Pinned Tweet
Finally finished my raspberry pi stand: water cooled 'treehouse' in solid walnut with leather trim
sam-burns.com/posts/water-co…
sam-burns.com/posts/water-co…
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It finally happened!! 🥳
A proof candidate for 17 squares: the 1998 packing cannot be beaten. s(17) = 4.67553009…
Built with @OpenAI Codex and @AnthropicAI Claude. Thanks to @ojoshe, @_Mira___Mira_, @guzhou0806 and @ManassehA06, whose work this builds on.
Try to break it: github.com/Kleddamag/the-…
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Sam B retweeted
Another major square packing result!
Alongside 11 squares, announced last week by @ManassehA06, 17 has been the most iconic open square packing problem.
It is now being reviewed. This is a very intense proof compared to n=11, because of so many “orbits,” or possible configurations that must be systematically addressed.
It has been amazing to see the explosion of results, now leading to this latest from @kleddamag which may be the most impressive achievement yet.
Much rapid progress now comes from collaboration using what amounts to a shared library of proof machinery. It is a lot like open-source software but with tools for proof.
This new @kleddamag proof builds on the results of @ManassehA06 who built on @kleddamag ’s own lower bound for 11 and work from @_Mira___Mira_ @guzhou0806 @wand_125 who improved lower bounds.
All those built on my own repo started in late Aug that had the first new but weaker lower bound proof for n=11 since 2003. I'd also like to credit @ctjlewis for resources and expertise on formalization and @evanbd for a vast number of other results and tools.
Alongside 11 squares, announced last week by @ManassehA06, 17 has been the most iconic open square packing problem.
It is now being reviewed. This is a very intense proof compared to n=11, because of so many “orbits,” or possible configurations that must be systematically addressed.
It has been amazing to see the explosion of results, now leading to this latest from @kleddamag which may be the most impressive achievement yet.
Much rapid progress now comes from collaboration using what amounts to a shared library of proof machinery. It is a lot like open-source software but with tools for proof.
This new @kleddamag proof builds on the results of @ManassehA06 who built on @kleddamag ’s own lower bound for 11 and work from @_Mira___Mira_ @guzhou0806 @wand_125 who improved lower bounds.
All those built on my own repo started in late Aug that had the first new but weaker lower bound proof for n=11 since 2003. I'd also like to credit @ctjlewis for resources and expertise on formalization and @evanbd for a vast number of other results and tools.
A proof candidate for 17 squares: the 1998 packing cannot be beaten. s(17) = 4.67553009…
Built with @OpenAI Codex and @AnthropicAI Claude. Thanks to @ojoshe, @_Mira___Mira_, @guzhou0806 and @ManassehA06, whose work this builds on.
Try to break it: github.com/Kleddamag/the-…
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Slowly, at first, then all at once 💪
New cube packing records, beating @konoha_ily2 packings, which were set today beating @AlejandroZarUrd packings
n=34: 3.82288
n=35: 3.86069
n=36: 3.89443
n=11 ties @AlejandroZarUrd
n=12 ties @yoheinakajima
only ~500 CPU hours!
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Sam B retweeted
If you've ever wondered where Go fits into the world of machine learning, this talk is a great place to start.
@samb_tech builds a custom neural network from scratch, using a Wordle-solving project to show how Go and the GPU can share the work, with Go running the show and CUDA nching. It's a nuts-and-bolts look at how the pieces fit together, from the model's design to the lessons learned along the way.
Watch the full talk here: youtu.be/xTkk-UHBJ6k
@samb_tech builds a custom neural network from scratch, using a Wordle-solving project to show how Go and the GPU can share the work, with Go running the show and CUDA nching. It's a nuts-and-bolts look at how the pieces fit together, from the model's design to the lessons learned along the way.
Watch the full talk here: youtu.be/xTkk-UHBJ6k
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Sam B retweeted
The optimality of the packing for 11 squares has been formalized in lean thanks to Astra and Claude! Huge thanks to @ojoshe, @kleddamag, @wand_125, @guzhou0806, and @ctjlewis for aiding in the process.
Image credit: jlevy.github.io/squares/cases/…
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Image credit: jlevy.github.io/squares/cases/…
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Sam B retweeted
Select is a cornerstone of how Go handles concurrency, but it can be tricky to get your head around, especially if you've come from a language where it looks just like a switch.
In this talk, @jespinog takes a deep dive into how select really works, following it through the rewrites your code, and into the runtime, which picks between channels fairly and keeps your program from getting stuck. Understand it once, and you'll write better concurrent Go for good.
