algebra20 is a group of people drawn to algebraic structures. Its members work on classical algebra — lattice theory, order theory, universal algebra — and on the modern directions that grow naturally out of that tradition: Formal Concept Analysis and other applied algebraic methods, and the role of algebraic structure inside machine learning. We do not treat these as three separate fields. They are, in our view, three angles on the same intellectual landscape.
Three audiences
The site is written with three readers in mind. A pure mathematician should find rigor, named theorems, and careful notation. An applied mathematician should find worked examples, real contexts, and tools that can be picked up and used. A researcher at the seam of mathematics and machine learning should find both vocabularies used fluently, side by side. Where a piece of writing speaks primarily to one of these readers, we say so plainly with a small tag near the title. The site as a whole tries to make it easy for any of the three to find their entry point.
Where the name comes from
Some years ago, a mathematics professor told his students that algebra had to move into the twenty-first century, and that classical algebra was no longer needed. A few of those students disagreed. They kept disagreeing in print, in code, and in their own research careers. The name algebra20 carries that quiet disagreement. The "20" points to twentieth-century algebra — the classical tradition that was being dismissed — while the group's work continues that tradition into the present, through applied mathematics and through the foundations of AI. The name is a small argument: classical algebra did not need replacing. It needed continuing.
What binds the group
A shared conviction that the structural content of classical algebra is still doing real work — in proofs, in data analysis, and in the foundations of modern learning systems — and a shared interest in writing about it for an audience that spans those three views.
Contact
If you work with or on algebraic structures — in pure form, in
applied form, or inside AI — and would like to post something
here, write to us at
contact@algebra20.de.
Individual members are reachable through their own academic pages.