iiinova — where your digital self keeps evolving

Michael Kinyon @profkinyon.bsky.social · 26/08/2026

Preparing talk slides. I haven't used this one in a while.

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Michael Kinyon @profkinyon.bsky.social · 03/08/2026

I hate it when my fellow academics talk like this to bright, eager students and actually mean it

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Michael Kinyon @profkinyon.bsky.social · 19/06/2026

I seem to be in the weights. Mistral 3.2 hallucinated that I am a former Republican mayor of Provo, Utah.

MICHAEL KINYON
MATHEMATICIAN SPECIALIZING IN QUASIGROUPS
> 354 STRENGTH * TOP 15% <
GPT-5.5 SAYS
AMERICAN MATHEMATICIAN KNOWN FOR WORK IN NONASSOCIATIVE ALGEBRA, QUASIGROUPS, LOOPS AND RELATED ALGEBRAIC STRUCTURES

followed by a bar graph featuring how much I show up (I guess) in a list of various LLMs.

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Michael Kinyon @profkinyon.bsky.social · 03/06/2026

I had no idea the "NP vs P" problem was settled three years ago. (shoutout to @lukasmathgraf.bsky.social for spotting this)

screenshot of a webpage for a Springer-published book called "Pedigree Polytopes" by Tirukkattuppalli Subramanyam Arthanari. It alleges to have settled the "P vs NP" problem.

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Michael Kinyon @profkinyon.bsky.social · 17/05/2026

Chilling on the back porch. Literally, because the weather is rapidly cooling off

A stunningly handsome 62 year old man with silver hair and matching Columbia jacket. He has large round glasses. The background is a baby blue exterior wall.

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Michael Kinyon @profkinyon.bsky.social · 14/05/2026

Out of idle curiosity, I asked Google's Gemini to try to humanize a proof generated by an automated theorem prover. In short, it didn't do very well. But, uh, this bit was interesting...

A Note on the Algebraic Structure

Since you are Michael Kinyon, you'll recognize this specific identity is essentially probing the autotopism group of the loop...

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Michael Kinyon @profkinyon.bsky.social · 11/05/2026

My friend and coauthor Des MacHale sent me a copy of his book (coauthored with Yvonne Cohen) _New Light on George Boole_ (2018). I am looking forward to reading it.

A stunningly handsome 62 year old man with blue eyes, silver hair, large round glasses and a green shirt, holding a mostly blue book entitled "New Light on George Boole". In the background are some messy bookshelves.

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Michael Kinyon @profkinyon.bsky.social · 26/04/2026

Film you've watched more than six times with a gif. Hard mode: no Star Trek, Star Wars, LOTR, DC, Marvel, Disney, Pixar, Spielberg, Cameron, Wachowskis, or Ghibli.

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Michael Kinyon @profkinyon.bsky.social · 15/04/2026

Check out the Schediphone. No idea what it would sound like.

Picture of a Schediphone, a rare brass instrument with two bells.

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Michael Kinyon @profkinyon.bsky.social · 08/04/2026

Helping my beleaguered undergrads get used to mathematical obnoxiousness

Snippet reading:
From this, it is ``easy to see'' (can you?)

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Michael Kinyon @profkinyon.bsky.social · 05/04/2026

Me, preparing for full cognitive surrender

Head shot of a grinning, incredibly good looking 62 year old man with short, silver hair and slightly tinted, round, wire-rimmed glasses.

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Michael Kinyon @profkinyon.bsky.social · 27/03/2026

Here is another version I found on reddit. It is probably made by the same elevator company. This one is a little clearer.

Elevator sign. Upper left shows icons for a man and a woman and says "8 MAX" but the wording is on its side. There is a no smoking icon in the lower left. In the lower right is a fire icon and a crossed out person. In the upper right are icons for an adult and a child, and a crossed out icon for an unaccompanied child. The bottom of the sign indicates room numbers on the various floors.

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Michael Kinyon @profkinyon.bsky.social · 25/03/2026

Strawberry Fields forever

$Blackboard bold F sub q (the field of order q) in WildStrawberry color. Generated by the following code: \documentclass[12pt]{amsart} \usepackage{amssymb} \usepackage[dvipsnames]{xcolor} \begin{document} \Huge \[ \color{WildStrawberry}\mathbb{F}_q \] \end{document}$

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Michael Kinyon @profkinyon.bsky.social · 18/03/2026

Source: R. Asera, _Calculus and Community: A History of the Emerging Scholars Program_, A Report of the National Task Force on Minority High Achievement, The College Board, May 2001, p. 12.

I recognized that mathematics is hard. I understood that math is highly condensed thought. But I liked math; I had personally spent hundreds of hours learning mathematics on my own, and I understood something about intensifying the experience, and about motivation. If students didn't have experience coming in, we could intensify their experience, but they needed a lot of time. People who did math on their own outside of class could outperform those who only did what was assigned in class. -- Uri Treisman, Professor of Mathematics and Director, Charles A. Dana Center, the University of Texas at Austin

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Michael Kinyon @profkinyon.bsky.social · 06/03/2026

You're trapped in the last TV show you watched. Where are you?

