Isaac retweeted
Mathematical Conversations
How Water and Billiards Compute, and Whether Planets Can ias.edu/math/events/mathemat…
Isaac retweeted
Single ball on 2D billiard table acts as universal Turing machine inkorr.com/en/odna-kula-na-d…
Isaac retweeted
Our paper with @Isaacramr__ is one of the most read article at @PNASNews 🎱
One of the most-viewed PNAS articles in the last week is “Two-dimensional billiards are Turing complete.” Explore the article here: ow.ly/ul1C50ZPTvW
For more trending articles, visit ow.ly/7lpu50ZPTvX.
ALT Billiard dynamics implementing the read–write operation. The blue and red rays correspond to reading a 0 or a 1, respectively.
Isaac retweeted
One of the most-viewed PNAS articles in the last week is “Two-dimensional billiards are Turing complete.” Explore the article here: ow.ly/ul1C50ZPTvW
For more trending articles, visit ow.ly/7lpu50ZPTvX.
ALT Billiard dynamics implementing the read–write operation. The blue and red rays correspond to reading a 0 or a 1, respectively.
Isaac retweeted
A single ball on a fixed table can compute: Eva Miranda and Isaac Ramos prove that two-dimensional billiards are Turing complete crm.cat/a-single-ball-on-a-f…
Isaac retweeted
Happy, those able to know the causes of things.Really insightful post by Nestor on how to frame the current progress in mathematics by LLMs and by AI companies.
birdsnfrogs.github.io/2026/0…
Isaac retweeted
@Isaacramr__ took this picture in Los Angeles in January 2024, when we were thinking about Navier–Stokes. Now that everyone else is thinking NS, we have proved that even a 2D-billiard can simulate a universal computer 🎱💻 What a joy to see our paper in the legendary PNAS! 🔥
With all the Navier–Stokes excitement, I almost forgot to say that our tiny billiard ball has made it to @PNASNews — and yes, it can run a universal computer! 🎱💻
Undecidability already lives in dimension two. Today with @Isaacramr__ at PNAS.
pnas.org/doi/10.1073/pnas.26…
Excited to share this amazing news. Our billiard paper with @evamirandag is finally published in @PNASNews!! 🎱🎱
With all the Navier–Stokes excitement, I almost forgot to say that our tiny billiard ball has made it to @PNASNews — and yes, it can run a universal computer! 🎱💻
Undecidability already lives in dimension two. Today with @Isaacramr__ at PNAS.
pnas.org/doi/10.1073/pnas.26…
Isaac retweeted
With all the Navier–Stokes excitement, I almost forgot to say that our tiny billiard ball has made it to @PNASNews — and yes, it can run a universal computer! 🎱💻
Undecidability already lives in dimension two. Today with @Isaacramr__ at PNAS.
pnas.org/doi/10.1073/pnas.26…
Congratulations Eva!! So happy to share these amazing moments with you ✨🎱🦆
This award belongs in so many ways to my wonderful collaborators and students. I am deeply grateful to all of them. And heartfelt thanks to the Dean of @FME_UPC for travelling all the way to Vienna to share this unforgettable moment with me.
Isaac retweeted
This award belongs in so many ways to my wonderful collaborators and students. I am deeply grateful to all of them. And heartfelt thanks to the Dean of @FME_UPC for travelling all the way to Vienna to share this unforgettable moment with me.
Isaac retweeted
El 20 feb 2026: "From Geometric Ideas to Computational Frontiers", workshop conjunto AQUACELL– Wolfram Institute sobre geometría, computación y fenómenos complejos, en @MatematicasUCM. Cierre con coloquio online de Stephen Wolfram (18:00). sites.google.com/upc.edu/sym…
Isaac retweeted
🔹 From Geometric Ideas to Computational Frontiers
📍 Feb 20, Facultad Mat, UCM
A joint venture with @WolframResearch launching a formal collaboration at the interface of geometry, dynamics & computation
👉 Info: sites.google.com/upc.edu/sym… @LegnaMath @FundacionBBVA @AgEInves
Isaac retweeted
Not chasing flashy Millennium Prize claims—this is the quieter work of 'mathematical monks' building verified foundations.
Working towards a fully machine-checked Lean formalization of @evamirandag and team's results on computational universality in dynamical systems: billiards, Euler flows, and Navier-Stokes as universal computers.
Zero sorries in the mechanized core. 🙏
github.com/Abraxas1010/miran…
cc @Isaacramr__ @LegnaMath @_ICMAT
Isaac retweeted
🎱 A ball.
🎱 A table.
🎱 A computation.
A sufficiently weird billiard table is Turing complete.
🕳️ The 8-ball hits the halting wall. Game over.
Our article with @Isaacramr__ is highlighted as Paper of the Month by @elisecutts here
reviewertoo.com/paper-roundu… @la_UPC @CRMatematica
Isaac retweeted
What’s next? Billiards are toy models for near-collision dynamics in the 3-body problem. If billiards can compute, undecidability should be hiding in celestial mechanics. In 2026 we plan to address this for the 3-body problem with @LegnaMath, D. Peralta #wisemen @stephen_wolfram
Our article with Isaac Ramos @Isaacramr__ is now live on arxiv arxiv.org/abs/2512.19156
Isaac retweeted
What’s next? Billiards are toy models for near-collision dynamics in the 3-body problem. If billiards can compute, undecidability should be hiding in celestial mechanics. In 2026, we will address this for the 3-body problem with @LegnaMath and Daniel Peralta. 🚀 #reyesmagos
Classical billiards can compute.
With @Isaacramr__ , we show that 2D billiard systems are Turing complete, implying the existence of undecidable trajectories in physically natural models from hard-sphere gases to celestial mechanics.
Determinism ≠ predictability. 🎱🧠@ETH_en
Isaac retweeted
This Christmas 🎄 the balls left the tree, bounced across a billiard table 🎱, and—inevitably—started computing.
With @Isaacramr__ Isaac Ramos, we show that billiard dynamics is undecidable: arxiv.org/abs/2512.19156
In the computational universe of Cris Moore and @stephen_wolfram
Classical billiards can compute.
With @evamirandag, we show that 2D billiards are Turing complete: even simple systems can have undecidable trajectories.
Determinism ≠ predictability.
So if you lose at pool, you can blame computability theory 🎱🤯
arxiv.org/abs/2512.19156