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I've taken all the cool stuff I've ever built and put it onto one page, here: davidryan59.github.io
I'll be adding to this over time, since I now have more free time 😀 in between helping people and companies solve their pain points using AI automation
Build!
After building the Leech explorer, I've been thinking about unimodular lattices
How the Leech lattice shell of 196560 vectors in 24D relates to the smallest 196883D representation of Monster group (spoiler: triality)
So I made a video. You might need to watch it more than once!
Then the triality: a symmetry that swaps ordinary and twisted states. It fuses 299 + 98,280 + 98,304 into one block, the Monster's smallest non-trivial representation, 196,883 = 47 × 59 × 71.
The 1 left over is fixed by every symmetry.
Turns out that to learn exciting exceptional mathematics, one must talk to the bot, and ask it to draw pretty pictures!
The future of education is bright. And I can easily learn cool new stuff. Nice!
Here's the vid again, if you deem it worthy to share:
xitter.cf/davidryan59/status/211…
Who doesn't love a good exceptional mathematical structure?
If you pack spheres as tightly as possible in 24 dimensions you get...
... yes! the Leech Lattice. Each sphere touches exactly 196,560 others. It's chiral, linked to much exceptional maths.
I built an explorer for it.
John Leech introduced this lattice in 1967, see his paper "Notes on sphere packings" here: doi.org/10.4153/CJM-1967-017…
To take the Leech lattice for a spin yourself, here's my interactive explorer at drbuild.uk/leech
If you feel inclined to share, here's the first tweet again 🙂
xitter.cf/davidryan59/status/211…
The Leech Lattice is connected to:
- Lattice theory, sphere packing
- many of the sporadic finite simple groups (symmetry theory)
- Error connecting codes
- Modular forms and number theory
- Vertex operator algebras, mathematical physics
Explore it here: drbuild.uk/leech
whoops! forgot to say Leech Lattice is linked to The Monster, an enormous sporadic group with 808017424794512875886459904961710757005754368000000000 elements!
Primes dividing it (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71) are supersingular
en.wikipedia.org/wiki/Monste…
David Ryan retweeted
interpretability might be the most important scientific problem in the world right now, as I don't think we can solve alignment if we don't know what we're building. I think I have good news about it. I co-authored early work in mechanistic interpretability at OpenAI and came away pessimistic, because neural networks appeared to fold into arbitrary tangled knots. years later, I started openai's first large-scale automated interpretability project, finding about 2% of neurons legible with the primitive tools we had
with modern agentic tools and a much closer look, the picture looks totally different. the vast majority in models up to trillions of parameters are legible, and their circuits beautiful. many famous examples of tangled neurons turned out to be misunderstood. The roadblocks I expected mostly aren't there. I now think ambitious interpretability will be solved by the time we need it most, and possibly quite soon, as automated scientists keep improving. it may be a bitter lesson for interpretability: the simple thing, at absurd scale, works
already-clean.goodfire.com/
Modulo Krinkle Tiling Explorer is now live! Miki Imura (@mk_tiling) found the Krinkle monotiles in 2025.
They can tile the plane non-periodically in a spiral, or periodically. The video below shows a wide variety of tile options and colours.
Explorer link in next tweet.
@KeishiroUeki looks like they made a physical Modulo Krinkle tiling on a tabletop! xitter.cf/KeishiroUeki/status/20…
平野たいるさん @tairu_mk のModulo Krinkle tilingを3Dプリントして遊んでいました。
楽しい
OK so Modulo Krinkle is exciting, fun, and beautiful art!
Look forward to see what people create with my new interactive explorer.
Link near the start of my tweet thread:
xitter.cf/davidryan59/status/210…
Modulo Krinkle Tiling Explorer is now live! Miki Imura (@mk_tiling) found the Krinkle monotiles in 2025.
They can tile the plane non-periodically in a spiral, or periodically. The video below shows a wide variety of tile options and colours.
Explorer link in next tweet.





