Here’s a question I’ve asked my kids and done some thinking about:

Suppose we gave everyone in the world a reliable test of mathematical ability. What sort of things do you think you’d have to have mastered in order to score in the top 1% on that test? Differential Geometery? Graph theory? Multivariable calculus?

Let’s see. 1% of 7 billion is 70 million. What sort of math do 70 million people on this earth know, that the rest of the world doesn’t know?

Here are some other thoughts and stats:

• about 2.7 billion, or 40% of the world’s population live on less than \$2 a day. My guess is that most, if not all of these people suffer from little or no education, and spend most of their lives eeking out basic survival needs, and because of this, I doubt learning math really figures prominently in their lives, sadly. It is tragic that so many people suffer in these conditions in today’s age.
• In the US, one of the highest developed country in the world, 15% of adults do not graduate from high school, this probably means they don’t master much more than basic arithmetic. Again, another tragic statistic. If we generalize this statistic to the be representative of the richest 1 billion, then we can say 150 million more adults haven’t mastered more than basic arithmetic.
• So, by this admittedly shaky logic, we’re close to saying mastering pre-algebra would easily put you in the top half of mathematical minds in the world.
• The college board reports that 300,000 students take an AP calculus exam. Around 1.8 million students go on to 2-4 year colleges every year, so we can roughly estimate the number of high school graduates taking calculus as around 16%. If 85% of adults graduate high school, and only 16% of those take take calculus, then 13% of adults in the developed world study calculus. And if this number is representative of the richest billion of the population (1/7 of the world), then taking calculus in high school puts you somewhere in the top 2% in terms of math understanding of the world’s population.

Now this is very sketchy, and my numbers are likely wrong, but I think there’s a decent argument to be made that if you’re studying algebra in the 8th or 9th grade, and on track to take calculus in high school, you are quite probably in the top few percent in terms of mathematical knowledge in the whole world. Of course, most of this is due to the innumeracy that plagues our country and others. But this gets me thinking—I have a number of students in 9th grade, who are familiar with sine, cosine, all sorts of geometric theorems, and solving equations, and yet they constantly say “I’m bad at math.” This is despite the fact that evidence would seem to indicate they are on track to be part of the top few percent of mathematical minds in the world.

Would this perspective help them to reframe their own view of their ability?

And if you are a wiser mathematical mind that me and/or you have access to better data, please do correct me.

1. January 6, 2011 7:39 pm

Your blog was just recently recommended to me and I’ve really enjoyed reading through your posts. My biggest critique of this thought experiment has nothing to do with the statistics and more to do with the fact that you’ve equated a “mathematical mind” solely with content. On a good day I might be more facile with multivariable calculus than Aristotle, but I would never in a million years call myself a greater mathematical mind. While this is a historical example, I believe the same can be said for contemporaries. I’ve taught many students who know much less content than I do that I would say have “better” mathematical minds.

• January 6, 2011 7:51 pm

Avery,
I think you’re right, mathematical mind isn’t the right word I’m looking for. Mathematical knowledge? Mostly, I’m trying to think of a way to shift how my students view math. Many of the concepts they are struggling with now in algebra and geometry were once reserved for a tiny handful of students fortunate enough to attend university, with many years more experience under their belts. I find it very discouraging when these students dismiss their own abilities and progress when they encounter a problem they can’t solve.

2. January 16, 2011 11:01 pm

I love this post. As a student in HS I thought I was bad at math, but when I got to college I realized that was not true. It’s funny that students always feel the need to compare themselves to other students and measure their learning and their achievement that way. I think that is the tricky mindset to overcome, but we are working on it!

December 30, 2013 7:27 am

Funny cause there are almost 10 million high school graduates in China every year and calculus is required for everyone in high school. Hell, here we have stuff taught in high school that resembles what’s found in a real analysis course in a US college. I’d say aside from those who have a math degree (and maybe physics and engineering) the vast majority of bachelor’s degree holders in the US would fail miserably on the math portion of the Chinese college entrance exam (which is taken by 9 million Chinese high schoolers every year.) I scored in the bottom 50% on that test, and then I proceeded to take ACT and SAT. Got perfect score on the Math section for both tests.

I’d say if you are in the US and you want to in the top 1% mathematically, you’d better have a B.S. in math.

• January 20, 2016 3:47 pm

The SAT has nothing to do with knowledge obtained or what level of math you understand. It has to do with reasoning skills. The level of math on the SAT is nothing more than 8th grade level however the way the questions are worded test your reasoning and logic skills or ‘natural aptitude’. You can have someone who understands basic differential calculus still do poorly on the SAT. Your GPA is what universities use to determine how much effort you put into your studies. Your course load is how universities determine what knowledge you have obtained and your SAT score is how universities determine your natural intelligence.

4. February 22, 2017 1:48 am

Who knows?

Math wasn’t good for anyone to be good at. Math is just there. An infinitude of math problems that exist in “REALITY.”

A person could drop out of HS because he hates the restriction of freedom and would rather just do nothing or do something free.

BTW, I do have the strong belief that there’s some kind’ve “BINARY” gene to math aptitude. Really, some brains are dead-locked and some are full of mathematical ideas and can prove anything given the determination and desire.

I don’t believe that anyone with the ordinary brain has a CHANCE to seriously learn higher level math.(You could say you have a math degree because your professors passed you anyways or because you printed out a paper or because your brain was scanned and you were deemed qualified, but the fact is there IS a gene.)

Question: Say we were to find a mental brain parameter to intelligence, and this SAME mental brain parameter resulted in The average “G INTELLIGENCE” of all Nobel Prize winners to be less than the IQ people who never even went to college.

Question: DOes this imply that the claimed G parameter is somehow “wrong” or that such records are irrelevant and that the smartest people are rebels who dropout because they’re lazy/disinterested/whatever?

OR does it mean that the NP winners are plagiarizers and that college graduates are merely “graduates” because their professor passed them either ways?

• February 22, 2017 1:52 am

RUsh limbaugh is more intelligent than Terence Tao.

Does this imply that the brain parameter is wrong or that RL isn’t as one perceives him to be?