# Mathematicians prove two-dimensional billiards can perform universal computation

_Published Tuesday, September 22, 2026 at 2:09 PM EDT · Science · Latest · Tier 2 — Notable_

![Mathematicians prove two-dimensional billiards can perform universal computation — Primary](https://scx2.b-cdn.net/gfx/news/hires/2026/billiards.jpg)

Researchers Eva Miranda and Isaac Ramos proved that a two-dimensional billiard system can simulate a universal Turing machine, meaning one ball moving among fixed walls can reproduce any algorithmic computation. Their construction maps a program's memory and state onto regions of a table, with corridors and walls directing the ball through each computational step.

The result, published in the Proceedings of the National Academy of Sciences, also transfers a fundamental limit from computer science to physical motion: no algorithm can always determine whether such a trajectory will eventually reach a designated finishing region. The construction is theoretical rather than a practical computing device.

## Sources

- [Phys.org](https://phys.org/news/2026-09-billiard-balls-reveal-limits.html)

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Canonical: https://techandbusiness.org/newswire/LIuZwoJXUlooNlHM9-oSL5
Published: 2026-09-22T18:09:05.362Z
Story chronology: 2026-09-22T17:40:01.000Z
Retrieved: 2026-09-22T19:44:29.515Z
Publisher: Tech & Business (techandbusiness.org)