iiinova — where your digital self keeps evolving

Henry Segerman @henryseg.bsky.social · 12h

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 · 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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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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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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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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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 biting an apple. 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

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 · 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

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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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 🧪

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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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Zeno Rogue @zenorogue.bsky.social · 13/02/2026

HyperRogue is now verified for SteamDeck! ✅ A perfect game/platform match: mostly only movement so no need for complex buttons, joystick is good for its non-Euclidean movement directions, bigger screen and more powerful hardware are a better fit for infinity than phones. #roguelike #steamdeck

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Dr. Martin Skrodzki @msmathcomp.bsky.social · 11/02/2026

Things have been rather busy at the #illustratingMath trimester at the Institut Henri Poincaré for the last two weeks. A number of illustration projects have been started. I'll share some highlights in this thread. (1/6)

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Henry Segerman @henryseg.bsky.social · 24/01/2026

Earlier this week I was challenged to come up with a mechanism that would illustrate the duality of the cube and the octahedron. I got as far as making this animation before discovering that I was scooped three months ago!

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Susan Goldstine @sgoldstine.bsky.social · 11/01/2026

#mathart #mathknitting #JMM2026 This year, the math art exhibition at the Joint Mathematics Meetings invited me to be a featured artist, giving me the chance to assemble this mini-retrospective of my knitted and beaded work. Links to the catalog entries are in the following posts. 🧶 #knitsky ☺️

My featured-artist display at JMM 2026 in Washington DC. Four of the works are hanging on a zig-zag of beige, custom-cut mats, and the fifth is on three black jewelry stands. All pieces were accepted into one or more juried exhibits at JMM or Bridges in the past decade. The blue knitted wall hanging, second from the left, is the solo piece that was accepted into this year’s exhibition.

A closer view of the first two panels of the folded mat backing. The three pieces were 28 inches tall and 14, 28, and 28 inches wide, which is bigger than it sounds when you’re carrying them.

On the left is Fundamental Frieze Scroll II from 2018, a tan knitted wall hanging which was the precursor for the new piece to its right. That new piece, The Fundamentals of Lace, is knitted in blue on smaller needles but is both wider and taller than the older work. Both wall hangings are composed of the same fundamental region, a small lace motif in a lambda or Y shape, and both have colored beads embedded in the fabric to mark the symmetries. For more details, go to the following post for the online catalog links.

A close up of the rightmost mat panel and the jewelry set. As before, for more details you can follow the catalog links in the following posts.

The last mat panel has two knitting wall hangings suspended from pins at the top of the panel. To the left is Float Free, Bumblebee, a wall hanging in two-color mosaic knitting with yellow and black yarn. Like the two pieces in the previous photo, the knitted fabric is rectangular and lashed to dowels at the top and bottom. The fabric is divided into horizontal and vertical strips with different repeating abstract designs.

On the right of the mat is Redistribution, a wall hanging that has the overall shape of an hourglass whose top segment is shorter than the bottom segment. The upper portion is fan-shaped, with a network of dark purple stitches over a background of pale green stitches. The lower portion is flared like a trumpet and juts away from the wall, with a network of light purple stitches on a background of dark green.

To the right of the folding backdrop is Map Coloring Jewelry Set, the oldest artwork in this display. A bead crocheted necklace with pendant, a bead crocheted bracelet, and bead woven earrings in eight matte colors with gold accents hang on a black necklace form and black bracelet and earring stands. This jewelry set won a prize in the JMM 2015 exhibit, and now and then, I still wear it.

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Sylvie Benzoni-Gavage @gavagesylvie.bsky.social · 08/01/2026

A grand piano, a concrete mixer, an overhead projector, and an eclectic selection of mathematical objects. 🤩 @cirm-math.bsky.social #illustratingMath

$Mathematical objects (polyhedra, fractals, hyperbolic surfaces, etc.) on a grand piano under a black cover. In the background: an overhead projector, ventilation grids, the bottom of a screen and of a blackboard. Behind the picture window, a concrete mixer next to a low wall that is being built.$

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Dr. Martin Skrodzki @msmathcomp.bsky.social · 04/01/2026

🚨The call for submissions for this year's @BridgesMathart conference is out: www.bridgesmathart.org/b2026/bridge.... Regular papers: 1 February Short paper: 1 March Workshop papers: 1 March Artworks: 15 March Math + Fashion Show: 15 April Short Film Festival: 09 May Family Day: 15 June

bridgesmathart.org

Bridges 2026 Call for Submissions – The Bridges Organization

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Henry Segerman @henryseg.bsky.social · 30/12/2025

New video out just now, on a mechanism that uses racks and gears to expand and contract, this time in all three dimensions! youtu.be/NEJZlGuWGV8

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Henry Segerman @henryseg.bsky.social · 20/11/2025

The OSU Museum of Art is in a beautiful old building that used to be a post office. They have a small but heavily-fortified room that used to be a safe. Not such a great location to view paintings, but will work nicely for light-based sculpture, like "(5,3,2) triangle tiling", by @saulsch and me.

