Eva Miranda
@evamirandag.bsky.social
Mathematician, Full Professor at UPC Icrea Academia @icreacommunity @CRMatematica @AvHStiftung @UniCologne living on a "mote of dust suspended in a sunbeam".
Proud about this!
Proceedings of the National Academy of Sciences@pnas.org · 4w agoOne of the most-viewed PNAS articles in the last week is “Two-dimensional billiards are Turing complete.” Explore the article here: https://ow.ly/zs8G50ZPTvY For more trending articles, visit https://ow.ly/YEYv50ZPTvZ.
A two-dimensional billiard table can simulate a universal Turing machine with one ball and fixed walls. Some long-term trajectory questions therefore cannot always be predicted by an algorithm. doi.org/hckdp6
What billiard balls reveal about computers and the limits of prediction
When is a billiard ball not a billiard ball? When mathematicians get involved and view a popular game as a model computer.
phys.org
One of the most-viewed PNAS articles in the last week is “Two-dimensional billiards are Turing complete.” Explore the article here: https://ow.ly/zs8G50ZPTvY For more trending articles, visit https://ow.ly/YEYv50ZPTvZ.
A group of 25 Fields Medalists, including myself, have made a joint declaration on Math and AI: mathandai.org . We welcome additional signatories. See also this article in the Economist announcing the declaration: www.economist.com/science-and-...
Declaration — Math and AI
Read the declaration and add your name.
mathandai.org
2D billiards are Turing complete! "We show that, even in 2D, billiard trajectories can simulate arbitrary Turing machines...Our results place undecidability, alongside chaos, as a fundamental obstruction to long-term prediction even in low-dimensional classical dynamics" www.pnas.org/doi/abs/10.1...
Two-dimensional billiards are Turing complete | PNAS
We show that two-dimensional billiard systems can simulate universal Turing machines. Billiards serve as idealized models of particle motion with e...
pnas.org
Before OpenAI announces the resolution of the next Millennium Prize Problem, allow me a little mathematical flex 😎. We proved that a single ball in a 2D billiard can simulate a universal Turing machine, solving a problem posed by Cris Moore.🎱🤖 Read it here @pnas.org: www.pnas.org/doi/10.1073/...
Two-dimensional billiards are Turing complete | PNAS
We show that two-dimensional billiard systems can simulate universal Turing machines. Billiards serve as idealized models of particle motion with e...
pnas.org
The day is not over yet...here it comes an announcement of OpenAI for Navier-Stokes... cdn.openai.com/pdf/32d9f210... It's been a long day...
cdn.openai.com
Before this becomes a story about which lab won: the ideas are Diego Córdoba's and Luis Martínez-Zoroa's. Buckmaster says so himself, and adds that he thinks Martínez-Zoroa deserves a Fields Medal. In the age of LLMs, who gets the credit, and who decides? cims.nyu.edu/~tristanb/st...
cims.nyu.edu
I wansn't paying attention and forgot to congratulate @evamirandag.bsky.social for this well deserved recognition!
RACiencias@raciencias.bsky.social · 5mo agoDamos la bienvenida a dos nuevos miembros ⚡️Eva Miranda, matemática de @la_UPC y experta en geometría y topología @evamirandag.bsky.social 🧬 Federico Morán, catedrático de Biología Molecular de la @ucm.es, dirige desde 2019 la Fundación para el Conocimiento Madri+d
Los fluidos como el agua, el aire o la lava de un volcán esconden trayectorias imprevisibles, según un estudio de la UPC www.upc.edu/es/sala-de-p...
Los fluidos como el agua, el aire o la lava de un volcán esconden trayectorias imprevisibles, según un estudio de la UPC - UPC Universitat Politècnica de Catalunya
upc.edu
Damos la bienvenida a dos nuevos miembros ⚡️Eva Miranda, matemática de @la_UPC y experta en geometría y topología @evamirandag.bsky.social 🧬 Federico Morán, catedrático de Biología Molecular de la @ucm.es, dirige desde 2019 la Fundación para el Conocimiento Madri+d
Turing complete Navier–Stokes steady states via cosymplectic geometry academic.oup.com/pnasnexus/ar...
Turing complete Navier–Stokes steady states via cosymplectic geometry
Abstract. In this article, we construct stationary solutions to the Navier–Stokes equations on certain Riemannian 3-manifolds that exhibit Turing completen
academic.oup.com
Tomorrow I'll give a colloquium for Prof. @evamirandag.bsky.social 's group at the Maths Dept at UPC, Barcelona I'll talk about the scope of forms of universality and unreachability in logic, spin models, Boltzmann machines, and philosophy. Everybody is welcome! imtech.upc.edu/2026/01/26/g...
