About

A Markdown corpus of Bourbaki's Éléments de mathématique with a permanent tag on every numbered statement, and this site built out of it. It is a study project. It is not Bourbaki's, it is not Springer's, and it is not a substitute for the books.

The site is generated by bourbaki publish out of committed Markdown and nothing else. No PDF, no scratch directory and no network at build time, so anybody with a clone of the corpus and the tooling gets the same bytes. Every number on this page is counted out of those files by the build.

What is here

One chapter of one Book, and the library holds forty three volumes. A site that looked like the Éléments and held chapter VIII of Algebra would be a worse thing than no site, so here is what is actually in it.

Where the text came from

The volumes are PDFs with a text layer, so the words are lifted off that layer by pdftotext -layout and assembled into sections by code. No model wrote those sentences and no model rewrote them, which is why the transcriptions are worth more than the translations are. The transcribed sections record 142 native, 26 native+ocr and 1027 ocr. Anything that is not native had a model somewhere in it, and the page for such a section says so at its foot.

What the machine did decide is where one statement ends and the next begins, and which of them is Proposition 6. That segmentation is the assembler reading the printed text, not markup the book carries, and the whole tag scheme sits on top of it. A statement cut in the wrong place is the failure to watch for, and it is what the printings report in the corpus is for: the French and the English of one chapter should hold the same statements section by section, and where they do not, one of the two is being read wrongly.

What a machine wrote

The en-mt is machine translation of the English and is not checked by a person. 132 sections of the 533 the English holds, written by gpt-5-6, gpt-5-6, gpt-5-6-mini, gpt-5-6, gpt-5-mini, gpt-5-6, gpt-5.4, gpt-5-6-mini, gpt-5-6-mini, gpt-5-6-mini, gpt-5-6, gpt-5-6-mini, gpt-5-6, gpt-5.4, gpt-5-6-mini, gpt-5-mini, gpt-5-6-mini, gpt-5-mini, gpt-5-6, gpt-5.4, gpt-5-6-mini, gpt-5-mini, gpt-5.4, gpt-5-6-mini, gpt-5.4, gpt-5-6-mini, gpt-5.4, gpt-5-6, gpt-5-6-mini, hy3-free, laguna-s-2.1-free, nemotron-3-ultra-free, gpt-5-mini, gpt-5-mini, gpt-5-6-mini, gpt-5-mini, gpt-5-6-mini, gpt-5-6, gpt-5-mini, gpt-5.4, gpt-5-mini, hy3-free, nemotron-3-ultra-free, laguna-s-2.1-free, gpt-5-6, gpt-5.4, gpt-5.4, gpt-5-6-mini, gpt-5.4, gpt-5-6-mini, gpt-5-mini, gpt-5.4, gpt-5-mini, laguna-s-2.1-free, hy3-free, laguna-s-2.1-free, hy3-free, gpt-5-mini, nemotron-3-ultra-free, gpt-5-6-mini, laguna-s-2.1-free, mimo-v2.5-free, hy3-free and nemotron-3-ultra-free, hy3-free, laguna-s-2.1-free against versions 30 and 34 of the terminology glossary, which is what a translation written over more than one run looks like. Every one of those pages carries its own line saying which model wrote it and which glossary it was held to, since that is what a reader needs before deciding whether to believe a sentence.

