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Henry Segerman

@henryseg.bsky.social
311 followers 100 following 64 posts

Mathematician and mathematical artist/maker. segerman.org, youtube.com/@henryseg, mathstodon.xyz/@henryseg

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Reposted by Henry Segerman
Sophie Huiberts @sophie.huiberts.me · 13h
Too many people are calling on the community to "change how we value papers". Not enough people are posting "this is what we look for in our next hiring round".
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John Golden @johngolden.bsky.social · 12/10/2026
Lovely guest post at @teorth.bsky.social's blog by @gelada.bsky.social and Kate Stange on #mathart and more. terrytao.wordpress.com/2026/10/11/i...
terrytao.wordpress.com
Illustration beyond Proof
[This is a guest post by Kate Stange and Edmund Harriss. This blog post was initially written in a different file format and converted using AI. — T.] In January a group of mathematicians, hi…
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robertfathauer.bsky.social @robertfathauer.bsky.social · 11/10/2026
This is the last week to submit your art for the exhibition to be held as part of the upcoming Joint Mathematics Meetings. Take advantage of this opportunity to share your work with over 5000 attendees this January in Chicago. You’ll need to submit by the 15th at gallery.bridgesmathart.org.
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Dr. Martin Skrodzki @msmathcomp.bsky.social · 08/10/2026
Tomorrow, Friday, October 9th, we will have our next #illustratingMath seminar online at 9am Pacific / 12pm Eastern / 6pm Central Europe. Things will be slightly different than usual: Instead of Show&Ask and a talk, we will have a panel on "The Role of Illustration." Tune in!
Poster for "On the Role of Illustration in a Large Language Landscape," a discussion on mathematical illustration and AI.   Features three speakers: Edmund Harriss (Univ. of Arkansas), Katherine E. Stange (CU Boulder), and Chaim Goodman-Strauss (MoMath), each shown in a circular portrait.   Event details: Friday, Oct 9 (9 AM Pacific / 12 PM Eastern / 6 PM Central Europe) on Zoom. Includes a QR code to join and links to illustratingmath.org for the Illustrating Math Seminar Online. Above the text is a photo of colorful geometric 3D shapes.
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Henry Segerman @henryseg.bsky.social · 03/10/2026
New video, on a surprising linkage motion that showed up when I was playing with chains of bevel gears. youtu.be/ujEZUFNgf50
youtu.be
A mysterious extra movement
YouTube video by Henry Segerman
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Henry Segerman @henryseg.bsky.social · 01/10/2026
(c)
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Henry Segerman @henryseg.bsky.social · 16/09/2026
New paper on (among other things) generating Cannon-Thurston maps from veering triangulations, joint work with Jason Manning and Saul Schleimer. arxiv.org/abs/2609.14598. We also made lots of pictures of these space-filling curves, available at math.okstate.edu/people/seger...
A sphere patterned by two different space-filling curves, one drawn as a black line and one as the boundary between green and purple regions.
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Henry Segerman @henryseg.bsky.social · 29/08/2026
New video on hyperboloids made out of sticks: why and how they move, with Sabetta Matsumoto, Tim Reinhardt, Jürgen Richter-Gebert, and me, at youtu.be/CJCL92W8Z9w
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Matt Henderson @matthen.com · 25/08/2026
Seamlessly loops every 10 seconds. But follow any dot and you will be watching for over an hour before it returns to its starting position.
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Henry Segerman @henryseg.bsky.social · 25/08/2026
MoMath will host a free online event on Friday, Aug 28 at 12:00pm US Eastern time premiering a new video by Sabetta Matsumoto, Tim Reinhardt, Jürgen Richter-Gebert, and me, on hyperboloids made out of sticks and how they move. Details and registration at momath.org/hyperboloids/
A hyperboloid of one sheet made out of wooden skewers next to Mae West, an enormous sculpture of a hyperboloid of one sheet in Munich. Next to the wooden skewers hyperboloid is written “This one doesn’t exist”.