Gemma de les Coves – IMTech
imtech.upc.edu
This Thursday I'll be at @museuciencies.cat discussing chaos theory, time and its implications with @evamirandag.bsky.social and @ricardsole.bsky.social. Looking forward to it! museuciencies.cat/activitats/2...
Teoria del caos: el món és predictible? | Museu de Ciències Naturals de Barcelona
museuciencies.cat
Podem predir el futur mitjançant les matemàtiques? Què ens diu la teoria del caos? Quins són els límits de la nostra capacitat de predir la complexitat? Parlarem amb Doyne Farmer, un dels pares de la teoria, i amb la matemàtica Eva Miranda @evamirandag.bsky.social museuciencies.cat/activitats/2...
My 25th (!) newsletter post shares my main takeaway from the #RockyWorlds4 conference: Hot rocks are what's cool in rocky exoplanet research right now. Lava planets, especially look like they're about to teach us a *ton* about how rocky planets work. So come on in, the lava's fine! 🧪🔭
Hot rocks are what's cool in rocky exoplanet research
Habitable zone? Pfft. For exciting planetary science discoveries, keep your eye on lava worlds and hot rocks.
reviewertoo.com
🎱 A ball. 🎱 A table. 🎱 A computation. With Isaac Ramos, we show that a sufficiently weird billiard table is Turing complete. 🕳️ The 8-ball hits the halting wall. Game over. Selected as one of the Papers of the Month by @elisecutts.bsky.social in Reviewer Too www.reviewertoo.com/paper-roundu...
Paper Roundup December 2025: computing billiards, an impossible atmosphere, and Roman constructions
Papers on big questions at the frontiers of science, curated by hand each month
reviewertoo.com
This month's paper roundup is live! This time around we've got 2D billiards that can compute, an atmosphere that shouldn't exist, a Roman construction site, and more. Check it out here: www.reviewertoo.com/paper-roundu... 🧪
Paper Roundup December 2025: computing billiards, an impossible atmosphere, and Roman constructions
Papers on big questions at the frontiers of science, curated by hand each month
reviewertoo.com
Fascinated once again to see @walkingthedot.bsky.social work his magic, explaining this story with the perfect touch. Happy to have contributed a small grain to it. Congratulations on this piece! It beautifully captures the emotion of the moment and the roller-coaster nature of research 🎢
Quanta Magazine@quantamagazine.org · 9mo agoUnderstanding the equations that describe a river current or a breeze is one of the greatest mathematical challenges. Researchers are tackling it with a new computational approach. @walkingthedot.bsky.social reports: www.quantamagazine.org/using-ai-mat...
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 A. Gonzalez, D. Peralta #wisemen @crmatematica.bsky.social @upc.edu
Eva Miranda@evamirandag.bsky.social · 10mo agoClassical billiards can compute. With Isaac Ramos, 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. 🎱🧠 @upc.edu @ricardsole.bsky.social
2025, you were: The Sant Cugat Prize, a feeling of recognition and belonging Gauss in May A Chinese Dragon in July re-energising, unstoppable. Zurich in winter A private concert at the Petite Malmaison Bach Oratorium at the Fraumünster and vermicelli closing the circle Thank you!
This is exciting for a lot of reasons. But I am smug every time I see this stuff because it further reinforces my theory that computation or something directly related to it is in some sense universal, and perhaps even fundamental, to our universe.
Eva Miranda@evamirandag.bsky.social · 10mo agoClassical billiards can compute. With Isaac Ramos, 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. 🎱🧠 @upc.edu @ricardsole.bsky.social
If there's an aesthetics of the intersection of CS and physics --and I think field-specific aesthetics is an insufficiently explored area in mathematics, programming, and data modeling-- this paper is surely in the purest Classical tradition.
Eva Miranda@evamirandag.bsky.social · 10mo agoClassical billiards can compute. With Isaac Ramos, 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. 🎱🧠 @upc.edu @ricardsole.bsky.social
It reaffirms my belief that anything sufficiently complex can serve as a universal computer and thus obeys the theorems regarding those. All is well.
After the Magic game, classical billiards as a Universal Turing Machine :)
John C. Baez@johncarlosbaez.bsky.social · 10mo agoNew result: you can build a universal computer using a single billiard ball on a carefully crafted table! More precisely: you can create a computer that can run any program, using just a single point moving frictionlessly in a region of the plane and bouncing off the walls elastically. (1/n)
