Here is a specific minimal example of how to use mathlib4: proofassistants.stackexchange.com/questions/2526/how-to-run-lean4-with-mathlib-manually/5299#5299
There are to ways in which the Collatz conjecture can fail:These are the only two options because if any sequence has an upper bound, it must sooner or later repeat an element, leading to a cycle.
- Collatz cycle: there is a cycle that loops forever and never reaches 1
- Unbounded Collatz trajectory: there is a sequence that grows without bound without looping
This section is about benchmarks designed to test mathematical reasoning.
This one focuses on improving speed of important numerical algorithms as compared to popular implementations.
The general pattern can be seen by observing the optimization of: algotune.io/aes_gcm_encryption_anthropic_claude-opus-4-1-20250805.html This shows the chat that the system had.
They define an OS interface to edit files and run right on the prompt, and tell at each stage how many credits are left for a given API and what the speedup was. Amazing. Each task has a $1 budget per provider. Then their software parses commands out of the LLM output and sends formatted responses back. Quite amazing that it works at all.
All pieces of code seem to be in Python, and the speedups come mainly from using more advanced external computing libraries, like compiling with Cython or using faster external libraries that are pre-compiled, or more parallel. So it is not that impressive from a purely algorithmic point of view, but it is not bad either.
Correctness is checked automatically by comparing the optimized solution to the original non-optimized one likely for certain inputs.
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 3. Visual Studio Code extension installation.
Figure 4. Visual Studio Code extension tree navigation.
Figure 5. Web editor. You can also edit articles on the Web editor without installing anything locally.Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact