Welcome to Pieces of Mathematics!
About Me & This Website
I am Francesco Macrì, a passionate, self-taught, and self-directed learner of mathematics. On this website, I share that ongoing journey. I write in three forms: dialogues, essays, and explorations.
The dialogues are held between two fictional characters called Intex and Certex. Intex makes mistakes, follows (sometimes wrong) intuitions, and pushes back when things don't seem to make sense. Certex doesn't just assert: he reasons, constructs counterexamples, and earns each conclusion.
Intex & Certex Lean Into Formalized Mathematics
In this series Intex and Certex take up Type Theory, Formal Proof, and Lean, the open-source programming language and theorem prover. This series shows mathematics not only in words and symbols but in code as well You will find the Lean code on my GitHub page. Within each dialogue I point to the relevant code.
Intex & Certex Explore Mathematical Concepts
In this series Intex and Certex take up a single mathematical concept, e. g. a definition, a curious fact, a question - and talk it through.
Intex & Certex Tackle Problems
In this series Intex and Certex take on problems and work them out together, showing the reasoning step by step. The dialogues show the false starts and the recoveries, not just the polished solutions.
Intex & Certex Meet in the Library
In this series Intex and Certex sit down with classic mathematics textbooks and read them together like a two-member book club. Rather than a standard, static review, they trace the structural connections between chapters and openly wrestle with the concepts exactly as the authors present them.
Intex & Certex Go (not the game) Philosophical
In this series Intex and Certex step back from doing mathematics and ask what it rests on: what mathematical objects are, how we come to know them, and what changes now that machines have entered the game.
Essays
Here you will find a written-out treatment of well-known pieces of mathematics, usually with the history of how the question arose in the first place.
Explorations
In this series I present a compact page for a single concept: definition, notation, a symbol table, an example, a non-example, and a jargon-free explanation at the end. This is aimed mainly at an audience that has already understood the material and wants a place to come back to.
Who This Is For
It's for anyone curious about mathematics. A good part of the site comes at it through type theory and formal proof. If that sounds interesting, there's plenty here; if not, the dialogues and essays stand on their own.
What This Isn't
- A complete curriculum.
- A textbook replacement.
- A path to passing exams quickly.
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.
Contact
Feel free to drop me a line at piecesofmathematics [at] gmail [dot] com.