stacks-project VS lila

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.

Personally, I love the Stacks Project webpage (https://stacks.math.columbia.edu/); they way it is laid out, the font, the seamless integration of LaTeX in the test (https://stacks.math.columbia.edu/tag/0A2U) has made me rethink mathematical text for the web.

For algebraic geometry, there is the Stacks project online, which builds up all mathematics needed to understand algebraic stacks, from foundations. This time, foundations truly mean its basic axioms. Everything is proven except maybe with a few exceptions in the introduction, and everything has links. As such, it is a monstrously large project (the pdf-version is around 7500 pages iirc). This one is I think among my suggestions closest to what you had in mind. The only thing is that it again only focuses on one area of math.

Some famous collaborative books: * https://github.com/HoTT/book * https://github.com/OpenLogicProject/OpenLogic * https://github.com/stacks/stacks-project * http://math.uchicago.edu/~amathew/cr.html

There is not really one good reference for algebraic geometry (even the EGA, SGA, FGA series, and that's assuming you can even plough through them all), but the Stacks Project (https://stacks.math.columbia.edu/) is at least very good for CAG.

The Stacks Project is a massive project covering algebraic geometry. The nLab is a wiki that covers a staggering amount of material from its own, rather specific, point of view.

Well, I talked to a friend who knows a lot of AG. He recommended "learning some things in topology like model categories" and discouraged learning about infinity categories without other stuff. Also, if you're interested in stacks, try the Stacks Project?

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> the player who committed more blunders lost 86% of the time

In some sense this is almost tautological. While finding an exact definition for a chess blunder isn't straightforward, here is one example from the Lichess UI:

https://github.com/lichess-org/lila/blob/b527746b179cdde6438...

Basically, if you make a move which decreases your winning probability more than 14% over the best move, that's a blunder. But winning probability is a nonlinear function of stockfish centipawns. A drop in 100 centipawns when you're up 15 points isn't a blunder. When the game was equal, it is.

Point is, by the time you know it's a blunder you already know something about the outcome of that move, that it swung the winning probability by more than 14%. So the analysis is kind of just measuring some function of winning probability and saying that it is highly correlated with winning probability.

If you want to improve make it your goal to play the best chess you can, not increase an arbitrary number. Watch YouTube series like John Bartholomew's "Climb the Rating Ladder" for some general insight into what you might be doing wrong. Read Irving Chernev's "Logical Chess: Move By Move" to see the thinking process of high level players. Do lots of puzzles (I like lichess.org for puzzles). And always analyze your games. When you analyze make it your goal to find at least two things you could have improved.

The easiest way to play against Stockfish is perhaps on https://lichess.org/, but it's not the only chess engine that evaluates positions with a neural network.

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