How each entry is written

I wrote the first entries for Algebrica in October 2023, and since then my process has remained largely manual. My background in engineering shapes the way I approach each topic. I have collected old notes from my studies, consulted many textbooks, lecture notes, and established reference works, and tried to write explanations that are essential, clear, and rigorous. Without the material I have consulted over the years, a knowledge base as extensive as Algebrica would not exist. What I add is the work done on that material, reconciling definitions and notation, and rewriting everything into a single exposition that follows a single line of reasoning from beginning to end.

Every source behind this work is listed in the bibliography.

Every entry is written from scratch. I compare different sources, look for common ideas and discrepancies, and then reorganise the material into a structure that is rigorous and easy to follow. The goal is not to collect information but to turn it into a coherent explanation, an original exposition revised until the mathematics is as clear and accessible as possible without losing precision.

Clarity and rigour do not always pull in the same direction, and this is one of the difficulties of mathematical writing. Academic sources are often dense for good reasons, and part of the work behind Algebrica is finding ways to make complex ideas more approachable while preserving their formal meaning. Whenever a simplification risks introducing ambiguity or inaccuracy, precision comes first.

Algebrica is also a living project. A page that seems complete today may be revised tomorrow, as related topics grow, new connections appear, or better explanations are found. Many improvements have come from readers who suggested corrections, pointed out inconsistencies, or proposed alternative explanations, and their help has made the project better over time.

All content is free, downloadable in Markdown format, and reusable for non-commercial purposes. Entries are progressively published and updated on GitHub through Algebrica's public repository, where anyone can inspect the source material, follow revisions, and contribute suggestions.

Tools that support the writing

Transparency is one of the principles Algebrica is built on, so I want to be open about the tools I use. English is not my native language, and I rely on Grammarly (no affiliation) for proofreading and stylistic refinement. Grammarly helps me express it more naturally for an international audience.

More recently, I have started using Codex and Claude Cowork (no affiliation) to improve internal linking between entries, fix sentences that sound too Italian, reorganize sentence structure, and keep the style consistent by replacing colloquial turns of phrase with more precise ones. I also use it to look for inaccuracies or mistakes, which I then verify individually. With hundreds of pages published, this is work I can no longer do manually page by page, and AI saves me a great deal of time while keeping content quality consistent. It works as a small support team that lightens the load, but the underlying writing is still my own.

A personal project, open to everyone

Algebrica is, in the end, a personal project built around a simple idea: mathematical knowledge should be clear, accessible, verifiable, and freely available to anyone who wishes to learn. If you notice mistakes, unclear passages, awkward English, or room for improvement, your feedback is always welcome. Many of the best refinements on the site began with a simple comment from a reader.