A scene from Natsume's Book of Friends where he, with his back to us, is hanging out at a sake party with a bunch of yōkai.

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Michael Kinyon @profkinyon.bsky.social · 03/03/2026

Witness the Blood Moon's rise. When its red glow shines upon the land... the aimless spirits of slain monsters return to flesh

A photo of the March 3 2026 lunar eclipse, aka, a blood moon

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Michael Kinyon @profkinyon.bsky.social · 01/03/2026

$Very early in our mathematical education - in fact in junior high school or in high school itself - we are introduced to polynomials. For a seemingly endless amount of time we are drilled, to the point of utter boredom, in factoring them, multiplying them, dividing them, simplifying them. Facility in factoring a quadratic becomes confused with genuine mathematical talent. -- I. Herstein, \emph{Topics in Algebra}, 2nd ed. (1975), p. 153$

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Michael Kinyon @profkinyon.bsky.social · 20/02/2026

Inspired by this, I asked for a very long sentence without the letter L. As you can see, the AI successfully wrote a gender neutral sentence satisfying the constraints, and... uh... oh.

Gemini's response:

Here is a very long sentence that does not use the letter L:
"If a person wants to win at this game, he must be sure to avoid every word with that common mark, even when it might seem tough or very hard to do so; for instance, he can try to speak of a bright sun, a red dog, or a deep pit, but he cannot ever mention a light, a yellow bird, or a small hill, as doing so would cause him to lose his status as a master of this craft."
Key Constraints Observed:
No "L": Words like "light," "look," "little," or "long" (the word itself contains an L) were carefully excluded.

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Michael Kinyon @profkinyon.bsky.social · 14/02/2026

I usually don't have any obstruction to lifting a map, it's folding it back up that's challenging.

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Michael Kinyon @profkinyon.bsky.social · 07/02/2026

Poof by (electrostatic) induction

Blue-eyed cat whose hair is standing up in all directions because of static electricity

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Michael Kinyon @profkinyon.bsky.social · 29/01/2026

The associate dean just sent around a message asking if anyone still uses clickers in classrooms. My brain immediately went to one particular kind of clicker, briefly wondering how anyone would use one in a mathematics class.

An image of a clicker from _The Last of Us_ games. A clicker is a particular type of infected enemy in the game. They find their way by echolocation, hence their name.

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Michael Kinyon @profkinyon.bsky.social · 27/01/2026

I'll let someone else write verses for analysis, topology, etc.

A Math Major's Lament

Groups and rings and finite fields
The dizzy dancing way I feel
When I consider prime ideals
Algebra seems like play

But now the term is almost done
I'll go outside and see the sun
And forget all the math I've done
It will all drift away

I've looked at math from both sides now
Compute and prove
But still somehow
There is no theorem I recall
I really don't know math at all

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Michael Kinyon @profkinyon.bsky.social · 26/01/2026

Neugebauer on the purpose of historical studies

$I do not consider it as the goal of historical writing to condense the complexity of historical processes into some kind of ``digest" or ``synthesis". On the contrary, I see the main purpose of historical studies in the unfolding of the stupendous wealth of phenomena which are connected with any phase of human history and thus to counteract the natural tendency toward oversimplification and philosophical constructions which are the faithful companions of ignorance. -- Otto Neugebauer, \emph{The Exact Sciences in Antiquity}, 2nd ed., Appendix II, {\S}84$

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Michael Kinyon @profkinyon.bsky.social · 25/12/2025

I really wanted a French monic baguette, but they were all out

A piece of a receipt that says "French Epi Baguette"

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Michael Kinyon @profkinyon.bsky.social · 18/12/2025

For the homologically minded, another Elf on a Shelf thing. (attn @courtneygibbons.phd )

An Introduction to Homological Algebra by Charles Weibel
sitting on top of the New English Bible
on top of a red tablecloth with a floral pattern

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Michael Kinyon @profkinyon.bsky.social · 18/12/2025

You've heard of Elf on a Shelf. Now get ready for

A golden shield with "GF(p^n)" in the center of it in black

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Michael Kinyon @profkinyon.bsky.social · 17/12/2025

What I've learned from AI is that if you are going to be wrong, do so with an authoritative tone.

