> The Greatest Educational Life Hack: Learning Math Ahead of Time (justinmath.com)

worked for me, can work for a lot of people, and is a good idea.

Partly:

(1) One way to win a 100 yard dash is to start running half way to the finish line and have no one object. The US educational system will usually overlook something like that starting half way to the finish line.

(2) Reasons: (a) The system assumes that their teaching is crucial and that no student really can learn on their own, i.e., the student didn't actually start half way to the finish line. (b) The system so wants more good students that they will overlook the evidence that the student was ahead at the start of the class. But, research in math mostly requires working alone directly from original papers, and working from a highly polished text is usually much easier -- so profs learn on their own, and students can too.

(3) Generally in math, independent study can work well. Basically for each lesson, (a) study the text, (b) work most of the exercises, especially the more challenging ones, and check the answers in the back of the text (need a suitable text or just get the book for teachers), and (c) in a quiet room, lean back, relax, and think a little about what the value, purpose, content of the lesson was, say, be able to explain it to someone who never studied math.

(3) So, take calculus in high school. And visit, call, whatever, and see what the popular college calculus texts are, get one or two of those (used can be a lot cheaper), and before college have worked hard on both the high school course and the college text(s). Then in college, right, take calculus, likely from a text have already done well in. So, will likely be one of the best students in the class. Then will get a good reputation that can be valuable.

(4) Will be ahead, so continue this way and stay ahead.

(5) Next math course, say, modern, abstract algebra, i.e., set theory, groups, fields, Galois theory, elementary number theory, maybe a start on linear algebra.

Next, linear algebra, maybe the most important and useful course. Work through a popular text that is relatively easy. Then work carefully through one or two of the classics, e.g., Halmos, Finite Dimensional Vector Spaces.

Likely next, "Baby Rudin", W. Rudin, Principles of Mathematical Analysis, calculus and somewhat more done with depth and precision. See the roles of open and closed sets, closed and bounded sets, i.e., compact sets, continuous functions, the powerful results of continuous functions on compact sets, Fourier series.

Advanced calculus, i.e., partial derivatives and Stokes formula.

Analysis, e.g., the real part of W. Rudin, Real and Complex Analysis, Lebesgue's alternate and nicer way to define integration (in short, partition on the Y axis instead of the X axis), the Fourier integral, Banach space, Hilbert space, the Radon-Nikodym theorem (can be used for grand approaches to information, Bayes Rule, the Neyman-Pearson result in best statistical hypothesis testing, and with von Neumann's proof based just on polynomials is charming, ...).

More, e.g., differential equations, probability, statistics, stochastic processes, optimization, complex analysis, number theory, whatever.

One consequence: Will learn how to write math. Too often people who don't know advertise that they don't know much math.

At some point in business, some of that math might be valuable. E.g., current AI uses steepest descent via calculus and optimization, linear algebra, and hypothesis testing.