Finite Group Databasebeta

About

"...intention was to produce a few pages which would coincide—word for word and line for line—with those of Miguel de Cervantes."

— Pierre Menard, author of the Quixote

Origin, or "Why do you create this useless exotic website?"

I've been intrigued by the structures and relationships of finite groups for decades. The amount of learning and dedication required to create a website like this, for both the mathematical theory and the computational algorithms, has been just beyond my reach... until AI coding arrived. The real work for this database started as an experiment of "can I find something an AI coding agent cannot do?". The experiment was a failure, to some extent. Once it started, I was hooked by the mesmerizing complexities where strange algorithms meet theoretical math that is completely new: Who would think of an algorithm that has O(e√n) time complexity? How often does one find a problem that has an O(n5) best solution? They are all so fascinating that I had to create them. This turned out to be a true testament to the tech superpower of AI coding agents. The experience itself was more than worth the effort. And I hope the outcome (this website) is of some marginal value to you.

Open Source?

One consequence of the prevalence of AI coding is, to put it bluntly: "no more open source". And I mean two different things by this.

First, in most cases, with AI coding one can create a project from verbal descriptions. You generally don't need the source code of the original project to start a "fork" of it. The advantage of lower cost or faster innovation for open source is under pressure here. Or conversely, with AI coding, everything is as good as open source. And this is great for everyone.

Second point though, is negative. An AI coding agent generates code with great speed and complexity. Despite plenty of comments, it is still daunting to understand what's going on. In this sense source code moves somewhere between old hand crafted code and binary machine code. So sharing the source code is not the same as sharing the design/architecture or thinking behind the source code. Sharing the prompt or chat history won't solve the lack of clarity either. So the problem is: How do you really share your design and thinking behind all the AI generated code? Well, use AI for that. And it works. AI, as a large language model, is very good at summarizing and distilling algorithms and design into write-ups. Once I realized this, the path to "true open source" is clear: there should be in-depth essays to explain difficult or interesting parts of the code (and there are a lot of them). This directive becomes the next steps of the website's evolution.

Acknowledgements