Antihydra in Magic: The Gathering by Ciro Santilli 37 Created 2025-05-21 Updated 2025-07-16
It is known that Magic: The Gathering is Turing complete, but it is cool to have a concrete specific example of an open problem in mathematics coded in it.
Figure 1.
Screenshot of the Antihydra in Magic: The Gathering construction
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List of LLM benchmarks by Ciro Santilli 37 Created 2025-05-21 Updated 2025-07-16
2x2 matrix multiplication by Ciro Santilli 37 Created 2025-05-21 Updated 2025-07-16
Commutative matrix multiplication algorithm by Ciro Santilli 37 Created 2025-05-21 Updated 2025-07-16
A "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.
Borg (cluster manager) by Ciro Santilli 37 Created 2025-05-21 Updated 2025-07-16
Strassen algorithm by Ciro Santilli 37 Created 2025-05-21 Updated 2025-07-16
Polanyi's paradox by Ciro Santilli 37 Created 2025-05-21 Updated 2025-07-16
AlphaEvolve by Ciro Santilli 37 Created 2025-05-21 Updated 2025-07-16
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.
Star Wars meme by Ciro Santilli 37 Created 2025-05-21 Updated 2025-07-16
Figure 1.
That's not my lightsaber Star Wars meme
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Multiplication of matrices of specific size by Ciro Santilli 37 Created 2025-05-21 Updated 2025-07-16
DeepMind 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:
Apple II by Ciro Santilli 37 Created 2025-05-21 Updated 2025-07-16
Apple I by Ciro Santilli 37 Created 2025-05-21 Updated 2025-07-16
Video 1.
Steve Jobs' Apple-1 sells for $945k
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Saint Eligius by Ciro Santilli 37 Created 2025-05-21 Updated 2025-07-16
Figure 1.
Saint Eligius by Petrus Christus
. Source. Eligius pool is named after Saint Eligius, patron of goldsmiths and miners[ref]
Magic: The Gathering is Turing complete by Ciro Santilli 37 Created 2025-05-21 Updated 2025-07-16
Video 1.
I Built a COMPUTER in Magic: The Gathering by Because Science (2019)
Source. Shows an explicit Turing complete Magic The Gathering setup with real cards in a standard "extremely lucky" 2 player game.

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