robinhouston
@robinhouston.mathstodon.xyz.ap.brid.gy
Watching for the card that is so high and wild I’ll never need to deal another
🌉 bridged from ⁂ https://mathstodon.xyz/@robinhouston, follow @ap.brid.gy to interact
🌉 bridged from ⁂ https://mathstodon.xyz/@robinhouston, follow @ap.brid.gy to interact
I had a cool experience on Saturday night at MathsJam. Mike Borcherds had brought a pile of 3D-printed puzzles for people to play with; and I recognised one of the puzzles in the pile as one I had designed!
(It was this one […]
(It was this one […]
Original post on mathstodon.xyz
mathstodon.xyz
November 24, 2025 at 10:31 AM
I had a cool experience on Saturday night at MathsJam. Mike Borcherds had brought a pile of 3D-printed puzzles for people to play with; and I recognised one of the puzzles in the pile as one I had designed!
(It was this one […]
(It was this one […]
From 2022, but new to me:
Computational Design of High-level Interlocking Puzzles
https://sutd-cgl.github.io/supp/Publication/projects/2022-SIGGRAPH-High-LevelPuzzle/index.html
Computational Design of High-level Interlocking Puzzles
https://sutd-cgl.github.io/supp/Publication/projects/2022-SIGGRAPH-High-LevelPuzzle/index.html
High-level Interlocking Puzzle
sutd-cgl.github.io
November 24, 2025 at 4:55 AM
From 2022, but new to me:
Computational Design of High-level Interlocking Puzzles
https://sutd-cgl.github.io/supp/Publication/projects/2022-SIGGRAPH-High-LevelPuzzle/index.html
Computational Design of High-level Interlocking Puzzles
https://sutd-cgl.github.io/supp/Publication/projects/2022-SIGGRAPH-High-LevelPuzzle/index.html
I am witnessing the birth of a rhombic dodecahedron
November 21, 2025 at 2:58 PM
I am witnessing the birth of a rhombic dodecahedron
Tim Berners-Lee on Desert Island Discs:
— The Bible: could I choose a different religious book if I want to?
— You can, yeah. Would you like to?
— Oh, I'll take the Bible, but I wanted to make sure I had the right to choose.
Never change, Sir Tim.
— The Bible: could I choose a different religious book if I want to?
— You can, yeah. Would you like to?
— Oh, I'll take the Bible, but I wanted to make sure I had the right to choose.
Never change, Sir Tim.
November 21, 2025 at 10:03 AM
Tim Berners-Lee on Desert Island Discs:
— The Bible: could I choose a different religious book if I want to?
— You can, yeah. Would you like to?
— Oh, I'll take the Bible, but I wanted to make sure I had the right to choose.
Never change, Sir Tim.
— The Bible: could I choose a different religious book if I want to?
— You can, yeah. Would you like to?
— Oh, I'll take the Bible, but I wanted to make sure I had the right to choose.
Never change, Sir Tim.
A shockingly short list. https://commons.wikimedia.org/wiki/Category:Hexagonal_buildings_in_England
Category:Hexagonal buildings in England - Wikimedia Commons
commons.wikimedia.org
November 19, 2025 at 5:39 PM
A shockingly short list. https://commons.wikimedia.org/wiki/Category:Hexagonal_buildings_in_England
Reposted by robinhouston
Thanks to a commenter on the Lean Zulip, the other day I learned of "safe" functions, which are an abstraction of what it means to have a function on tuples of binary strings (outputting a binary string) that is polynomial-time computable. See for example section 4.1 of […]
Original post on mathstodon.xyz
mathstodon.xyz
November 17, 2025 at 6:13 AM
Thanks to a commenter on the Lean Zulip, the other day I learned of "safe" functions, which are an abstraction of what it means to have a function on tuples of binary strings (outputting a binary string) that is polynomial-time computable. See for example section 4.1 of […]
Continuing their long tradition of being the most geometrically adventurous chocolate manufacturer, Toblerone have a range of enneahedral chocolates.
