How to Learn Mathematics Effectively: Two Approaches That Actually Work

Browsing YouTube for something useful, I came across two interesting videos about how to learn math. Each has nearly 2 million views — one is for everyone, the other is for those tackling advanced topics. I’ll save you some time: here are the key takeaways.

Video 1: How to Get Good at Math

The first video covers foundational math learning strategies that apply to students at any level.

1. Talent isn’t everything
Success in mathematics depends not on innate ability, but on the right learning strategies. The video’s author, Khan, once struggled with the subject herself — but later earned a degree in mathematics and operations research from Columbia University.

2. Passive learning doesn’t work
Simply reading textbooks and copying notes won’t cut it. Without active engagement, real understanding never comes.

3. Active learning is the key
Solving problems, discussing them with others, and explaining concepts to someone else are the methods that actually work.

4. A practical approach to problem-solving

• Try to solve the problem on your own.
• If you’re stuck — look at the solution.
• Understand the logic behind it.
• Try solving the problem again from scratch.

Repeat this cycle until you can solve it without mistakes.

How to Learn Math Without Wasting Hours of Your Time

5. Manage your time efficiently
Instead of agonizing over a single problem for hours, it’s better to look at the solution quickly, understand the approach, and move on.

6. Understanding beats memorization
Use the Feynman technique: explain a concept in simple words to test whether you truly understand it.

7. Math anxiety is normal
Even at an advanced level, people feel anxious when faced with difficult problems. That’s part of the process.

8. Don’t skip the fundamentals
If something isn’t clicking, chances are you’ve missed an important foundational concept somewhere along the way.

9. Intuition grows with practice
Repeatedly working through problems gradually shifts complex reasoning from slow, deliberate thinking to fast, intuition-based processing.

10. Believe in yourself
The most important thing is believing that you are capable of getting good at mathematics.

Video 2: How to Learn Math Effectively on Your Own

The second video focuses on self-study strategies for learning math independently — particularly useful for more advanced topics.

1. Prepare everything you need
A comfortable pen or pencil, a sharpener, a timer, and blank unlined paper. The goal is physical comfort.

2. Find a quiet place to study
A library or a secluded space free from distractions is ideal.

3. Choose a textbook and a topic
Start with something that interests you and sits just outside your comfort zone. Use multiple textbooks — different authors explain things differently, which deepens your understanding.

4. Use a timer
Study in sessions of about one hour to maintain maximum focus.

Math Learning Strategies for Deep, Independent Study

5. Engage actively with the material

• Write out definitions from memory.
• Work through examples without looking at the solutions.
• Move on to problems that have no worked examples — applying only what you’ve read.

6. Reflect after each session
Think about what you absorbed and identify what’s still unclear. This helps you plan the next session more effectively.

7. The freedom of self-directed learning
You can study any topic you choose, at whatever pace suits you.

8. Textbooks contain more than you think
Textbooks often hold more depth and breadth than a university course ever covers.

9. Embrace discomfort
Moments of confusion are a normal part of the process. That’s exactly how learning happens.

10. Study at the edge of your ability
Pushing into difficult material drives growth and solidifies new knowledge more than staying in familiar territory.

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Which approach resonates with you more? The structured practice method from the first video, or the self-directed deep-study method from the second — or perhaps a combination of both?