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If I haven’t tested it myself, I don’t write about it. 16 years of building sites, breaking things, and figuring out what actually works.
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Russian Peasant Multiplication is an ancient technique that multiplies any two numbers using only doubling and halving. No multiplication tables needed. I explain the method step by step, prove why…
Think you're good at mental math? Try this quick test. Start with 1000, add 40, add another 1000, add 30, add 1000 again, then add 20. What's your answer? Most…
Two math problems that'll make you think. First: find the smallest autobiographical number where each digit tells you how many times a digit appears. Second: a classic puzzle involving a…
Pursuit problems are some of the most elegant challenges in classical mechanics. A fox chases a rabbit, both moving at constant speed. What path does the fox follow? I present…
Weierstrass shocked the mathematical world in 1872 by constructing a function that's continuous everywhere but differentiable nowhere. Not at a few points. At no points whatsoever. I walk through the…
Memory isn't fixed. You can train it. I've compiled ten practical methods to improve how you retain and recall information: from simple repetition and spaced practice to visualization techniques and…
I've spent years collecting free calculus textbooks. Not scanned copies with missing pages. Real textbooks that professors and universities have made freely available online. This curated list covers single-variable calculus,…
Most math students use real numbers without ever understanding how they're constructed. Dedekind solved this with his theory of cuts. He showed how to build the real numbers rigorously from…
I've compiled 20+ free algebra and topology ebooks. Not sketchy PDFs from torrent sites. Real textbooks that professors and universities have made freely available. Covers abstract algebra, linear algebra, algebraic…
The D'Alembert Ratio Test is one of the most reliable tools for determining whether an infinite series converges or diverges. I cover the theorem statement, proof, worked examples, and the…
When a molecule absorbs light, the energy has to go somewhere. It can trigger a chemical reaction, release heat, or emit light as fluorescence or phosphorescence. The Jablonski diagram maps…
Problem solving in mathematics isn't about memorizing formulas. It's about knowing what to look for. I break down the essential steps every math student needs: understanding the problem, devising a…
