Learning Math From Zero (Again)

At some point in school, I stopped actually learning math and started performing it.

I could pass tests. I could follow the steps. But if you asked me why the steps worked — I had nothing. I was running a program without understanding the code underneath.

This bothered me more and more as I started taking programming and CS seriously. Because CS is built on math. And I realized I had a fragile foundation.

The Moment I Knew

I was trying to understand binary search — really understand it, not just implement it. And I hit a wall when I got to the proof of why it runs in O(log n). Logarithms. I knew what log meant symbolically. But why? What does it actually mean for something to be logarithmic?

I couldn't answer it. Not properly.

So I went back. Not to a textbook from my current grade — back to where the concept actually comes from.

What I Did

I found a method that works for me: start from the question, not the definition.

Instead of reading "a logarithm is the inverse of an exponentiation," I asked myself: if 2^10 = 1024, then how many times do I have to multiply 2 by itself to get 1024? That's a logarithm. Now I own that concept.

I applied the same approach to everything I had been faking:

• Fractions and ratios (actually understanding proportions, not just cross-multiplying)
• Exponents and their properties
• Basic algebra — why can you add the same thing to both sides?
• Functions — what does it mean for something to be a function?

It took weeks. Some concepts I had "learned" in 5th grade took me days to really understand at 16.

What Changed

The main thing that changed: I stopped being afraid of math problems I hadn't seen before.

Before, I needed to recognize a pattern from something I'd practiced. Now, when I see something new, I have actual tools — not templates, but understanding.

That's the difference. And it's massive.

The Lesson

Fake understanding compounds badly. The longer you carry it, the more it costs you later.

If something doesn't make sense, don't paper over it. Stop. Go back. Ask why. It's slower in the short term and faster in every other timeframe.