Watch the full talk here: youtu.be/fH5hoZJL_tQ
In this talk, @jespinog takes a deep dive into how select really works, following it through the rewrites your code, and into the runtime, which picks between channels fairly and keeps your program from getting stuck. Understand it once, and you'll write better concurrent Go for good.
Watch the full talk here: youtu.be/fH5hoZJL_tQ
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Sam B retweeted
It has been a busy time for research on the square packing problem! For all the recent arguments about AI-assisted math, I want to share some delightful news and stories of collaboration.
For those who don't know, square packing is a long-standing open problem in geometry. It is famous math problems. A child can undestand it: find the size of the smallest square that holds n non-overlapping unit squares.
There is something poetic and beautiful about this problem. Some of the best packing solutions are so mind-bendingly odd that one wonders whether square packing is God's joke on us or math's joke on God. See the best way to pack 11 or 17 or (to take a favorite of mine) 53 squares.
The work involves proving both upper bounds (constructing packings) and lower bounds (complex geometric arguments about the impossibility of building a packing) for different values of n (the number of squares being packed). The lower bound proofs are done with constructions that use exact arithmetic so require code that must be verified as part of the proof review.
Early in September, I published a few new results, including a new lower bound for n=11 and a several other values of n. I provided strategy and tooling and oversight. Codex and Claude did most the thinking and all of the writing.
I was partly motivated by seeing what agents can do, but my extensive experience with agent coding has taught me how much is about building context and loops: setting up the right workflows, distilling knowledge, building efficient tooling. In short, it worked very well. The Squares Project repo does all this. And I think the agentic workflow patterns are reusable for other kinds of problems. (Linked below.)
Since then, it has been exciting to see others jumping in to do more research on the problem using these tools.
So: we have significant new results!
@kleddamag has significantly raised the best lower bound for n=11 to s(11) > 3.875 using a much more powerful and clever extension of the weighting argument I used. This puts the lower bound *very* close to the upper bound of the Trump packing s(11) <= 3.87708.
@guzhou0806 improved the lower bound on n=17 and this was built upon by @kleddamag so we now have s(17) > 4.6601, also using work of @_Mira___Mira_.
Separately, Evan Daniel has recently shown s(32) = 6, s(21) ≥ 5000/1001 and s(12) ≥ 15680/3951.
Others, including @samb_tech @tokoharu_procon @MathCompSciFTW have been working on the problem too.
After my first results, I was fortunate to communicate with Walter Stromquist, the mathematician who proved the previous major result for n=11, over 20 years ago. He was gracious and excited by how AI can help with tool explorations like this and gave a few pointers for future work.
With some more creative strategies (see the repo for ideas), it seems quite possible n=11 could be “solved” soon, which is to say the best known packing could be proven optimal.
The GitHub repo (linked below) has a comprehensive survey of all known research on the problem, with citations, proofs, credits, and confirmations. It also includes code to build the video and printable high-resolution PDFs of all best known square packings from 1 to 324.
Everything is open source. I encourage anyone who wants to tackle this problem to check it out and chat with their agent about it. It also illustrates the use of a couple useful tools I use for other agent coding, softschema and tbd. These help orchestrate more complex workflows like this. These are also available as CLIs+skills my GitHub.
I think the future of math research is chaotic and fast moving. But unlike some who feel discouraged about the future of math, or those who say doing math is akin to an obsolete skill now agents are smarter, I am very optimistic.
I think collaboration like this makes the future of math both more mechanized *and* more human, as more people can participate, ponder, and reflect on what problems they care about.
This is a video to illustrate the best known packings and best results at the moment for n from 1 to 100. I think it needs a soundtrack. Any suggestions?
For those who don't know, square packing is a long-standing open problem in geometry. It is famous math problems. A child can undestand it: find the size of the smallest square that holds n non-overlapping unit squares.
There is something poetic and beautiful about this problem. Some of the best packing solutions are so mind-bendingly odd that one wonders whether square packing is God's joke on us or math's joke on God. See the best way to pack 11 or 17 or (to take a favorite of mine) 53 squares.
The work involves proving both upper bounds (constructing packings) and lower bounds (complex geometric arguments about the impossibility of building a packing) for different values of n (the number of squares being packed). The lower bound proofs are done with constructions that use exact arithmetic so require code that must be verified as part of the proof review.
Early in September, I published a few new results, including a new lower bound for n=11 and a several other values of n. I provided strategy and tooling and oversight. Codex and Claude did most the thinking and all of the writing.
I was partly motivated by seeing what agents can do, but my extensive experience with agent coding has taught me how much is about building context and loops: setting up the right workflows, distilling knowledge, building efficient tooling. In short, it worked very well. The Squares Project repo does all this. And I think the agentic workflow patterns are reusable for other kinds of problems. (Linked below.)
