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The Stacks Project: A Wikipedia of algebraic geometry (2022) (columbia.edu)
103 points by gone35 41 days ago | hide | past | favorite | 21 comments


The Stacks Project, a new model for organizing and visualizing mathematics - https://news.ycombinator.com/item?id=30222302 - Feb 2022 (24 comments)

Stacks project hits 5000 pages - https://news.ycombinator.com/item?id=11054837 - Feb 2016 (1 comment)

The Stacks project is meant to be a comprehensive Bourbaki-style textbook, not an encyclopedic survey, so the Wikipedia comparison is a miss. (The WP has a textbook level of detail on some topics, with proofs and examples, but these are few and far between and come from enthusiastic editors going above and beyond the WP's declared goals.)

Stacks is not finished, however -- still a lot of "Proof. Omitted.". From what I understand, the goal is to fill them all in (otherwise there would be references to the literature in their stead), but ultimately it is still mostly a one-person project (see https://github.com/stacks/stacks-project/graphs/contributors ).

I once filled in one of those missing proofs, only to see Johan replace it by a much better one that I would never have thought of. And this was (for him) a technical lemma, not one of the crown jewels of the project. His dedication to the project is truly incomparable to anything except Bourbaki and Serre. And the usefulness of the work extends far beyond algebraic stacks, just like Bourbaki is much more than a textbook on Lie algebras.

Μy favorite example of mathematical typesetting on the web. I sent them some emails asking for directions to mimic their design for my personal webpage, but did not get any replies. My crude attempt at web mathematics in that style is here: https://ykonstant1.github.io/power-draft.html

But I would love if they made a tutorial or blog post describing in simple terms how to get a design like that going; many many professors could incorporate that and make mathematical resources much easier to access for students. I always have an online Class Diary for my classes, and my students would love to have rendered equations directly in the webpage.

Stacks project is available on github, so in theory (if you're bored enough) it should be possible to reverse engineer their design from their make-project file https://github.com/stacks/stacks-project/blob/master/documen...

At a high level they use plastex https://github.com/plastex/plastex to convert latex to html (you seem to be using pandoc?) and so can control the rendering to any fine accuracy they want. I liked this general style as well, so I tried using plastex but couldn't get my head around it and so started using LateXML https://github.com/brucemiller/LaTeXML

My usecase: I wanted to have a "dependency graph" of lemmas to make it easier to see proofs without having to jump back and forth through a pdf, and this was sort of similar to lean formalization blueprint graphs https://teorth.github.io/pfr/blueprint/dep_graph_document.ht... (which also uses plastex) but without the lean parts. There's still a lot of work to be done, but I think I have a pretty okay implementation using latexml which meets 50% of my requirements for now, so I'm happyish https://texviz.arsricharan.in/ghrss24/

If you are already using LaTeXML, it is also easy to get the ar5iv rendering (example article: https://ar5iv.labs.arxiv.org/html/1910.06709)

You can either copy the CSS asset from: https://github.com/dginev/ar5iv-css

and add "--css=ar5iv.css --nodefaultresources" to the command line options for latexmlpost (or latexmlc).

Or alternatively, for people not interested in learning how to install and configure latexml, they can try the self-contained Dockerfile at:


> And it’s de Jong’s exacting standards that also set the Stacks Project apart from other crowdsourced publications on the web. “Johan gets very mad when I call it Stackopedia,” said Kedlaya. “He reads every line that goes in.”

> The one-editor model allows the Stacks Project to maintain one voice and a high level of quality control. But unlike the peer-reviewed literature that it attempts to corral into one place, the Stacks Project is designed to evolve. Long after de Jong is gone, this accumulation of knowledge will continue to grow.

Is there any path to this scaling beyond one contributor? It sounds like after de Jong stops contributing it will just become frozen.

OEIS is perhaps the best model. I'm not sure if Neil Sloane looks at every sequence that goes in but he approved my entries. It's now in a trust and will definitely continue once he stops contributing.

Are there any specific lessons you think would apply to a collaborative encyclopedias of scientific topics? It seems to me that OEIS can only scale because it enjoys some of the same advantages as Wikipedia: the individual articles are highly compartmentalized (non-leaky abstractions), and there is very little need for adjudication of technical disputes. These would not apply to Stack Project or other comprehensive technical encyclopedias.

Does anyone know if there's something similar for plain old geometry? I need some proofs beyond basic ones (for ex, I need to know how to find out intersection points of 2 rotated ellipses on Cartesian space).

The title says “A wikipedia of algebraic geometry” but the site is organized more like a book not like Wikipedia. Do we know what publishing platform he is using?

“As we build theory we adhere to the following basic rules: […] (5) every statement explicitly states all of its assumptions…”

This is great, but is it possible?

Yes, through nomenclature. Algebraic geometry has a lot of terms. Almost anything having two properties gets a name.

I would like to see better quality of graph pictures.

What do you mean by better quality of graph pictures? If you're talking about 2D string diagrams/box and wiring diagrams/ or functorial box/tube diagrams a la Meilles or McCurdy, I agree! If there is something else you have in mind, I am curious!

Can you give me some examples of articles we could improve, and describe what you'd like to see?

For example, I want to see any text on the picture named "An alternative visualization of how the Cohen structure theorem and related concepts intersect. " Seems it has to be a way to see high-res but a click doesn't work.

Those PNG thumbnails don't have any higher resolution, they're literally there as examples of what users of The Stacks Project produce as visualisations using the lemma tags:


So to create your own visual you'd pull the metadata and create a graph on concepts that link to (say) https://stacks.math.columbia.edu/tag/032A

Better quality than this?! Can you link to a picture you think is lacking?


I do not see a way to observe higher resolution picture of this

Oh those images aren't from the project itself. The news article just uses some pictures from some of the blog posts that are at a meta level about the project. From a reverse image search that specific image can be found on this post:


Specifically this image I believe:


The other images seem to be from the project author's home page:


Why don't you make some?

i wonder if you can train an ai on this?

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