Welcome to the notebook

This is the algebra20 notebook. It is a place where members of the group write — informally and irregularly — about ideas in progress, conference notes, expository pieces, and the small observations that don’t yet belong in a paper but are worth recording out loud. It is not a personal blog. Over time, more voices than mine will appear here.

A short note on what algebra20 is, since this is the first piece on the new site. The group began as a quiet disagreement. Some years ago, a teacher of ours announced that classical algebra had run its course; that algebra, to remain serious, had to become something else. A handful of his students did not agree, and have spent the years since making the opposite case in their work. The name is shorthand for that case. The “20” points at twentieth-century algebra — the classical tradition that was supposedly behind us — and the work of the group is to carry that tradition into the present, by way of applied mathematics and by way of AI.

The notebook is written with three audiences in mind. The first is pure mathematicians: people who care about lattices, orders, and universal structure for their own sake, and who want the precision that comes with that. The second is applied mathematicians: people working with Formal Concept Analysis, with knowledge representation, with the algebraic side of data. The third is researchers at the seam of mathematics and machine learning: people who want algebraic vocabulary used fluently next to the vocabulary of learning, interpretability, and inference. Every notebook post carries a small tag near its title naming its primary audience. The tag is a courtesy, not a wall — much of what shows up here will speak to more than one of the three at once.

You can subscribe via RSS, or browse the notebook by audience or by author. Welcome.