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Dave Richeson @divbyzero.bsky.social · 22/08/2026
More impossible arrows 
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Dave Richeson @divbyzero.bsky.social · 22/08/2026
Here is another impossible arrow. It occurred to me that you can get the same effect by putting it on a mirror! 
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Yuri Sulyma @yurisulyma.bsky.social · 18/08/2026
👏 arxiv.org/abs/2608.16066
Mathematicians are currently being instrumentalised in a large scale advertising campaign by AI companies competing for market monopoly. Public grant money is being paid to companies which then receive free advertising from us, often while showing little regard for our research priorities. More seriously, as part of this advertising campaign, some companies are pushing misinformation about the goals of mathematical research. This misinformation has the real potential to influence government funding decisions in a way that funnels money away from scientific goals, and towards private interests.
This advertising campaign has more serious collateral damage. Mathematics depends on a human research ecosystem which continually generates new problems and sustains the community capable of recognising and pursuing them. Human generated research problems are a scarce and essential part of this mathematical ecosystem. Conceptually incoherent and empirically unsupported rhetoric portraying mathematicians as replaceable threatens a pipeline of early career researchers already in precarious employment conditions. Damaging either undermines the infrastructure on which future mathematical progress depends.
While the author *does* want to be transparent about the use of computer assistance in the preparation of the current manuscript, he does not want to participate in this advertising campaign and contribute to this destruction of the commons. As such, the model and company name will remain absent from this manuscript, but are available upon request.
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Matt Henderson @matthen.com · 16/08/2026
Drawing all 16,777,216 possible 12 bit RGB colours in one 2D image, each exactly once. Pixels are mapped from the 256³ colour cube, following a three dimensional Hilbert curve, to a two dimensional Hilbert curve filling the square. so nearby colours stay close.
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Henry Segerman @henryseg.bsky.social · 16/08/2026
Everyone who does math is a mathematician (if they want to be called that). Everyone who photographs cats is a cat photographer (if they want to be called that).
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Dave Richeson @divbyzero.bsky.social · 12/08/2026
A new impossible object 
A photograph of an arrow reflected in a mirror and pointed the other direction
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Dave Richeson @divbyzero.bsky.social · 08/08/2026
At family day at Bridges I volunteered to help Nick Sayers with his giant pantograph. Trace the outline of the person, and a small copy is drawn by the pen. It was fun for kids and adults of all ages. Here is @ayliean.bsky.social as a model and an artist. 
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Zeno Rogue @zenorogue.bsky.social · 06/08/2026
A solar eclipse in a wrapped world. #eclipse #rogueviz #mathart
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Henry Segerman @henryseg.bsky.social · 22/07/2026
The plane is 2d because at every point there are two perpendicular directions you can move in. Same for the sphere. Really the point of the photo is to show that the sphere and the plane are almost the same. So, going up to 3d, the idea is that the three-sphere is almost the same as 3d space.
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Henry Segerman @henryseg.bsky.social · 22/07/2026
Backing up a bit, in the photo in which a light casts shadows from a sphere onto a plane: I would say that is a 2d object mapping to a 2d object. That is, both the sphere and the plane are two-dimensional.
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Henry Segerman @henryseg.bsky.social · 21/07/2026
You can cast a shadow on a 2D plane, no need for any 3D object that the plane is part of.
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robertfathauer.bsky.social @robertfathauer.bsky.social · 19/07/2026
The Dice Lab's popular Skew dice gamer's set is now available in purple and Malachite. mathartfun.com/DiceLabDice....
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Henry Segerman @henryseg.bsky.social · 19/07/2026
The 3d version of stereographic projection tells you that the 3-sphere is the same as ordinary euclidean 3-space, plus one point, “at infinity”. Here’s a picture, with analogous designs in 2d (left) and 3d (right).The 2-sphere is cut into 8 triangles. The 3-sphere is cut into 16 tetrahedra.