The Vietnamese is machine translation of the English and is not checked by a person. 664 sections of the 533 the English holds, written by gpt-5-6, gpt-5-6, copied, gpt-5-6, gpt-5-6-mini, gpt-5-6, gpt-5-6-mini, copied, gpt-5-6, gpt-5-6-mini, copied, gpt-5-mini, gpt-5-6, gpt-5-6-mini, gpt-5-mini, gpt-5-6, gpt-5-6-mini, gpt-5-mini, gpt-5.4-mini, gpt-5-6, gpt-5-6-mini, gpt-5.4, gpt-5-6, gpt-5-6-mini, gpt-5.4, gpt-5.4-mini, gpt-5-6, gpt-5-6-mini, gpt-5.4-mini, gpt-5-6, gpt-5-6-mini, gpt-5.4-mini, gpt-5-mini, gpt-5-6, gpt-5-mini, gpt-5-6-mini, gpt-5-6, gpt-5-mini, gpt-5.4, gpt-5-6, gpt-5.4, gpt-5-6, gpt-5.4, copied, gpt-5-6, gpt-5.4, gpt-5-6-mini, gpt-5-6, gpt-5.4-mini, gpt-5-6, gpt-5.4-mini, gpt-5-6-mini, gpt-5-6-mini, gpt-5-6-mini, copied, gpt-5-6-mini, gpt-5-6, gpt-5-6-mini, gpt-5-6, gpt-5-mini, gpt-5-6-mini, gpt-5-6, gpt-5-mini, copied, gpt-5-6-mini, gpt-5-6, gpt-5-mini, gpt-5.4-mini, gpt-5-6-mini, gpt-5-6, gpt-5.4, gpt-5-6-mini, gpt-5-6, gpt-5.4-mini, gpt-5-6-mini, gpt-5-6, gpt-5.4-mini, gpt-5-mini, gpt-5-6-mini, gpt-5-mini, gpt-5-6-mini, gpt-5-mini, gpt-5-6, gpt-5-6-mini, gpt-5-mini, gpt-5.4, gpt-5-6-mini, gpt-5-mini, gpt-5.4, gpt-5-6, gpt-5-6-mini, gpt-5-mini, gpt-5.4-mini, gpt-5-6-mini, gpt-5-mini, gpt-5.4-mini, gpt-5-6, gpt-5-6-mini, gpt-5.4, gpt-5-6-mini, gpt-5.4, gpt-5-6, gpt-5-6-mini, gpt-5.4, gpt-5-6, gpt-5-mini, gpt-5-6-mini, gpt-5.4, gpt-5-mini, gpt-5-6-mini, gpt-5.4, gpt-5.4-mini, gpt-5-6-mini, gpt-5.4, gpt-5.4-mini, gpt-5-mini, gpt-5-6, gpt-5-6-mini, gpt-5.4-mini, gpt-5-6-mini, gpt-5.4-mini, gpt-5-6, gpt-5-6-mini, gpt-5.4-mini, gpt-5-6, gpt-5-mini, gpt-5-6-mini, gpt-5.4-mini, gpt-5-mini, gpt-5-6-mini, gpt-5.4-mini, gpt-5.4, gpt-5-mini, gpt-5-mini, gpt-5-6, gpt-5-mini, gpt-5-6, gpt-5-6-mini, gpt-5-mini, gpt-5-6, gpt-5-6-mini, gpt-5.4, gpt-5-mini, gpt-5-6-mini, gpt-5-mini, gpt-5-6-mini, gpt-5-6, gpt-5-mini, gpt-5-6-mini, gpt-5.4-mini, gpt-5-6, gpt-5.4, gpt-5.4, copied, gpt-5.4, gpt-5-6, gpt-5.4, gpt-5-6, gpt-5-6-mini, gpt-5.4, gpt-5-6, gpt-5-mini, gpt-5-6-mini, gpt-5.4, gpt-5-6-mini, gpt-5.4, gpt-5-6-mini, copied, gpt-5.4, gpt-5-6-mini, gpt-5-6, gpt-5.4, gpt-5-6-mini, gpt-5-6, gpt-5-mini, gpt-5.4-mini, gpt-5.4, gpt-5-6-mini, gpt-5.4-mini, gpt-5.4, gpt-5-mini, gpt-5-6-mini, gpt-5.4, gpt-5.4-mini, gpt-5.4, gpt-5.4-mini, gpt-5-mini, gpt-5.4, gpt-5.4-mini, gpt-5-mini, gpt-5-6, gpt-5-6-mini, gpt-5.4-mini, gpt-5.4-mini, gpt-5-6-mini, gpt-5.4-mini, gpt-5-6-mini, gpt-5-6, gpt-5.4-mini, gpt-5-mini, gpt-5.4-mini, gpt-5-mini, gpt-5-6-mini, gpt-5.4-mini, gpt-5-mini, gpt-5-6-mini, gpt-5-6 and gpt-5.4-mini, gpt-5.4 against versions 27, 29 and 34 of the terminology glossary, which is what a translation written over more than one run looks like. Every one of those pages carries its own line saying which model wrote it and which glossary it was held to, since that is what a reader needs before deciding whether to believe a sentence.

