more number of people are proficient at it.

Mathematical communication skills will become more important in the information age with huge amount of quantitative data.

* A strong mathematical background does not guarantee success in science.

* There's a large amount of foundational theory and work which involves thinking in images and facts, not mathematics.

* Maths phobia deprives science of an immeasurable amount of talent.

* True maths talent is probably at least partially hereditary.

* Maths and conceptual work are complements, not replacements.

http://www.worldcat.org/title/letters-to-a-young-scientist/o...

Statistics and programming is way way higher than eighth grade from what I've seen.

But taking his premise above, then I think no one is arguing for the general public to learn more than the aforementioned eighth-grade maths. It's just that the majority of the population isn't any where near that. Specifically in statistics, programming, and a bit of logical reasoning, I might add (around modus tollens).

I might be mistaken here, but I've always thought that when someone talks about "higher maths" the public should learn, it is capped around calculus I, or some basic linear algebra. Which is like half a year more study over the list of the author.

On the other hand I tend to believe - possibly misguided - that a lot of my thinking is influenced by having gone through the math education. I may seldom need exponential functions but I know what is linear and exponential by heart. Consultants, engineers, architects and managers work with long levers and knowing how things scale up and down and when they don't matter. Understanding linear systems, frequency domain and where nonlinearity starts mattering informs quite a number of my decisions.

Math as a filter for hiring is questionable as imho. most grades. The skills that matter every day are mostly not analytical skills. Universities as they are set up are not well geared towards filling that educational need.

I learnt chemistry, physics, biology and all that from middle to high school. Now as a software engineer they're totally useless and I have long forgotten all those details that I spent months and years to memorize and master. Even reading a science-101 book in one day now will teach me more than what I can remember. Unless you plan to major in those fields, should we just take some introduction courses instead?

Also I can testify that I rarely need use any math beyond 8th grade since graduate school as a software engineer, I mean those calculus, matrix theory, fuzzy logic, neural network, etc. Well I may pick up some AI stuff now, but it's more like a start-from-scratch-now as I forgot what I learnt then totally already.

So yes the education system can be optimized to be more efficient.

I used to work as an aerospace engineer, doing trajectory analysis. We used high school trig and algebra, as well as first semester calculus pretty much all the time. But, I don't think any of the other required math classes for my aerospace degree were ever used (3 semesters calc, 2 semesters linear algebra, diff. eq, IIRC). I did end up using a fair amount of stats, which was not required for my degree, but really should have been.

Statistics was the one ongoing use of math in my former roles as a manufacturing engineer. Beyond that I haven't used much math directly. However, I have replied upon my knowledge of engineering core courses to understand and solve problems. I needed to understand calculus-based math in order to understand that coursework. So math is important.

There is a saying among teachers that in K-3 you "learn to read" and from then on you "read to learn". The same principle holds for math. Math itself may not be the end goal for many degrees, but after you "learn to math", you "math to learn".

The vast majority of human beings will never do anything intellectually intensive post-college. Even those in STEM fields. Not that an undergrad degree is "intellectually intensive" anyway.

EDIT:

>The second argument is the one I always hear around the mathematics department: mathematics helps you to think clearly. I have a very low opinion of this self-serving nonsense. In sports there is the concept of the specificity of skills: if you want to improve your racquetball game, don't practice squash! I believe the same holds true for intellectual skills.

Dear God, I'm so happy to see this in writing. For a while, I was afraid that I was the only one who had realized this. This observation has several useful immediate corollaries. For one, it shows that those "brain training" games that some people like to play are a waste of time. Also, it shows that if you ever catch yourself saying "I'm working on my X to help with Y", it probably means that you're just afraid of the failure that will inevitably come when you initially begin to practice Y, and that fear can only be ameliorated if you just dive in and start doing Y.

Of course I know it's the elites among the upper echelons of the society who are more than happy to see and maintain such a situation, and unfortunately this article might well be another addition, a so-called academic/think-tank publication that serves their agenda. It can't get more obvious at the end of the article: "leave elite education to those who 'need' it! Keep the mass ignorant!" Yeah, sure, so that the children of the elites always stay powerful and the mass keep remaining ignorant. It doesn't matter for the massive power wielded by the US, the state terrorism employed by Uncle Sam, but it matters, a lot, for genuine empowerment of the people and true democracy, which people including the author here doubtlessly want to stop at all costs.

