Learning Higher-Grade Math Ahead of Time is the Greatest Educational/Career Life Hack
Higher-grade math unlocks specialized fields that students normally couldn't access until much later -- and on average, the faster you accelerate your learning, the sooner you get your career started, and the more you accomplish over the course of your career.
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When a student learns a lot of advanced math ahead of time, they unlock the opportunity to delve into a wide variety of specialized fields that are usually reserved for graduates with strong mathematical foundations.
This fast-tracks them towards discovering their passions, developing valuable skills in those domains, and making professional contributions early in their career, which ultimately leads to higher levels of career accomplishment.
I’m not exaggerating here – this is actually backed up by research. On average, the faster you accelerate your learning, the sooner you get your career started, and the more you accomplish over the course of your career.
For instance, in a 40-year longitudinal study of thousands of mathematically precocious students, researchers Park, Lubinski, & Benbow (2013) concluded the following:
- "The relationship between age at career onset and adult productivity, particularly in science, technology, engineering, and mathematics (STEM) fields, has been the focus of several researchers throughout the last century (Dennis, 1956; Lehman, 1946, 1953; Simonton, 1988, 1997; Zuckerman, 1977), and a consistent finding is that earlier career onset is related to greater productivity and accomplishments over the course of a career. All other things being equal, an earlier career start from [academic] acceleration will allow an individual to devote more time in early adulthood to creative production, and this will result in an increased level of accomplishment over the course of one's career.
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[In this study] Mathematically precocious students who grade skipped were more likely to pursue advanced degrees and secure STEM accomplishments, reached these outcomes earlier, and accrued more citations and highly cited publications in STEM fields than their matched and retained intellectual peers."
But to be clear: in all this discussion about learning advanced math, I’m talking about higher-grade math, not grade-level competition problems.
When a middle or high school teacher has a bright math student, and the teacher directs them towards competition math, it’s not because that’s the best option for the student. Rather, it’s the best option for the teacher. It gives the student something to do while creating minimal additional work for the teacher.
Competition math problems generally don’t require students to learn new fields of math. Rather, the difficulty comes from students needing to find clever tricks and insights to arrive at solutions using the mathematical tools that they have already learned.
A student can wrestle with a competition problem for long periods of time, and all the teacher needs to do is give a hint once in a while and check the student’s work once they claim to have solved the problem.
But if you look at the kinds of math that most quantitative professionals (like rocket scientists and AI developers) use on a daily basis, those competition math tricks don’t show up anywhere. But what does show up everywhere is university-level math subjects like multivariable calculus, linear algebra, differential equations, and (calculus-based) probability and statistics.
So, given that most students who enjoy math are going to end up applying math in some other field (as opposed to becoming mathematicians) – wouldn’t it be more efficient for them to get a broad view of math as early as possible so that they can sooner apply it to projects in their field(s) of interest?
The countering view is that “students should go ‘deep’ with the math that they’ve already learned – they’ll learn the other math subjects when they’re ready.” But, in practice, this is not true.
If students “learn the other math subjects when they’re ready,” then when is that? Is it when they complete a quantitative major during college? No – even most math majors only learn a tiny slice of all the math that’s out there.
(If you know someone who majored in a quantitative field, ask them if they took algebraic geometry, convex optimization, and control theory. Chances are, they haven’t taken any. On rare occasions, they may have taken one. These are just three out of hundreds of university-level math subjects.)
Do students “learn the other math subjects when they’re ready” after college, on the job? No – if you’re trying to solve cutting-edge problems that nobody has solved before, then there is no “known path” that can tell you what additional math you need. And to even realize that a field of math can help you solve your problem, you generally need to have learned a substantial amount of that field in the first place.
In practice, the only way for students to “learn the other math subjects when they’re ready” is to learn as much math as possible during school.
Read the extended essay: The Greatest Educational Life Hack: Learning Math Ahead of Time
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