Since then, it has been exciting to see others jumping in to do more research on the problem using these tools.
So: we have significant new results!
@kleddamag has significantly raised the best lower bound for n=11 to s(11) > 3.875 using a much more powerful and clever extension of the weighting argument I used. This puts the lower bound *very* close to the upper bound of the Trump packing s(11) <= 3.87708.
@guzhou0806 improved the lower bound on n=17 and this was built upon by @kleddamag so we now have s(17) > 4.6601, also using work of @_Mira___Mira_.
Separately, Evan Daniel has recently shown s(32) = 6, s(21) ≥ 5000/1001 and s(12) ≥ 15680/3951.
Others, including @samb_tech @tokoharu_procon @MathCompSciFTW have been working on the problem too.
After my first results, I was fortunate to communicate with Walter Stromquist, the mathematician who proved the previous major result for n=11, over 20 years ago. He was gracious and excited by how AI can help with tool explorations like this and gave a few pointers for future work.
With some more creative strategies (see the repo for ideas), it seems quite possible n=11 could be “solved” soon, which is to say the best known packing could be proven optimal.
The GitHub repo (linked below) has a comprehensive survey of all known research on the problem, with citations, proofs, credits, and confirmations. It also includes code to build the video and printable high-resolution PDFs of all best known square packings from 1 to 324.
Everything is open source. I encourage anyone who wants to tackle this problem to check it out and chat with their agent about it. It also illustrates the use of a couple useful tools I use for other agent coding, softschema and tbd. These help orchestrate more complex workflows like this. These are also available as CLIs+skills my GitHub.
I think the future of math research is chaotic and fast moving. But unlike some who feel discouraged about the future of math, or those who say doing math is akin to an obsolete skill now agents are smarter, I am very optimistic.
I think collaboration like this makes the future of math both more mechanized *and* more human, as more people can participate, ponder, and reflect on what problems they care about.
This is a video to illustrate the best known packings and best results at the moment for n from 1 to 100. I think it needs a soundtrack. Any suggestions?
For some reason this post sent me (and Opus, Fable, Sol, and Astra) down a fascinating rabbithole last week.
I'm pleased to announce I now have math psychosis.
And that s(11) ≥ 381/100.
This appears to be the first significant result in 23 years on the open problem of packing wer bound proof verifiable with ~300 lines of Python exact rational arithmetic.
There are also some cool visualizations of the proof argument, which is via placement of 1,121 unavoidable weighted dots within the containing square.
It is a bit complex but quite understandable math. An explainer paper with interactive graphics is at jlevy.github.io/squares
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Video of my GoLab Florence talk has been released sam-burns.com/posts/golab-20…
Post-quantum cryptography features in Go
Post-quantum cryptography features in Go
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Made an automatic plant watering system with an Arduino Nano, a pump, and a moisture sensor
sam-burns.com/posts/automati…
sam-burns.com/posts/automati…
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Sam B retweeted
For some reason this post sent me (and Opus, Fable, Sol, and Astra) down a fascinating rabbithole last week.
I'm pleased to announce I now have math psychosis.
And that s(11) ≥ 381/100.
This appears to be the first significant result in 23 years on the open problem of packing wer bound proof verifiable with ~300 lines of Python exact rational arithmetic.
There are also some cool visualizations of the proof argument, which is via placement of 1,121 unavoidable weighted dots within the containing square.
It is a bit complex but quite understandable math. An explainer paper with interactive graphics is at jlevy.github.io/squares
I'm pleased to announce I now have math psychosis.
And that s(11) ≥ 381/100.
This appears to be the first significant result in 23 years on the open problem of packing wer bound proof verifiable with ~300 lines of Python exact rational arithmetic.
There are also some cool visualizations of the proof argument, which is via placement of 1,121 unavoidable weighted dots within the containing square.
It is a bit complex but quite understandable math. An explainer paper with interactive graphics is at jlevy.github.io/squares
The universe has a sense of humor.
This is the most efficient known way of packing 11 identical squares into a larger square (with no overlap). Found by mathematician Walter Trump.
Figure credit: Wikimedia/Walter Trump
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Sam B retweeted
Post-lunch pick 🍽️
Dave Cheney's back on the Google Track with his talk Numbers.
And on the loveholidays Track, Veronika Volokitina digs into one definition of valid.
Where are we landing?
#gopherconuk26 #golang
Dave Cheney's back on the Google Track with his talk Numbers.
And on the loveholidays Track, Veronika Volokitina digs into one definition of valid.
Where are we landing?
#gopherconuk26 #golang
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