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.

---

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.

-----

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."

But even with excel spreadsheet, if you leave out the "why" you still end up with a boring class of formulas and UI work through tutorials that will leave you questioning relevance just the same. And your school paid MS how much?

If you're developing a game, or designing a building, or analyzing online sales, or trying to build a web site, you now have the context, but you probably don't have the education unless you took special courses in higher education which is practically the only place they teach with context. Maybe they just need to add more context to lower and general levels as well?

Anecdotally, it's fair to say good students manage to identify context beforehand and keep things relevant. It really helps with learning when you're driven by purpose, not obligation.

Can you use this result to go back and justify that we don't need math beyond 8th grade?

I beg to differ. I only can provide anecdote. As myself are not bad at math, I find myself use calculus and linear algebra all the time. In fact, I think differently. As another anecdote, my son, who I consider is not nearly good at math, he is in middle school and he uses trigonometry all the time.

You use what you have. Knowledge changes the way we think and work. With knowledge, you simply see the world differently.

But I left academia over a decade ago, and have never used any of that. I have, however, used a few things above 8th grade maths, such as linear algebra, regression analysis, and some basic numerical analysis. I used once a FFT.

All in all the author is spot on. And I believe an advanced degree in maths is not a legitimate requirement for anything but a handful of positions, and most of those aren't particularly desirable.

I still remember fondly my days studying Baby Rudin, though. Definitely one of the courses that made an impact in my education. But in hindsight, it's been as useful in my career as my study of Latin.

I detest utilitarian arguments, that something is worth learning only because it is useful in my day-to-day. I haven't had the faintest use in my daily life for knowing anything about igneous rocks, sorghum, golgi bodies, Chandragupta Maurya, black holes, playing hockey. Yet, it would be singularly depressing to not know it or something to this level of detail.

Second, regarding the argument that only a select few will be interested in ascending the peak and that the rest are content in the plains. While that is true, it takes a whole community of people interested in an area for there to be a star. A Messi or Usain Bolt comes out of having a sporting culture, in addition to athletic and soccer academies of a high enough standard.

Trigonometry is useful in so many ways. It's even useful for projects around the house, let alone for a lot of careers. Last I checked it comes after 8th grade.

On the other end of the spectrum he concedes Harvard philosophy undergrads might want to read "The Road to Reality". Bullshit - No undergrad can understand all the math in this book and no one is proposing that they should. Reductio ad absurdum.

And don't forget gaming. Lots of young people these days dream about a career at a game studio and there are a lot more options if you have good math.

He mentions Sputnik but it's not the 1950's anymore. The number of careers that benefit from math will only continue to grow.

[1] https://www.quora.com/Working-at-Google-1/What-is-the-worst-...

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.

    This is a conjecture that desperately needs resolving with solid statistics and in-depth interviews. 

I think more empirical data is needed. If I go on the street or the math is comparable to 5th grade (at the very best) and in a business setting might bump up to 8th grade.

Does that preclude there being opportunities to need/use/benefit from math? No...

I think it just means there are opportunities that nobody is taking advantage of. Left open and collecting dust.

The answer I came up with was N0e^-λt. Exponential decay. Set N0 to 1. I could set t in various ways, I decided to make it days, so today is 0, yesterday 1, the day before yesterday 2 etc. The lambda I tunes, right now it is 0.04 (or -0.04 times t). So the score added for each use decays as it ages, giving new additions a chance at the top.

Worked real well. Straight out of calculus. I never learned exactly what e was until college. Who knows what I would have done if I didn't know what exponential decay, e etc. was. I can't even think of an "eight-grade math" solution of the type this article mentions.

I had to hash a small list of small numbers once when I had the epiphany - Goedel numbering! I Google'd that and saw the solution was unoriginal, but I wouldn't have even saw those pages without knowing what to Google.

