How an Outsider Optimized Sphere-Packing
The Quanta Podcast
Quanta Magazine
4.7 • 638 Ratings
🗓️ 19 August 2025
⏱️ 29 minutes
🧾️ Download transcript
Summary
How many oranges can you fit in a box? Mathematicians are obsessed with perfecting their answer to this question in not just our familiar three-dimensional world, but in higher and higher dimensions beyond it. For several decades, they've made only minimal progress toward finding an optimal solution. Then, this past April, an outsider to the field named Boaz Klartag posted a proof that bested these previous records by a significant margin.
In this episode of The Quanta Podcast, host Samir Patel and Quanta math staff writer Joseph Howlett discuss how Klartag resuscitated an old technique that experts had abandoned decades earlier to optimize sphere packing in any arbitrarily high dimension. This topic was covered in a recent story for Quanta Magazine.
Each week on The Quanta Podcast, Quanta Magazine editor in chief Samir Patel speaks with the people behind the award-winning publication to navigate through some of the most important and mind-expanding questions in science and math.
Audio coda created by Daniel Simion
Transcript
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| 0:00.0 | Picture a tower of oranges at your local supermarket. |
| 0:08.0 | Orderly, efficient, stable, at least until you pull one out from the bottom. |
| 0:13.0 | Mathematicians appreciate it too. |
| 0:15.0 | It was in the early 17th century that Johannes Kepler figured that this was the most efficient |
| 0:20.7 | way to pack spheres. |
| 0:22.3 | That's what this question is called sphere packing into a given space. |
| 0:26.6 | It turns out he was right. The oranges take up about 74% of the space, and they can't be |
| 0:32.6 | squeezed together any more than that without making juice. But it wasn't that long ago, nearly 400 years later, that it was finally definitively proven. |
| 0:42.8 | That doesn't mean the sphere packing problem is solved. |
| 0:45.5 | In fact, it seems to be one of mathematicians' favorite puzzles, because they get to try to figure it out in higher and higher dimensions. |
| 0:58.1 | Thank you. it out in higher and higher dimensions. Welcome to the Quanta podcast where we explore the frontiers of fundamental science and math. |
| 1:02.9 | I'm Samir Patel, editor-in-chief of Quanta magazine. |
| 1:06.4 | It seems like the world does sphere packing was a little sleepy until the last couple of decades, |
| 1:12.2 | and just in the last year, Quanta has reported on advances in it a couple of times. |
| 1:17.5 | It's exciting, in a mathy way, for how it brings together different parts and techniques from the |
| 1:23.3 | spheres, sorry for that, of the math world. |
| 1:26.8 | Our math writer Joe How, recently covered one of |
| 1:29.4 | these advances in a story called New Sphere Packing Record stems from an unexpected source, |
| 1:34.9 | and he's here to talk with us about it today. Welcome back to the show, Joe. |
| 1:38.9 | Thanks, Samir. Excited to talk about spheres. So what's the big idea of the story? |
| 1:44.4 | Yeah, so mathematicians are obsessed with how many balls can you get in a box. |
| 1:50.7 | And like you said, have been for many hundreds of years. |
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