gpt-5-6, gpt-5-6-mini, gpt-5-6, gpt-5-mini, gpt-5-6, gpt-5.4, gpt-5-6-mini, gpt-5-6-mini, gpt-5-6-mini, gpt-5-6, gpt-5-6-mini, gpt-5-6, gpt-5.4, gpt-5-6-mini, gpt-5-mini, gpt-5-6-mini, gpt-5-mini, gpt-5-6, gpt-5.4, gpt-5-6-mini, gpt-5-mini, gpt-5.4, gpt-5-6-mini, gpt-5.4, gpt-5-6-mini, gpt-5.4, gpt-5-6, gpt-5-6-mini, hy3-free, laguna-s-2.1-free, nemotron-3-ultra-free, gpt-5-mini, gpt-5-mini, gpt-5-6-mini, gpt-5-mini, gpt-5-6-mini, gpt-5-6, gpt-5-mini, gpt-5.4, gpt-5-mini, hy3-free, nemotron-3-ultra-free, laguna-s-2.1-free, gpt-5-6, gpt-5.4, gpt-5-6-mini, gpt-5.4, gpt-5-6-mini, gpt-5-mini, gpt-5.4, gpt-5-mini, laguna-s-2.1-free, hy3-free, gpt-5-mini, nemotron-3-ultra-free, gpt-5-6-mini, laguna-s-2.1-free, mimo-v2.5-free, hy3-free, gpt-5-6, gpt-5-6-mini, gpt-5-6, gpt-5-6-mini, copied, gpt-5-6, gpt-5-6-mini, copied, gpt-5-mini, gpt-5-6, gpt-5-6-mini, gpt-5-mini, gpt-5-6, gpt-5-6-mini, gpt-5-mini, gpt-5.4-mini, gpt-5-6, gpt-5-6-mini, gpt-5.4, gpt-5-6, gpt-5-6-mini, gpt-5.4, gpt-5.4-mini, gpt-5-6, gpt-5-6-mini, gpt-5.4-mini, gpt-5-6, gpt-5-6-mini, gpt-5.4-mini, gpt-5-mini, gpt-5-6, gpt-5-mini, gpt-5-6-mini, gpt-5-6, gpt-5-mini, gpt-5.4, gpt-5-6, gpt-5.4, gpt-5-6-mini, gpt-5-6, gpt-5.4-mini, gpt-5-6, gpt-5.4-mini, gpt-5-6-mini, gpt-5-6-mini, gpt-5-6-mini, copied, gpt-5-6-mini, gpt-5-6, gpt-5-6-mini, gpt-5-6, gpt-5-mini, gpt-5-6-mini, gpt-5-6, gpt-5-mini, copied, gpt-5-6-mini, gpt-5-6, gpt-5-mini, gpt-5.4-mini, gpt-5-6-mini, gpt-5-6, gpt-5.4, gpt-5-6-mini, gpt-5-6, gpt-5.4-mini, gpt-5-6-mini, gpt-5-6, gpt-5.4-mini, gpt-5-mini, gpt-5-6-mini, gpt-5-mini, gpt-5-6-mini, gpt-5-mini, gpt-5-6, gpt-5-6-mini, gpt-5-mini, gpt-5.4, gpt-5-6-mini, gpt-5-mini, gpt-5.4, gpt-5-6, gpt-5-6-mini, gpt-5-mini, gpt-5.4-mini, gpt-5-6-mini, gpt-5-mini, gpt-5.4-mini, gpt-5-6, gpt-5-6-mini, gpt-5.4, gpt-5-6-mini, gpt-5.4, gpt-5-6, gpt-5-6-mini, gpt-5.4, gpt-5-6, gpt-5-mini, gpt-5-6-mini, gpt-5.4, gpt-5-mini, gpt-5-6-mini, gpt-5.4, gpt-5.4-mini, gpt-5-6-mini, gpt-5.4, gpt-5.4-mini, gpt-5-mini, gpt-5-6, gpt-5-6-mini, gpt-5.4-mini, gpt-5-6-mini, gpt-5.4-mini, gpt-5-6, gpt-5-6-mini, gpt-5.4-mini, gpt-5-6, gpt-5-mini, gpt-5-6-mini, gpt-5.4-mini, gpt-5-mini, gpt-5-6-mini, gpt-5.4-mini, gpt-5.4, gpt-5-mini, gpt-5-mini, gpt-5-6, gpt-5-mini, gpt-5-6, gpt-5-6-mini, gpt-5-mini, gpt-5-6, gpt-5-6-mini, gpt-5.4, gpt-