A doorway into the safe, with a pattern of light and shadow visible inside.

A 3D-printed sphere is patterned with triangular holes. It casts shadows onto the wall.

Closeup of the 3D printed sphere. It is mounted on a pipe coming down from the ceiling, which also holds an LED light.

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Dave Richeson @divbyzero.bsky.social · 09/11/2025

Giant cardioid: version 2.5. Version 1.0 was made using Pex tubing and grommet tape. Version 2.0 was made from laser-cut pieces. The wood was too fragile, and it broke during construction. In version 2.5, I made the pieces wider and I used thicker wood. Success, I'd say! The diameter is about 5 ft.

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Alison Martin @alisonmartin57.bsky.social · 06/11/2025

Understanding geometry through model making

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robertfathauer.bsky.social @robertfathauer.bsky.social · 05/11/2025

Everyone is invited to attend the SCULPT 2025: Show & Tell, a digital gathering that celebrates creative exploration across art, geometry, design, and fabrication. Date: Friday, November 7, 2025 Time: 8:00 – 10:30 AM (PST) Zoom Link: cca.zoom.us/j/9826107944...

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Dave Richeson @divbyzero.bsky.social · 10/10/2025

There's a nice article by Siobhan Roberts about the Bridges 2025 conference in Eindhoven in the NY Times. I can now say that I am in The NY Times! (A photo credit for the shot of Chaim Goodman-Strauss and Edmund Harriss,... but still!) www.nytimes.com/2025/10/10/s...

nytimes.com

Every Artist Has a Favorite Subject. For Some, That’s Math.

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Dr. Martin Skrodzki @msmathcomp.bsky.social · 06/10/2025

The #illustratingMath Seminar Online returns on Friday, October 10th, 9 am Pacific / 12 pm Eastern / 6 pm Europe. @3blue1brown.com will be "Exploring Zeta Function Visualizations." Gabriel and Jim will provide some "Show and Ask" input. See you online on Friday!

A dark-themed event poster titled "EXPLORING ZETA FUNCTION VISUALIZATIONS." The poster includes an abstract about visualizing the Riemann Zeta function. A colorful, three-dimensional plot of a mathematical function dominates the right side. The bottom features a circular photo of the presenter, Grant Sanderson from 3Blue1Brown. The event is scheduled for Friday, October 10, with times listed, and will be held on Zoom.

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robertfathauer.bsky.social @robertfathauer.bsky.social · 25/09/2025

Submissions are now being accepted for the Exhibition of Mathematical Art to be held as part of the Joint Mathematics Meetings, Washington, DC, in January of 2026. Apply online through October 15 at gallery.bridgesmathart.org. pic.x.com/MGSEyexSzo

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Henry Segerman @henryseg.bsky.social · 24/09/2025

New dice from The Dice Lab (me and Robert Fathauer), which may (?) be useful if you regularly write equations. youtube.com/shorts/fgMox...

Dice with greek letters on the faces, on a sheet of paper with a very long equation on it.

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Henry Segerman @henryseg.bsky.social · 14/09/2025

This image (made with Saul Schleimer) shows two different ways to approximate the Cannon-Thurston map associated to the figure-eight knot. Cannon-Thurston maps are space-filling curves, a bit like the Hilbert curve except that these fill a sphere rather than a square.

A very squiggly black curve on a sphere. The sphere is divided into green and purple regions by a less squiggly, but more sphere-filling curve.

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robertfathauer.bsky.social @robertfathauer.bsky.social · 05/09/2025

Submissions are now being accepted through September 14 for SCULPT 2025. Accepted work will be presented in a ZOOM Show and Tell event on November 7. In addition, works will be digitally showcased in the exhibition section of SCULPT 2025 and in a proceedings volume.

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Dr. Martin Skrodzki @msmathcomp.bsky.social · 13/08/2025

Starting the #illustratingMath talks at the @icerm.bsky.social today is Elliot Kienzle, who aims to settle the question how "To draw a torus." Like all good answers, his is based on differential geometry, taking the geometry of the torus into account when drawing. And Escher's there, too😄

A person is giving a talk, with a split screen showing them and a slide with a hand-drawn diagram of a perfectly smooth torus with the title "The Perfect torus?".

A split screen shows a person presenting and a slide with a hand-drawn diagram illustrating the difference between "Mathematical Precision" and "Mathematical Imprecision" when constructing a torus.

A split screen shows a speaker and a slide with a hand-drawn diagram explaining the "Gauss map/Normal map," using a torus and a sphere to illustrate the concept.

A person presents with a split screen, showing them and a slide with a sketch of M.C. Escher's "Hand with Reflecting Sphere" and the word "Torus" written below it.

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