November 12, 2025 at 2:34 PM
Continuing their long tradition of being the most geometrically adventurous chocolate manufacturer, Toblerone have a range of enneahedral chocolates.
RE: https://mathstodon.xyz/@robinhouston/115519011082424073
At least one person read this as an excoriating criticism. It wasn't meant to be! I enjoyed the interview a lot!
At least one person read this as an excoriating criticism. It wasn't meant to be! I enjoyed the interview a lot!
A curious feature of the interview is that they didn‘t refer at all even to the existence of any sort of literature on these puzzles. They are treated rather like objects that have fallen from outer space, rather than products of human culture – perhaps because that is how the young Grant […]
Original post on mathstodon.xyz
mathstodon.xyz
November 10, 2025 at 7:45 AM
RE: https://mathstodon.xyz/@robinhouston/115519011082424073
At least one person read this as an excoriating criticism. It wasn't meant to be! I enjoyed the interview a lot!
At least one person read this as an excoriating criticism. It wasn't meant to be! I enjoyed the interview a lot!
There's a new episode of the Mathematical Objects podcast where the hosts (@stecks and @peterrowlett) interview Grant Sanderson (3blue1brown) about his love of wooden puzzles – specifically the three pictured below.
November 9, 2025 at 9:21 AM
There's a new episode of the Mathematical Objects podcast where the hosts (@stecks and @peterrowlett) interview Grant Sanderson (3blue1brown) about his love of wooden puzzles – specifically the three pictured below.
A surprising tessellation
November 8, 2025 at 5:15 PM
A surprising tessellation
Reposted by robinhouston
I can't believe I didn't know this fact before today - it seems so fundamental.
If you have a real symmetric matrix A, and pick some unit vector x, then x.Ax (the Rayleigh quotient) is bounded by the smallest and largest eigenvalues. So what happens if I pick […]
[Original post on mathstodon.xyz]
If you have a real symmetric matrix A, and pick some unit vector x, then x.Ax (the Rayleigh quotient) is bounded by the smallest and largest eigenvalues. So what happens if I pick […]
[Original post on mathstodon.xyz]
November 8, 2025 at 5:17 AM
I can't believe I didn't know this fact before today - it seems so fundamental.
If you have a real symmetric matrix A, and pick some unit vector x, then x.Ax (the Rayleigh quotient) is bounded by the smallest and largest eigenvalues. So what happens if I pick […]
[Original post on mathstodon.xyz]
If you have a real symmetric matrix A, and pick some unit vector x, then x.Ax (the Rayleigh quotient) is bounded by the smallest and largest eigenvalues. So what happens if I pick […]
[Original post on mathstodon.xyz]
I *thought* it was weird that we hadn’t heard more from mathematicians using AlphaEvolve.
It turns out they were just biding their time to drop an 80-page mega-paper describing its use on 67 different problems(!)
https://arxiv.org/abs/2511.02864
It turns out they were just biding their time to drop an 80-page mega-paper describing its use on 67 different problems(!)
https://arxiv.org/abs/2511.02864
Mathematical exploration and discovery at scale
AlphaEvolve is a generic evolutionary coding agent that combines the generative capabilities of LLMs with automated evaluation in an iterative evolutionary framework that proposes, tests, and refines algorithmic solutions to challenging scientific and practical problems. In this paper we showcase AlphaEvolve as a tool for autonomously discovering novel mathematical constructions and advancing our understanding of long-standing open problems. To demonstrate its breadth, we considered a list of 67 problems spanning mathematical analysis, combinatorics, geometry, and number theory. The system rediscovered the best known solutions in most of the cases and discovered improved solutions in several. In some instances, AlphaEvolve is also able to generalize results for a finite number of input values into a formula valid for all input values. Furthermore, we are able to combine this methodology with Deep Think and AlphaProof in a broader framework where the additional proof-assistants and reasoning systems provide automated proof generation and further mathematical insights. These results demonstrate that large language model-guided evolutionary search can autonomously discover mathematical constructions that complement human intuition, at times matching or even improving the best known results, highlighting the potential for significant new ways of interaction between mathematicians and AI systems. We present AlphaEvolve as a powerful new tool for mathematical discovery, capable of exploring vast search spaces to solve complex optimization problems at scale, often with significantly reduced requirements on preparation and computation time.
