This project initiated by Terence Tao aims to find the relations between various statements in abstract algebra by using a combination of automated theorem proving and human effort. As mentioned by Terence himself, this is a bit similar to the idea of the Busy Beaver Challenge:
Commutative matrix multiplication algorithm by 
Ciro Santilli 37 Created 2025-05-21 Updated 2025-07-16
Ciro Santilli 37 Created 2025-05-21 Updated 2025-07-16A "commutative matrix multiplication algorithm" is a matrix multiplication algorithm that requires the ring to be commutative. Such algorithms are inferior because you cannot use them to create more efficient algorithms for general matrix matrix multiplication by decomposing the bigger matrix into smaller ones.
For example, the Strassen algorithm is based on reduction to non-commutative 2x2 matrix multiplication optimized to be done in 7 multiplications rather than 8 as in the native algorithm.
For 3x3 matrix multiplication, the best algorithms as of 2025 are:and beating the Strassen algorithm using 3x3 matrices would require a non-commutative algorithm with 21 multiplications.
- commutative: 21 multiplications
- non-commutative: 23 multiplications
Blog post: deepmind.google/discover/blog/alphaevolve-a-gemini-powered-coding-agent-for-designing-advanced-algorithms/
Whitepaper: storage.googleapis.com/deepmind-media/DeepMind.com/Blog/alphaevolve-a-gemini-powered-coding-agent-for-designing-advanced-algorithms/AlphaEvolve.pdf
Basically they require users to hand-code a metric and provide a program skeleton with some parts of the code marked to be replaced, and then the system focuses on modifying the code regions in question to optimize the metric.
All the novel results they announced were in constraint satisfaction problems or optimization problem. Their results are still awesome, but it's not very different from AlphaGo style things.
Multiplication of matrices of specific size by Ciro Santilli 37 Created 2025-05-21 Updated 2025-07-16
Ciro Santilli 37 Created 2025-05-21 Updated 2025-07-16DeepMind likes coming up with new improved algorithms for these more specific cases, e.g. it was announced in 2025 that AlphaEvolve found a novel 4x4 complex valued algorithm that uses 48 multiplications.
Bibliography:
- fmm.univ-lille.fr/ attempts to keep an up-to-date list for various sizes
Steve Jobs' Apple-1 sells for $945k
. Source. Semiconductor device fabrication bibliography by Ciro Santilli 37 Created 2025-05-21 Updated 2025-07-16
Ciro Santilli 37 Created 2025-05-21 Updated 2025-07-16
Saint Eligius by Petrus Christus
. Source. Eligius pool is named after Saint Eligius, patron of goldsmiths and miners[ref]Related: Antihydra in Magic: The Gathering.
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 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.
Figure 3. Visual Studio Code extension installation.
Figure 5. . 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. 
- 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