Michael Kinyon

@profkinyon.bsky.social

Mathematics professor at the University of Denver. Quasigroups, Semigroups, Automated Deduction. He/Him. Occasionally drop in at Mathstodon, but not as much as I used to.

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.

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.

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.

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...

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.

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

The elephant bird from Horton Hatches an Egg

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

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

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.

$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}$

$\rightsquigarrow$

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

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.

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

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

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.

A gif of a guy with a red jacket against a black background, struggling to refold a foldable map

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

Front cover of the original 2016 edition of the book "Are Numbers Real?" by Brian Clegg, subtitled "The Uncanny Relationship of Mathematics and the Physical World". There is also a review blurb at the bottom of the cover; I will spare you and myself from that.

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.

Elmo from Sesame Street saying "Rocco's just a rock!"

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

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

A parody of Michaelangelo's "Creation of Adam" where Adam is holding a coffee pot and pouring coffee into a cup held by God.

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

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

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

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

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

A unbelievably handsome man with unkempt silver hair and glasses, next to a merle Australian shepherd

Picture of classic Universal Studios monsters: the Mummy, the Invisible Man, Dracula, Creature from the Black Lagoon, the Phantom of the Opera, Frankenstein's monster, the Bride of Frankenstein, the Wolfman.

On Dracula's chest, there is an upside down A.

Pennywise with a backwards E on his forehead

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

Image generated by skircle.me consisting of the avatars of those with whom I have had some interaction. It has some overlap with the skycle version, but they are not identical.

(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))

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