5-mini, gpt-5-6-mini, gpt-5-mini, gpt-5-6-mini, gpt-5-6, gpt-5-mini, gpt-5-6-mini, gpt-5.4-mini, gpt-5-6, gpt-5.4, gpt-5-6, gpt-5-6-mini, gpt-5.4, gpt-5-6, gpt-5-mini, gpt-5-6-mini, gpt-5.4, gpt-5-6-mini, gpt-5.4, gpt-5-6-mini, copied, gpt-5.4, gpt-5-6-mini, gpt-5-6, gpt-5.4, gpt-5-6-mini, gpt-5-6, gpt-5-mini, gpt-5.4-mini, gpt-5.4, gpt-5-6-mini, gpt-5.4-mini, gpt-5.4, gpt-5-mini, gpt-5-6-mini, gpt-5.4, gpt-5.4-mini, gpt-5.4, gpt-5.4-mini, gpt-5-mini, gpt-5.4, gpt-5.4-mini, gpt-5-mini, gpt-5-6, gpt-5-6-mini, gpt-5.4-mini, gpt-5.4-mini, gpt-5-6-mini, gpt-5.4-mini, gpt-5-6-mini, gpt-5-6, gpt-5.4-mini, gpt-5-mini, gpt-5.4-mini, gpt-5-mini, gpt-5-6-mini, gpt-5.4-mini, gpt-5-mini, gpt-5-6-mini, gpt-5-6 and gpt-5.4-mini, gpt-5.4 are a cut down version of the model the rest of the language was written by. Nobody chose that, the account was moved down between one section and the next, and the sections it wrote say so on their own pages rather than only in the audit.

What is not recorded anywhere is when a translation was written. The front matter carries the run it came from and the hash of the English it was made from, and staleness is decided on the hash rather than on a date, so a date would be decoration.

Solutions to the exercises are machine written and machine judged and are not Bourbaki's. None are in the corpus yet, so every exercise page says there is no solution. When they land, the note above them does not go away.

What is wrong with it

The numbers that do not flatter it are generated with the rest of them.

Most of what does not resolve is a reference out of the chapter, to a Book this corpus does not hold yet, and that is the ingestion order rather than a fault. Every one of them is named in the reports, one file per question, and each report is regenerated and diffed on every change so that none of them can quietly go stale.

Licence

Éléments de mathématique is copyright N. Bourbaki and its publishers, Hermann, Masson, Springer and Springer Nature. Nothing here transfers or diminishes that. The transcriptions, the translations and the solutions are derived works made for personal study and they are not for commercial use. No source PDF is in either repository or served from this site. The tooling that builds all of it is separate and is under the MIT licence.