Left: a 3d print showing the edges of an octahedron and their stereographic projection. Right: the shadow of the edges of the analogous four-dimensional polyhedron, the 16-cell.
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Henry Segerman @henryseg.bsky.social · 19/07/2026
My favourite way to think about the three-sphere is to use stereographic projection. For each dimension, there is a stereographic projection mapping the n-sphere (minus its north pole) to ordinary euclidean n-space. Here’s a picture of the two-sphere minus its north pole mapping to the plane:
A 3d printed sphere patterned with a curved grid. A light shining from its north pole casts a straight line grid on the table.
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robertfathauer.bsky.social @robertfathauer.bsky.social · 05/07/2026
Over 5,500 mathematical artworks can now be browsed in an attractive new gallery-wall layout on the Bridges website, thanks to the efforts of Nathan Selikoff: gallery.bridgesmathart.org/gallery?seed...
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Henry Segerman @henryseg.bsky.social · 01/07/2026
I gave a talk at www.ias.edu/pcmi yesterday, in which I described this 3D printed knot complement (by François Guéritaud, Saul Schleimer, and me) as what's left after a very well-trained worm tunnels out a knotted hole. Elise Brod was in the audience and drew the well-trained worm!
A 3d printed sculpture showing the complement of the figure-eight knot.A drawing of a well-trained worm forming the figure-eight knot inside of an apple.
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robertfathauer.bsky.social @robertfathauer.bsky.social · 25/06/2026
The website for the 2026 Bridges Conference Exhibition of Mathematical Art, Craft, and Design is now live, featuring the work of more than 150 artists. gallery.bridgesmathart.org/exhibitions/...
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Henry Segerman @henryseg.bsky.social · 22/06/2026
The papers for this year's Bridges math/art conference are out now! I wrote a paper on expanding gadgets based on rack and pinion mechanisms. archive.bridgesmathart.org/2026/bridges...
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Dave Richeson @divbyzero.bsky.social · 11/06/2026
Two different figure-eight knots made with curved origami. The blue one has a fold angle of 90°, and the purple has a fold angle of 60°. The latter can be made with one strip of paper. The former required two.
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Owen Maresh @graveolens.bsky.social · 10/06/2026
arxiv.org/abs/2606.10047 /On the Group Structure of "Magic" Leatherworking Braids/ William Hobkirk, Abigail Hollingsworth, Elisabetta A. Matsumoto, Corbin Reid
arxiv.org
On the Group Structure of "Magic" Leatherworking Braids
\emph{Magic braids} are used in leatherworking to make intricate straps and bands. They appear to be impossible to make. To determine which braids can be made with this leatherworking technique, we ex...
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Doug Mack @douglasmack.bsky.social · 08/06/2026
Just need everyone to know that the Belgium men's soccer team has new jerseys based on the art of Rene Magritte and this is the official photo shoot
Soccer player wearing fedora and with a green apple floating in front of his face, mimicking the Magritte painting "The Son of Man." The soccer player is wearing a jersey with a pattern of pink and blue stripes with half-visible spheres.Soccer player wearing fedora and with a green apple floating in front of his face, mimicking the Magritte painting "The Son of Man." The soccer player is wearing a jersey with a pattern of pink and blue stripes with half-visible spheres.Soccer player biting an apple. The soccer player is wearing a jersey with a pattern of pink and blue stripes with half-visible spheres.Soccer player wearing fedora and with a green apple floating in front of his face, mimicking the Magritte painting "The Son of Man." The soccer player is wearing a jersey with a pattern of pink and blue stripes with half-visible spheres.
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ꭓle Ormsby 𓆙 @e-infinity.space · 03/06/2026
Fantastic and important reporting by Siobhan Roberts in the NYT. 🧮 Gift link: www.nytimes.com/2026/06/02/s...
