How I Fell in Love with Math: A Practical Guide for Self-Learners

How I Fell in Love with Math: A Practical Guide for Self-Learners

Mathematics can seem intimidating, especially if your school memories are filled with confusion and frustration. But what if you could turn that around and make math a rewarding part of your daily life? In this article, I’ll share my journey from struggling with trigonometry in seventh grade to dedicating hours each week to advanced math—and how you can do it too.

Introduction: From Math Anxiety to Analytical Confidence

Hi everyone! My name is Renat. I’m 23, originally from Moscow, and currently living in Cyprus, working as an analyst. Until I was 19, I had no idea what truly motivated me. Math certainly wasn’t on my radar—my school experience left me convinced I’d never enjoy it. Fast forward a few years, and I now spend 10–15 hours a week tackling math problems, watching lectures, and preparing for graduate school entrance exams. Here’s how I reignited my passion for learning math, found motivation, and built habits to avoid burnout.

1. Revisiting School Math: Foundation, Not Frustration

If you barely remember your school math beyond cold mornings and long walks to class, don’t worry. You don’t need to master every detail of the curriculum. What matters most is understanding the core concepts. Gaps in knowledge often fill themselves as you dive into higher mathematics.

Key topics to refresh:

  • Geometry
  • Trigonometry
  • Number theory
  • Functions
  • Polynomials

My Approach to Refreshing School Math

  1. Practice with Problem Books: I bought a high school exam (EGE) problem book and solved what I could. For tougher problems, I watched YouTube walkthroughs. Don’t get bogged down in the hardest problems—focus on the 20% that gives you 80% of the understanding.
  2. Watch Lectures Efficiently: I watched relevant lectures at 1.5x speed, focusing on the main ideas rather than taking detailed notes. Then, I tackled 10–20 problems per topic, using ChatGPT to clarify anything unclear.
  3. Keep Moving Forward: If I got stuck, I made a note and moved on, planning to revisit the topic later with more experience.

Tip: 1–2 months of focused review is usually enough to rebuild your foundation. Don’t stress about perfection—understanding is more important than rote memorization.

2. Diving into Advanced Math: Calculus, Linear Algebra, and Beyond

Mathematical Analysis (Calculus)

Calculus (often called «matan» in Russian universities) is foundational but can be daunting. Initially, I didn’t see its value, but over time, I realized how crucial it is to truly understand the concepts, not just solve problems for a grade.

Advice:

  • Find Your Motivation: Connect calculus concepts to real-world problems or your work. Understanding their applications can make abstract ideas more tangible.
  • Pace Yourself: Don’t binge-watch lectures. Start with one per day or a few per week, and balance with problem-solving.
  • Switch Topics When Stuck: If you hit a wall, move to another topic and return later with fresh eyes.
  • Seek Community: Discussing problems and proofs with others is invaluable. Friendly competition or collaboration can boost motivation.

Timeline: With a few hours per week, you can cover basic calculus in 2–3 months. More advanced topics may take 6–8 months, but the journey is rewarding.

Linear Algebra and Analytic Geometry

Linear algebra («linal») and analytic geometry («angem») often go hand-in-hand. At first, matrices and vectors seemed like abstract symbols, but visual explanations and animations (especially on YouTube) helped me appreciate their beauty and utility.

Advice:

  • Don’t Blame Yourself: If a topic feels tough, try a different textbook or lecturer.
  • Solve Problems Multiple Ways: Approach problems both algebraically and geometrically to deepen your understanding.
  • Focus on Proofs: Understanding the logic behind theorems is more valuable than just memorizing results.
  • Progress is Faster: The structure of linear algebra is often more straightforward than calculus, so you may see quick gains.

3. The Power of Community: Math Clubs and Study Groups

Learning math alone can be isolating. Finding like-minded peers was a game-changer for me. I joined an online math club organized by MIPT (Moscow Institute of Physics and Technology) alumni, where we:

  • Prepare for graduate programs together
  • Participate in sprints, workshops, and problem-solving sessions
  • Take turns teaching topics, which reinforces our own understanding

Tips for Joining a Community:

  • Don’t be intimidated by others’ knowledge—everyone started somewhere.
  • Create a study calendar to track your progress and stay organized.
  • Take advantage of trial periods in clubs or online groups to find the right fit.

Personal Note: The supportive, friendly atmosphere of my club kept me motivated and accountable. If you can, find a group or even just a study buddy—it makes a huge difference.

4. Overcoming Common Challenges: Procrastination, Fear, and Burnout

Self-learning isn’t always smooth sailing. Here’s how I tackled the most common obstacles:

  • Procrastination: Break topics into micro-tasks and share progress with friends or family. I studied with my younger sister, which made learning more interactive and fun.
  • Fear: Replace thoughts like “I’m not a math person” with “Anyone can learn step by step.” I recommend Barbara Oakley’s book A Mind for Numbers for mindset tips.
  • Burnout: Don’t try to learn everything at once. Take breaks and remember that progress can be slow but steady. Regular practice leads to breakthroughs.
  • Failure: Struggling with tough problems is normal. A year ago, I couldn’t solve most advanced problems—now I can tackle many. Celebrate progress, not perfection.

5. What’s Next? Keeping the Journey Open

Eventually, you’ll reach a point where you’ve covered the basics and might wonder what’s next: Should you explore probability, graph theory, or data science? Consider formal study or research? My advice: treat math as an open-ended journey. Take breaks when needed, explore new areas when curiosity strikes, and enjoy the process as much as the results.

6. Recommended Resources

Here are some resources that helped me along the way:

In Russian

Other Topics

In English

Conclusion: Math is for Everyone

I hope my story encourages you to give math another shot—or to approach any challenging subject with a fresh perspective. No matter your age or background, math can become a lifelong companion if you find the right approach. I’m still early in my journey, but I’ve learned that persistence and curiosity matter more than innate talent.

Key takeaways:

  • Focus on understanding, not memorization
  • Build a support network
  • Break learning into manageable steps
  • Celebrate progress, not perfection

Enjoy the process, and don’t hesitate to share your experiences or questions in the comments. Happy learning!