I was looking at a large NP hard problem many years ago and thought I could program a solution. After a complexity class later on, I realized the futility of that approach, in a direct manner any how.

I am not sure where the line is between math and CS. Graph theory underlies graphs and trees and the algorithms which run on them. Math functions and theory of computation underlie functions and methods. Statistics and probablity underlie ML. Geometry and matrix math and algebra underlie computer graphics. I don't get people here who say they program without needing post high school math.

Or seeing the garbage code out there maybe I do. Github is beset with people who make basic errors in mutual exclusion, critical section violations, lack of understanding of concurrency etc. I forget and make these mistakes myself sometimes. I hardly think there is a problem in over-education in these things. On the contrary, race conditions are spun out all over the software infrastructure by people writing code who don't have the needed math and CS understanding of what they're doing. Understanding mutual exclusion and critical sections and avoiding critical sections is not something picked up in an hour, a day, or even a week.

To convince others I often use examples. One is the discipline issues over the years. All BS. (1) totally made up. No data.

(1)http://www.snopes.com/language/document/school.asp

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.

I use math all the time, especially when I help my kids with their homework because they don't understand their math assignments properly because the school can't hire anyone with a decent math understanding to teach because those people all took high paid jobs elsewhere..

looks like they [relaunched this year](https://en.wikipedia.org/wiki/Arthur_Andersen)

It isn't even correct on the employment front, though, because it is attempting to unimaginatively extrapolate from the current state of employment.

John Nagle's comment at https://news.ycombinator.com/item?id=12422307 probably expresses this better than I can, but if you're going to make an advance in a scientific or engineering field — any advance — you need math. If you're planning to spend your working life as a button-pusher, carrying out algorithms that other people have designed, or proceeding blindly by trial and error, you don't need math.

But those button-pusher and blind blunderer jobs will be automated in five, ten, or maybe twenty years. And the article's comment section suggests that even today they aren't nearly as common as the article asserts.

There are other categories of work, such as child care, elder care, sex work (which, defined broadly, includes trophy wives, Hollywood, and a substantial fraction of secretaries and maids), sales, and family counseling. So there will probably still be employment that doesn't require math as long as there are humans, even if it's not the kind of employment the article discusses.

But the bigger question is whether education should be directed at employment. Is being an employee what you aspire to in your life? It is very good to be useful to other people. Allowing other people to employ me has benefited me greatly, and that's true for most people I know. But being used by others is not the only or even the primary good in life.

Education is what makes us human. Education is a process of personal evolution from a dumb beast into a human being. Education gives us control over our impulses and prevents us from being suckered by predatory salespeople, politicians, lawyers, preachers, and others. At its best, education makes democracy possible despite such predators, although democracy is rarely possible because the people is nearly always sufficiently uneducated to vote it down unintentionally. Education begins before schooling and doesn't end when schooling ends, but I, like many people, have found that schooling can speed education up considerably.

And mathematics is fundamental to education in all of these senses. Even if mathematics isn't necessary for someone else to use you — which is all this "Math Myth" article tries to show — mathematics is necessary for you to judiciously choose when and how you will be used, and mathematics is necessary for citizenship.

Also to be measured in how sure I am about something being right.

It is fair to say that there is an old and strong belief that a person who has studied broadly, and deeply through, say, college, in math, physical, biological, medical, social, and computer science, and the humanities will have a significant advantage in much of the rest of life. Lacking a better name, here I call such study a broad education.

To argue this belief in the context of the OP, the OP seems to claim that for 90% or so of people, it is enough for them to stop their math education, and by extension all their education, after the eighth grade. But in life it is fairly easy to tell the difference between the OP's eighth grade education and a broad education as I described it. So, there is a difference. Maybe the difference is significant and the broad education an advantage and worthwhile.

One point not mentioned very often is that, whatever 90% of the students do, the broad education was hoping that some of the students would find some really good uses of some of the education well past the eighth grade. The educators could have that hope even without knowing just what the good uses might be.

I studied a lot of math and physics heavily, but not entirely, because I hoped that they would help me make money. Well, early in my career within 100 miles of the Washington Monument, that hope was fully correct. I used what I had and was learning more as fast as I could drinking from a fire hose. Of course that work was mostly for US national security; there the math and physics were crucial.

