# Built with AI this week: a machine-checked maths proof, a tutor that makes you type, and more

> Our weekly roundup of genuinely impressive things people made with AI, all credited and linked. This week, an algorithm with a formal proof no human ever read, and a backlash against letting AI do your thinking.

- Published: 2026-06-11
- Topic: [AI](https://futuretechnologyhq.com/topic/ai/)
- URL: https://futuretechnologyhq.com/built-with-ai-showcase-june-11/
- Publisher: [Future Technology](https://futuretechnologyhq.com/), free to read. Quote as "Future Technology" with a link to the article.

## Key points

- An AI wrote a geometry algorithm plus a formal proof in one shot, and a proof checker verified it with no human reading the code
- The most upvoted AI project this week is one that refuses to do the work for you
- Every project here is open source, credited, and free to try today

## Article

Every Thursday we round up the most impressive things people actually built with AI that week. No vapourware, no demos that never ship. Everything below is live, [open source](/meta-llama4-billion-downloads-open-source/), and credited to its maker.

## An algorithm nobody read, proven correct anyway

The standout this week comes from GitHub user [schildep](https://github.com/schildep/verified-polygon-intersection), who published what they believe is the first formally verified polygon intersection algorithm. The kind of geometry that powers vector editors and mapping software, and that is notoriously full of nasty edge cases.

Here is the remarkable bit. The implementation and its mathematical proof were written autonomously by [Claude Opus 4.8](/ai-model-leaderboard-june-2026/), in one shot, and no human has ever reviewed that code. They did not need to. The proof is checked by Lean 4, a proof assistant that verifies every logical step by machine. A human only reads 87 lines of specification. The author had been stuck on the project since January because earlier models needed the proof spelled out step by step. The latest one just did it.

Why it matters: this flips the trust problem with AI code. You do not trust the model. You trust the checker. [The Hacker News thread](https://news.ycombinator.com/item?id=48405264) is full of people realising the same thing.

## Lathe makes the AI teach, not do

The week's most upvoted AI project on Hacker News pushes in the opposite direction. [Lathe](https://github.com/devenjarvis/lathe), by Deven Jarvis, uses your coding agent to generate a proper hands-on tutorial on any technical topic, with sources. Then you work through it yourself, typing the code by hand in a purpose-built local app.

Prompt something like "build a 3D slicer in Erlang" and it produces a multi-part course instead of finished code. It works with [Claude Code](/alibaba-bans-employees-claude-code/), Cursor, Codex and most other agents. A clever answer to the worry that AI is making developers forget how to think.

## A self-hosted library of 30 mentors

[Agora Cosmica](https://github.com/chipmates/agoracosmica) began three years ago when its founder asked a chatbot to interpret a dream as Carl Jung. The conversations felt too personal for big AI providers, so he built his own. It is now a German nonprofit and the code is open source under AGPL. Thirty historical figures, each with narrated stories and Q&A, all runnable on your own hardware.

## One for the dashboard tinkerers

Small but handy: [claude-quota](https://github.com/grzegorz-raczek-unit8/claude-quota) by Grzegorz Raczek puts live gauges for your Claude Code usage limits in the macOS menu bar. If you have ever hit a rate limit mid-task, you will get it immediately.

That is the week. Four projects, four makers, all linked above. If you build something with AI that deserves a spot here, the contact page is open.

## Key takeaways

- The first formally verified polygon intersection algorithm was published on GitHub, written autonomously by an AI model.
- The algorithm's mathematical proof was checked by a machine, with a human only reviewing 87 lines of specification.
- The proof assistant Lean 4 verifies every logical step, eliminating the need for human review of the code.
- A new AI project, Lathe, generates hands-on tutorials on technical topics, allowing users to work through the code themselves.
- Agora Cosmica is a self-hosted library of 30 historical figures, each with narrated stories and Q&A, that can be run on users' own hardware.
- A new tool, claude-quota, provides live gauges for Claude Code usage limits in the macOS menu bar.

## Sources

- [Verified polygon intersection on GitHub](https://github.com/schildep/verified-polygon-intersection)
- [Hacker News discussion](https://news.ycombinator.com/item?id=48405264)
- [Lathe on GitHub](https://github.com/devenjarvis/lathe)
- [Agora Cosmica on GitHub](https://github.com/chipmates/agoracosmica)
- [Claude quota gauges on GitHub](https://github.com/grzegorz-raczek-unit8/claude-quota)