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 my ongoing journey into mathematics. 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 seem not 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 doesn't show math solely 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 Discover 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.
Essays
Here you will find a written-out treatment of a basic piece 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 more aimed towards 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, really - but especially for students and self-learners who are looking for a different - and hopefully interesting - presentation.
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.