Friend, after reading your question, the first thing that popped into my head wasn’t a book or a website—it was another person.
Someone very much like you.
Around this time last year, I received a letter from a reader. He had dropped out of junior high school, and his math foundation was—quote—“roughly at elementary-school level, with scattered, uneven knowledge.” He was interested in mathematics—not the kind of interest typical of problem-solving “exam-takers,” but the kind driven by a desire to understand complex economics and social network analysis. That path demands mathematical fluency—and he knew it. He’d tried textbooks; he’d tried online courses—but never stuck with any for more than a week. He asked me: Can someone like me really learn math?
I couldn’t answer him directly—my own math background wasn’t weak, so I had no idea whether my experience would apply to him. Yet something deep down told me there must be a tool designed precisely for people like him. So I reached out and asked if he’d be willing to try it for one month—and write down his most honest, unfiltered experience.
He agreed.
A month later, he sent me his report—and I read it twice. He wrote that on Day One, he rediscovered the “gaming feel”: the system automatically lowered difficulty when he got things wrong, and raised it again when he succeeded; green feedback popped up with satisfying immediacy, and he earned experience points. In that month, he learned the unit circle, trigonometry, logarithms, and factoring—topics you might consider basic junior-high material, but for him, they represented a massive leap forward. He’d “tried traditional methods countless times—never lasting beyond a week”—but this time, he renewed for a second month.
Then he kept going—for a full year.
A year later, he sent me another report. He’d completed Algebra II and stood at the threshold of precalculus. He used to get headaches just seeing “tan” or “sin”; now he could solve entire problem sets. He no longer chased experience points—he found himself spontaneously wondering, Where does this formula actually come from?, spending thirty minutes or even an hour deriving it himself—and feeling an intense rush of satisfaction upon success. He wrote: “Math, for me, has shifted from Mount Everest to Mount Wutai—yes, climbing still takes effort, but it won’t kill you.”
Do you know what line moved me most?
He wrote: “Our schools constantly undermine this kind of confidence. They don’t fill in foundational gaps based on your level; they don’t pause for any individual student. Everyone marches forward under standardized pacing—and those who fall behind become the ‘stupid’ people who ‘can’t do math.’”
Friend, you asked how someone without a high-school diploma can self-study math. Before answering, let me tell you this: You call yourself a “free agent,” say you’re “short on money and talent,” and think your grasp of junior-high math is merely average—all these labels likely reflect not your true capacity, but scars left by conventional education.
You flipped open a college-entrance exam paper and found yourself unable to proceed. That’s completely normal. Those exams weren’t designed for self-learners—they were built for students who’ve sat in classrooms for three years, drilled repeatedly on identical problem types by teachers. Using them as your starting point is like a complete beginner trying to squat double their body weight without ever having touched a barbell—not because you lack talent, but because you’ve walked through the wrong door.
So where is the right door?
The reader I mentioned reached precalculus from Algebra II in one year—not through talent, not through textbooks, not through online courses—but through one tool: Math Academy (MA).
Hear me out before rolling your eyes.
At its core, MA is an adaptive math-learning system. And it offers four things no book or online course can deliver:
First: A knowledge graph. Math isn’t a straight line—it’s a web. If you can’t solve quadratic equations, it’s probably not because you’re “dumb,” but because you’re shaky on fraction arithmetic. Traditional textbooks won’t tell you that—they’ll just leave you floundering in the quadratic chapter. MA breaks every concept into thousands of micro-topics, clearly mapping their dependencies. When you get stuck, the system traces backward along the graph to locate your actual knowledge gap—and starts filling it from there.
Second: Mastery-based learning. To advance, you must correctly solve several consecutive problems on each new concept—not just “kind of get it,” not just “understand the solution when you see it,” but solve it yourself. This eliminates the false sense of security that comes from thinking “I get it” while failing under real pressure.
Third: Spaced repetition. Learning doesn’t end once you’ve grasped something. The system reintroduces concepts just as you’re about to forget them—forcing you to retrieve them from memory. Each successful retrieval strengthens neural connections. That reader once studied only on weekends—missing out on spaced-repetition benefits—and found himself stuck on a single problem for half an hour during review, suffering intensely. But that pain proves the method works.
Fourth: Minimal cognitive load. Every concept is introduced with extreme brevity, followed immediately by practice problems. Cognitive science tells us working memory can hold only about four information chunks at once. Traditional textbooks cram pages with formulas and proofs—overloading your brain instantly. MA uses the “minimum effective dose”: giving you only what you need right now—and letting you cement it through practice.
None of this is mysticism—it’s cognitive science, rigorously validated over the past century.
I won’t lie to you: MA is paid—and not cheap. You said you’re “short on money,” and that’s a real barrier. But here’s another set of numbers: That reader tracked his usage for a full year and found his average weekly net study time was only 2–5 hours—occasional sprints, mostly part-time rhythm. Even then, his progress matched that of full-time students—even though his problem-solving speed was half the official estimate. If you can afford it, MA may be the best investment you ever make in learning—cheaper than private tutoring, far more effective than buying a stack of unread textbooks.
If MA is currently out of reach, at least internalize its underlying principles—and apply them to your own learning:
First: Don’t start with college-entrance exams or high-school textbooks. Your foundations may be weaker than you realize—you need to begin earlier. Find a clearly tiered curriculum (even Khan Academy will do), start with algebra fundamentals, and take diagnostic tests seriously.
Second: Never let a concept slide with a vague “sort of got it.” If you can’t solve problems, step back and identify the missing prerequisite knowledge. Don’t rush. Don’t skip. Math is brutally fair: every debt you defer multiplies in cost later.
Third: Don’t just read—practice relentlessly. Learning is memory; memory is retrieval. Reading something ten times is less effective than deriving it once yourself. If you stall on a problem for ten minutes with zero progress, consult the solution—but then close it, and solve it again from scratch.
One more thing: Your curiosity about math is your most precious asset—don’t let frustration kill it. That reader told me his first glimpse of “mathematical beauty” came while learning the area formula for equilateral triangles—the seemingly arbitrary \frac{\sqrt{3}}{4} \times \text{side}^2. When he derived it independently via trigonometry, the Pythagorean theorem, and geometric area formulas—and saw all three converge on the same result—he experienced a moment of pure insight. You look at college-entrance papers and see only hard problems and red X’s. But once your foundations are solid, you’ll see an entirely different landscape.
You asked whether you must master high-school math first. The answer is: High-school math is simply a combination of algebra, geometry, trigonometry, and functions. You don’t need to “finish high school math” as a monolith—you need to find your true starting point, then walk forward, step by step. As that reader put it: “For me, math is now only a matter of time—and only time.”
Finally, you called yourself a “free agent.” I disagree.
Someone who picks up a college-entrance exam paper out of idle curiosity—or who visits Zhihu to earnestly ask how to self-study math—isn’t “free-floating.” They’re curious. Don’t let anyone—including yourself—stick a “can’t learn” label on you. Math’s door has never been closed to you. You’ve just been knocking on the wrong entrance.
Now—go find your real entrance.
Original
https://www.zhihu.com/question/1907168323269039022/answer/2039766110875166207