To think of mathematics in terms of precise and neatly stated problems, like high school exams or the list of Erdos problems, is to misunderstand and diminish what makes mathematics so powerful and significant. Mathematics is not just about solving problems — it is also the cultivation of ideas, understanding, judgment, and human insight.We want to affirm certain values that have characterized the profession: openness, honesty, giving credit where credit is due, sharing, transparency about methodologies, and access for independent verification of results.

An aspect of mathematics that is cherished by mathematicians is that it is one of few successful examples of a gift economy — that is to say, its economy is somehow an island of idealism in our society. As director of graduate studies in the mathematics department at Columbia, I read the personal statements of all the applicants every year, several hundred, and they are still idealists.

The tech industry proceeds in accordance with commercial logic, which is antithetical to the values of mathematics.This situation has put mathematicians in a troubling ethical position. Without their consent, their published work is being used as strategic training data for the development of general-purpose A.I. The resulting models are being commercialized for many purposes, including military applications, that raise grave ethical concerns. Most mathematicians never imagined, much less consented, that their work would be used for such purposes.OCHIGAME Mathematics is a rich form of cultural expression with an ancient history, and I am not worried that any technology will ever render it obsolete. Its most precious aspects, such as the collective quest to understand beautifully intricate ideas, and to explore the limits of the human imagination, cannot ever be automated. What I am worried about is that a handful of corporations are mobilizing their vast financial resources to impose an impoverished view of mathematics so forcefully — at a moment when scientific research is already under political attack — that they may well end up destroying the social institutions that allow mathematics to flourish. What could be futile about resisting that?
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robertfathauer.bsky.social @robertfathauer.bsky.social · 24/05/2026
New hand-built ceramic piece, with bamboo and leather; mathematically, a Hopf link with Seifert surface. www.mathartfun.com/robertfathau...
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Henry Segerman @henryseg.bsky.social · 21/05/2026
But even better would be to not name it after a person at all. We could have a name that helps you understand what the sequence is. Perhaps it should be the "Add previous two" sequence? Although that's a bit clunky. What would be a better descriptive name for it?
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Henry Segerman @henryseg.bsky.social · 21/05/2026
The so-called "Fibonacci sequence" was introduced to European mathematicians by Fibonacci, but was first described by the Indian mathematician Pingala over 1400 years earlier. So perhaps we should be calling it the "Pingala sequence".
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ꭓle Ormsby 𓆙 @e-infinity.space · 13/05/2026
The vanishing loci of homogeneous polynomials in four variables form surfaces in projective space. This project renders four views of such surfaces in the ball model of ℝℙ³, with a fifth ball rotating between them. Click and drag to interact! kyleormsby.github.io/projective-s... 🧮 #MathArt
Screenshot of an interactive web visualization titled "Surfaces in Real Projective 3-Space." A long expanded polynomial expression for the Clebsch cubic is displayed at the top, along with controls: a dropdown showing "Clebsch cubic — Σx³ − (Σx)³" selected, a text input for custom polynomials, a "PLOT" button, and two parameter sliders labeled a and b (both set to 1.00 and currently inactive). Below the controls is a row of four small ball-model renderings of the Clebsch cubic, each showing the surface from a different perspective and labeled "centered at [1:0:0:0]", "[0:1:0:0]", "[0:0:1:0]", and "[0:0:0:1]." A larger ball below shows the same surface in an interpolated view, labeled "[0:0:1:0] → [0:0:0:1]," with a "PAUSE" button beneath it. The surfaces are rendered as translucent, glassy amber-brown shapes against a cream background; the Clebsch cubic's characteristic curving sheets and openings are visible in each view.
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Henry Segerman @henryseg.bsky.social · 02/05/2026
We saw $7.89 in Palo Alto yesterday.
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Quanta Magazine @quantamagazine.org · 22/04/2026
Mathematicians have built beautiful, snowflake-like codes to untangle some of the trickiest knots. @ericaklarreich.bsky.social reports: www.quantamagazine.org/a-powerful-n...
quantamagazine.org
A Powerful New ‘QR Code’ Untangles Math’s Knottiest Knots | Quanta Magazine
With a newly discovered mathematical tool, researchers are hoping to gain unprecedented insight into the structure of complex knots.