Yes, it does appear that away from the work of US national security, the math and physics are less commonly used.

Still, in US commercial work, there are significant applications of the math and physics. Examples:

(A) How to operate an oil refinery. In simple terms, here is a list, with prices, of crude oil can buy and put into the refinery and a list, with prices, of refined products get out of the refinery, so a question is what to buy, produce, and sell to make the most money? First cut, the problem is linear programming, and for a while there was good money in selling IBM mainframe computers just for that work. Of course, past the first cut, the problem is in non-linear optimization.

A practical challenge is: It's a good guess that the first refinery management that did well seeing and exploiting this opportunity was well paid for their insight. Since much of the crucial core of that work was some college and/or grad school applied math and numerical analysis, knowing some math could have been an advantage for the management trying to understand and make good decisions.

(B) Take a big hammer and hit the ground and send an acoustic pulse through the ground. That pulse is commonly partially reflected at the boundaries of layers of rock, sand, etc. So, the acoustic signal that comes back is a convolution of the original. Doing a deconvolution, can map the underground layers and get some good hints of where to drill for oil. The deconvolution is basically some Fourier theory, and the fast way to do the computations is the fast Fourier transform (FFT). After Cooley, Tukey, etc. invented the FFT, such acoustic processing had an explosion that is still active. So, again, oil prospecting management needed to see, understand, and actively exploit the FFT. For that, some math was no doubt an advantage.

There are more commercial applications of math and physics. Some of the applications have been valuable already, and likely some more will be valuable in the future. So, in looking for what might be valuable in business, some math and physics stands to be an advantage.

So, in part, with a broad education we are fishing for advantages in the future. We are not sure just what subjects will lead to what advantages in the future, but we are quite sure that there will be powerful, valuable new work where, for successful exploitation, some studies will be important.

Or, the OP is concentrating on what the 90% of the people actually are using now. Well, in a sense the education wants to concentrate on what is new no one is doing yet.

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).

At the level of societies, maybe. Can a poor society with lots of mathematicians "beat" a society with lots of wealth and infrastructure and comfortable niceties but whose individuals can only use Excel? Probably not, certainly not in < 1 generation. It certainly didn't turn out great for the soviets.

The analogy with sports fails miserably and the author seems to not understand this. Math is a brain skill and we do need to apply brain to understand a given situation in a better manner, to abstract away some things and focus on some other things. So, if you expect someone to better understand complex situations, then you need them to have some knowledge of higher math.

One may ask where do you encounter such situations? Insurance, debates of fiscal policies, debates about racial biases and social structures, anything to do with modern finance, language structures, medical decisions. Take your pick.

So, if you have to do anything complicated in such social areas too, you need to have some knowledge of higher math.

Skills in sports are not of such versatile nature, hence the analogy fails.

"People say that we should train people for factory jobs, but everyone I know is gainfully employed in agriculture, and we don't have any factories where I live."

As a college professor, let me assure the author that statistics and programming is not a standard part of an eighth graders program. In fact, the ones I teach have passed the 12th grade, and most are woefully unprepared in algebra, statistics, probability and programming.

For me, understanding slightly advanced math (the type discussed in Taleb's Fooled By Randomness) helped me realize that Financial academic math is complete B.S. (in its use of the Gaussian Dist. in non-Gaussian processes). Yes, that's how learning more math has benefited me: it helped me discover how math is used to support complete B.S.

> I find it difficult to find anyone who uses more than Excel and eighth grade level mathematics (=arithmetic, and a little bit of algebra, statistics and programming)

I think even that's a bit optimistic; I think people whose further studies or jobs don't require that level of mathematics forget it pretty quickly. For a base level of "everyday life," you probably only need basic arithmetic operations.

As anecdotal evidence, look to all those times that a relatively convoluted expression is posted on Facebook or Reddit and people argue for weeks about what the proper solution is. Of course there's plenty of people who get it right, but the wrongs range from a subtle misunderstanding of order of operations to a complete lack of knowledge about it.