$search prompt: centralizer of an element of a symmetric group snippet of response: Example: g = (1,2)(3,4,5) in S_5 * Cycle Type: 2^1 3^1 (one 2-cycle, one 3-cycle) * Z Factors: Z_1 (for the single 2-cycle) x Z_1 (for the single 3-cycle) * S factors: S_1 (for the single 2-cycle) x S_1 (for the single 3-cycle) * Result: C_{S_5}(g)\equiv Z_1 x Z_1 x S_1 x S_1 = {e}, the trivial group (only the identity) because there are no cycles to permute or power. Example: g = (1,2)(3,4) in S_4 * Cycle Type: 2^2 (two 2-cycles) * Z Factors: Z_2 (for the two 2-cycle, think powers of (1,2) and (3,4) * S factors: S_2 (permuting the two 2-cycles, e.g., swapping (1,2) and (3,4)) * Result: C_{S_4}(g)\equiv Z_2 x S_2 (order 2x2=4), which includes e,(1,2),(3,4),(1,2)(3,4) and elements like (1,3)(2,4)$

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Michael Kinyon @profkinyon.bsky.social · 16/12/2025

One Ring to rule them all, One Ring to find them, One Ring to bring them all and in the darkness bind them

$\mathbb{Z}[x_1,\ldots,x_n]$

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Michael Kinyon @profkinyon.bsky.social · 12/12/2025

Brazil, where hearts were entertaining June We stood beneath an amber moon And softly murmured "someday soon."

Snippet of a google search
The question was: is i^i real
Google's response (under "All", not the AI's response):
(i^i) Brazil real =
0.2.7879576 Brazil reais

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Michael Kinyon @profkinyon.bsky.social · 22/11/2025

I hope my coauthor shares my optimism.

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Michael Kinyon @profkinyon.bsky.social · 08/09/2025

One of these things is not like the others, WolframAlpha

(In response to "plot arcsec(|x|)")
Related Queries
plot ln|sec^(-1)(abs(x))|
plot 1/sec^(-1)(abs(x))
invert colors image of sec^(-1)(abs(x))
how many people die every day vs how many people are born every day
series sec^(-1)(abs(x))

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Michael Kinyon @profkinyon.bsky.social · 21/06/2025

I just hope it's also injectivtive so then it would be bijectivtive. (I probably made this typo, but I'm still going to blame my coauthor.)

$Hence $\phi$ is surjectivtive [sic]$

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Michael Kinyon @profkinyon.bsky.social · 10/06/2025

It's also fun to discuss nonconvex quadrilaterals. Showing them to students and pointing out that they still satisfy the definition of quadrilateral can be mind opening for them. We had an especially good discussion of how one precisely defines "convex".

A nonconvex quadrilateral which roughly has a V-shape. (Created with GeoGebra)

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Michael Kinyon @profkinyon.bsky.social · 04/06/2025

If you're the type of mathematics teacher who likes to give exercises requiring exact values of trig functions, but is bored with the old 30°-45°-60° grind, then the Ailles rectangle may be for you! (Seriously, this thing is why I can write down sin(15°), cos(75°) etc without using identities.)

The Ailles rectangle, a drawing of a rectangle with a 45°-45°-90° triangle inscribed in it. All sides are labeled with their lengths. Besides the "usual" values of trig functions, one can see the values of, for example, sin(15°) just by taking ratios. For more information, see:

https://en.wikipedia.org/wiki/Ailles_rectangle

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Michael Kinyon @profkinyon.bsky.social · 31/05/2025

One reason my back often hurts is that someone won't allow me to push my chair closer to my desk

A top view of my blue merle Australian shepherd Rusalka sleeping on the floor in front of my chair

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Michael Kinyon @profkinyon.bsky.social · 29/05/2025

My students have accused me of having boring title slides so here is what I am using today.

Title: Ph'nglui mglw'nafh Cthulhu R'lyeh wgah'nagl fhtagn
MATH 3400
29 May 2025

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Michael Kinyon @profkinyon.bsky.social · 25/05/2025

We are visiting eastern Utah for the long weekend. This is the Great Hunt, a petroglyph located in Nine Mile Canyon. It is believed to have been created by the Fremont people (ca 950-1200 CE). The depicted animals are bighorn sheep, probably during the fall mating season.

A petroglyph on red rock. It depicts several stylized big horn sheep interspersed by hunters with bow and arrow. The top central figure is a typical Fremont trapezoid shaped human with horns.

For more information:

https://www.nps.gov/places/great-hunt-panel-site.htm

https://www.gjhikes.com/2014/01/great-hunt-panel_3.html

https://trustlands.utah.gov/stewardship-project/great-hunt-panel-site-protection/

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Michael Kinyon @profkinyon.bsky.social · 22/05/2025

Remember that if you want to stretch terminology in a mathematics book or paper, you are allowed to do so if you announce your intentions in French.

Definition. With the above notation acute angles XPQ and X'PQ are called *angles of parallelism* for segment PQ. Lobachevsky denoted their congruence class [or, par abus de langage, any angle congruent to them] by Pi(PQ).
(I have underlined the French phrase in red.)

From M.J. Greenberg, _Euclidean and non-Euclidean geometries: development and history_, 4th ed., W.J. Freeman, 2008, p. 260

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