About
Math by First Principles is a free, self-study math site for middle- and high-school students. The goal is simple: explain math clearly, build ideas from what students already know, and show why the rules work instead of asking students to memorize them.
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Who is behind the site
Math by First Principles is created and maintained by Shyam Mishra. I am a technology enthusiast and a dad of two students, one in middle school and one in high school. I enjoy finding clearer, more intuitive ways to explain math and making high-quality learning material freely available.
Why I built it
I wanted math explanations that do more than give students a rule and a set of exercises. The lessons build ideas step by step, show where the rules come from, and help students understand enough to solve problems that look different from the examples they have seen.
Editorial standards
Math by First Principles is developed with AI assistance, but I am responsible for the editorial direction and everything published on the site. AI is used to help draft, edit, review, and improve lessons.
Before publication, content is reviewed for:
- Mathematical accuracy: explanations, examples, and solutions should be correct.
- Clarity: ideas should be explained in plain language and built step by step.
- Age appropriateness: lessons should be understandable for students at the level the subject is intended for.
- Prerequisite consistency: lessons should rely only on ideas students have already learned or clearly introduce what they need.
- Practice accuracy: questions, answers, and worked solutions should agree and be mathematically sound.
The goal is not to make every lesson exhaustive. It is to make each lesson correct, clear, focused, and useful for learning the next idea.
Found a mistake?
Despite review, mistakes can get through. If you find one, please report it and tell me the lesson and the step that looks wrong. Corrections are welcome and help make the site better for everyone.
Help make it better
Math by First Principles is actively developed and refined. Lessons may be updated as I find clearer explanations, better examples, or better ways to help students learn.
If something is confusing, incorrect, especially helpful, or simply could be better, I would love to hear about it. Feedback from students, parents, and educators helps decide what to improve next. And if you find the site useful, please share it with others.