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 40 Created 2025-05-21 Updated 2025-07-16
Ciro Santilli 40 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.
That's not my lightsaber Star Wars meme
. Source. Multiplication of matrices of specific size by Ciro Santilli 40 Created 2025-05-21 Updated 2025-07-16
Ciro Santilli 40 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 40 Created 2025-05-21 Updated 2025-07-16
Ciro Santilli 40 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.
Updates Translation of Xi Jinping saying those against raise their hands by Ciro Santilli 40 Created 2025-05-21 Updated 2025-07-16
Ciro Santilli 40 Created 2025-05-21 Updated 2025-07-16I can't believe I had missed that meme until now, and I couldn't resist the temptation to translate it
Xi Jinping saying those against raise their hands (2017)
Source. Xi Jinping saying those against raise their hands (2022)
Source. Those against raise their hands Xi Jinping remix by Ciro Santilli
. Source. I also couldn't resist a Kdenlive exercise in voice sampling. It was remarkably easy to do, not bad. There are unlisted articles, also show them or only show them.