arxiv.org
November 6, 2025 at 5:24 PM
I *thought* it was weird that we hadn’t heard more from mathematicians using AlphaEvolve.
It turns out they were just biding their time to drop an 80-page mega-paper describing its use on 67 different problems(!)
https://arxiv.org/abs/2511.02864
It turns out they were just biding their time to drop an 80-page mega-paper describing its use on 67 different problems(!)
https://arxiv.org/abs/2511.02864
Need to pack a lot of identical regular tetrahedra together efficiently? This may help!
From https://arxiv.org/pdf/1012.5138, brought to my attention by @liuyao
From https://arxiv.org/pdf/1012.5138, brought to my attention by @liuyao
![Figure S5. Details of the highest density (ф = 0.8503) packing of hard tetrahedra observed in this study. This density was obtained by compressing a 2x2x2 cell of the (3,4,37,4) approximant with 656 tetrahedra. (a) For ease of viewing, the 2x2x2 cell has been periodically continued into a 2x2x8 cell. (b) In the translucent image, the twelve- fold logs can be identified. The logs arrange into triangle (c) and square (d) tiles with 9.5 and 22 tetrahedra, respectively. The ratio of the packing densities of the tiles is Triangle / square = 19 / 11V3. (e) Thin rhombi are frequently observed in connection with zipper motion, a dynamical mechanism to rearrange squares and triangles [26]. A rhomb is a structural defect. It consists of 11 tetrahedra and has half the volume of a square. As can be seen in the image, tetrahedra in the middle form a spiral of two interpenetrating logs (light red).](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:nhakixcsmdow4avnqxtfy6c6/bafkreigy4bdtldppaqyjuaq7bgp65xfdafqp2qebraokbmylgojfy2rvka@jpeg)
November 6, 2025 at 11:56 AM
Need to pack a lot of identical regular tetrahedra together efficiently? This may help!
From https://arxiv.org/pdf/1012.5138, brought to my attention by @liuyao
From https://arxiv.org/pdf/1012.5138, brought to my attention by @liuyao
Have you ever read a C program that uses K&R function declaration syntax and C99 // comments in the same function?
It seemed an unusual combination to me, but maybe it's not.
It seemed an unusual combination to me, but maybe it's not.
November 3, 2025 at 10:26 AM
Have you ever read a C program that uses K&R function declaration syntax and C99 // comments in the same function?
It seemed an unusual combination to me, but maybe it's not.
It seemed an unusual combination to me, but maybe it's not.
I've just come across this really nice animated explanation of the Demaine et al. theorem that hinged dissections always exist between two polygons that have the same area. https://youtu.be/kTka84UJp2I
November 3, 2025 at 9:07 AM
I've just come across this really nice animated explanation of the Demaine et al. theorem that hinged dissections always exist between two polygons that have the same area. https://youtu.be/kTka84UJp2I
I've just got this book. I hadn't realised that the whole thing is hand lettered!
November 2, 2025 at 9:40 AM
I've just got this book. I hadn't realised that the whole thing is hand lettered!
Travelling from Heathrow Terminal 2 recently, I was struck by the unusual organic geometry of the Luis Vuitton cafe/shop there.
It turns out it was designed by Marc Fornes, who has done a lot of interesting work of that sort. Here's his website: https://theverymany.com/
And a TED talk he gave […]
It turns out it was designed by Marc Fornes, who has done a lot of interesting work of that sort. Here's his website: https://theverymany.com/
And a TED talk he gave […]
Original post on mathstodon.xyz
mathstodon.xyz
November 2, 2025 at 9:35 AM
Travelling from Heathrow Terminal 2 recently, I was struck by the unusual organic geometry of the Luis Vuitton cafe/shop there.
