Welcome to Pieces of Mathematics!
About Me & This Website
I am Francesco Macrì, a passionate, self-taught, and self-directed learner of mathematics with an academic degree in a non-mathematical discipline. That is, I don't have a degree in mathematics of any kind.
I came to math late, on my own, driven by curiosity rather than curriculum. I'm self-taught—which means I spent and still spend a lot of time confused, stuck, and frustrated. On this website, I share my ongoing journey. But instead of presenting the content in a encyclopedic style, I want to create a place where the confusion is part of the explanation. Where you see ideas being worked out, not just presented. Where someone asks the "dumb" questions that aren't actually dumb at all.
A textbook often presents: "Definition. Theorem. Proof." Don't get me wrong, I love this style. They're written by people who understood the material so long ago that they've forgotten what it felt like not to understand. The confusion has been edited out. But that's not how anyone actually learns. I write in dialogues. The dialogue shows the stumbles, the questions, the "Wait, why?" moments. It seems to me that this is closer to how mathematical understanding actually develops. Textbooks are essential—I use them constantly, and I couldn't do any of this without them. But they record the finished thought, not the process of arriving at it.
Adventures of Intex & Certex
The heart of this site is a pair of characters: Intex, who is learning and often confused, and Certex, who guides without lecturing. Intex makes mistakes, follows wrong intuitions, and pushes back when things don't make sense. Certex doesn't just assert—he reasons, constructs counterexamples, and earns each conclusion. If you've ever thought "but why does that work?"—Intex has probably asked it.
Who This Is For
It's for anyone curious, really—but especially for students who find textbooks frustrating, self-learners approaching math for the first time (or the fifth), anyone who wants to understand rather than memorize, and teachers looking for a different way to present ideas.
What This Isn't
- A complete curriculum.
- A textbook replacement.
- A path to passing exams quickly.
This is a place to slow down and actually think.
The Journey - My Journey
I'm still learning. The site grows as I grow. Some pages are rough. Some will be rewritten. If you find an error, tell me—I'd rather be corrected than wrong. One thing I love about mathematics: it doesn't care who you are. A proof is valid or it isn't. The integers don't check your CV. This means anyone can participate—and anyone can be wrong. Including me.
Contact
Feel free to drop me a line at piecesofmathematics [at] gmail [dot] com.