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Henry Segerman @henryseg.bsky.social · 20/04/2026
It’s possible, although I may want to shrink some components when I give that a try!
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Henry Segerman @henryseg.bsky.social · 20/04/2026
Here's a second, geared mechanism that transforms between cube and octahedron forms. Full video at youtu.be/T9BNMLFHXUw
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Dr. Martin Skrodzki @msmathcomp.bsky.social · 18/04/2026
This is a result of our fabulous #illustratingMath trimester at the institute Henri Poincaré in Paris, which ran from January till March this year. Attached is an image of the piece in the #art exhibition at the Maison Poincaré. Definitely give Henry's video a look!
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Henry Segerman @henryseg.bsky.social · 18/04/2026
Good question!
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Henry Segerman @henryseg.bsky.social · 18/04/2026
I haven’t made any of them but they are just sitting there in the platonic realm. I think that a dodecahedron/icosahedron linkage would be even more unruly than the cube/octahedron one. The geared version should work, although it would be a big mechanism!
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Henry Segerman @henryseg.bsky.social · 18/04/2026
New video, on mechanisms that illustrate the duality between the cube and the octahedron! Here's one of them: a linkage with fabric panels designed by Sabetta Matsumoto. Full video at youtu.be/T9BNMLFHXUw
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Henry Segerman @henryseg.bsky.social · 07/04/2026
Too easy… the effective frustum is everything, so it doesn’t matter where you are relative to the rest of humanity.
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Henry Segerman @henryseg.bsky.social · 07/04/2026
They are in the frustum of the camera’s view. I think that’s the idea. I wonder how easy it would be to take a photo with everyone else in the frustum without a space mission. Seems like it should be possible with a fisheye lens up high if you wait for any passing planes or space stations.
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Joseph O'Rourke @josephorourke.bsky.social · 28/03/2026
There is research on fabricating micropolyhedra using lithographic techniques via self-assembly / self-folding of nets that fold to, e.g., a cube as illustrated. Note the tiny size: 0.2mm. The goal is to minimize mis-foldings. doi:10.1371/journal.pone.0004451 cs.smith.edu/~jorourke/Ma... #MathSky 🧪
Cube net folding.
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Henry Segerman @henryseg.bsky.social · 25/03/2026
I took this photo in Heidelberg a decade ago. I wonder how many driveways have it globally!
A very similar pattern to Robert’s post, on another driveway.
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Jessica Rosenkrantz @nervousjessica.bsky.social · 24/03/2026
We’ve been experimenting with the transparency toolkit from HeyGears to create optically clear models of radiolarians, microscopic single-celled marine organisms that build intricate glass skeletons with stunning geometric complexity. #sciart #3dprinting (Printer + materials provided by HeyGears)
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Christian Lawson-Perfect @christianp.mathstodon.xyz.ap.brid.gy · 19/03/2026
I'm enormously happy to finally be able to announce the date of the #BeachSpectres project: 7th June, 2026. #WhitleyBay beach, UK. If you can make it to the beach and join in with the tiling effort, I'll be very happy to see you and glad of the help! Lots […] [Original post on mathstodon.xyz]
Poster: Beach Spectres, we want to make the largest aperiodic tiling ever!
What's an aperiodic tiling?
It's when you cover a flat surface with copies of a shape like the one above,
without any repeating patterns. The Spectre monotile was only discovered in
2023, and mathematicians are really excited about it!
What are you doing?
We're going to use large “cookie cutter” tools in the shape of the Spectre to
cover the beach with the aperiodic tiling.
You can help: come to the beach and we'll show you what to do.
Where and when?
Whitley Bay beach, 7th June 2026.
Come and join in, just watch, or talk to some very
enthusiastic mathematicians!
beachspectres.com
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