It turns out it was designed by Marc Fornes, who has done a lot of interesting work of that sort. Here's his website: https://theverymany.com/
And a TED talk he gave […]
It turns out it was designed by Marc Fornes, who has done a lot of interesting work of that sort. Here's his website: https://theverymany.com/
And a TED talk he gave […]
Reposted by robinhouston
What Abbotsbury Road needs in that empty unit is a restaurant selling burgers, kebabs and pizza IN THAT ORDER.
October 27, 2025 at 8:44 AM
What Abbotsbury Road needs in that empty unit is a restaurant selling burgers, kebabs and pizza IN THAT ORDER.
There's a famous classification of fun into three types: https://essentialwilderness.com/type-1-2-and-3-fun/
If you draw this in a 2×2 matrix, it becomes clear there's one missing.
I propose we refer to the missing type as Type 0 fun: enjoyable at the time but, in retrospect, regrettable.
If you draw this in a 2×2 matrix, it becomes clear there's one missing.
I propose we refer to the missing type as Type 0 fun: enjoyable at the time but, in retrospect, regrettable.
October 27, 2025 at 9:17 AM
There's a famous classification of fun into three types: https://essentialwilderness.com/type-1-2-and-3-fun/
If you draw this in a 2×2 matrix, it becomes clear there's one missing.
I propose we refer to the missing type as Type 0 fun: enjoyable at the time but, in retrospect, regrettable.
If you draw this in a 2×2 matrix, it becomes clear there's one missing.
I propose we refer to the missing type as Type 0 fun: enjoyable at the time but, in retrospect, regrettable.
I love the feeling of going to bed leaving a search algorithm running. Will it have found anything by the time I wake up tomorrow? So exciting.
October 24, 2025 at 9:26 PM
I love the feeling of going to bed leaving a search algorithm running. Will it have found anything by the time I wake up tomorrow? So exciting.
I think this is the first time I've seen ChatGPT credited in the acknowledgements of a paper.
https://arxiv.org/abs/2509.22333
https://arxiv.org/abs/2509.22333
October 24, 2025 at 12:42 PM
I think this is the first time I've seen ChatGPT credited in the acknowledgements of a paper.
https://arxiv.org/abs/2509.22333
https://arxiv.org/abs/2509.22333
Reposted by robinhouston
New video: I went to see the Pascaline! They did not let me touch it.
youtu.be/CROrLQpN6dc
youtu.be/CROrLQpN6dc
Pascal's 1630 Machine: The First Calculator! Pascaline Review / HowTo
YouTube video by Chris Staecker
youtu.be
October 24, 2025 at 11:38 AM
New video: I went to see the Pascaline! They did not let me touch it.
youtu.be/CROrLQpN6dc
youtu.be/CROrLQpN6dc
I fear CAD could become a dangerous addiction.
October 21, 2025 at 12:31 PM
I fear CAD could become a dangerous addiction.
This is up there with “Can One Hear the Shape of a Drum” in the annals of great titles.
Was the 1960s an especially auspicious time for excellent titles?
Was the 1960s an especially auspicious time for excellent titles?
October 20, 2025 at 4:06 PM
This is up there with “Can One Hear the Shape of a Drum” in the annals of great titles.
Was the 1960s an especially auspicious time for excellent titles?
Was the 1960s an especially auspicious time for excellent titles?
I'm going to invent a new kind of building block toy based on the tetragonal disphenoid tetrahedral honeycomb. I think we've all had enough fun with cubes by now.
October 19, 2025 at 3:22 PM
I'm going to invent a new kind of building block toy based on the tetragonal disphenoid tetrahedral honeycomb. I think we've all had enough fun with cubes by now.