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.
Reposted by Michael Kinyon
Quick explanation of what it feels like to learn more advanced #mathematics. Specifically, how do you answer the question
"How many intersections do two algebraic varieties have?"
You could probably do this with any math subject tbh...
#mathsky #maths #scisky
"How many intersections do two algebraic varieties have?"
You could probably do this with any math subject tbh...
#mathsky #maths #scisky
January 28, 2026 at 9:11 PM
Quick explanation of what it feels like to learn more advanced #mathematics. Specifically, how do you answer the question
"How many intersections do two algebraic varieties have?"
You could probably do this with any math subject tbh...
#mathsky #maths #scisky
"How many intersections do two algebraic varieties have?"
You could probably do this with any math subject tbh...
#mathsky #maths #scisky
When my advisor taught calculus, he used the Stieltjes integral whenever possible. For "substitution" or integration by parts, he refused to introduce new variables, he'd just move stuff past the d, e.g.,
\int x cos(x) dx = \int x d(sin(x)) = x sin(x) - \int sin(x) dx = x sin(x) + cos(x) + C
\int x cos(x) dx = \int x d(sin(x)) = x sin(x) - \int sin(x) dx = x sin(x) + cos(x) + C
I've learned recently from snooping on discussions about formalising explicit estimates in number theory that integration by parts
\\[ \int_a^b f'(x)g(x)dx = \big[f(b)g(b) - f(a)b(a)\big] - \int_a^b f(x)dg(x)\\]
can be done with a pair of functions \\(f,g\\) (on an interval in the reals, with […]
\\[ \int_a^b f'(x)g(x)dx = \big[f(b)g(b) - f(a)b(a)\big] - \int_a^b f(x)dg(x)\\]
can be done with a pair of functions \\(f,g\\) (on an interval in the reals, with […]
Original post on mathstodon.xyz
mathstodon.xyz
January 29, 2026 at 1:06 AM
When my advisor taught calculus, he used the Stieltjes integral whenever possible. For "substitution" or integration by parts, he refused to introduce new variables, he'd just move stuff past the d, e.g.,
\int x cos(x) dx = \int x d(sin(x)) = x sin(x) - \int sin(x) dx = x sin(x) + cos(x) + C
\int x cos(x) dx = \int x d(sin(x)) = x sin(x) - \int sin(x) dx = x sin(x) + cos(x) + C
Let p(n) denote the partition function, the number of ways of writing n as the sum of positive integers.
Heffernan-MacHale Conjecture: If p(n) divides n!, then
n ∈ { 1,2,3,7,9,10,11,12,14,15,16,17,18,19,20,21,24,28,32,33,39 }.
Verified for n ≤ 2x10^6. See oeis.org/A046668
Heffernan-MacHale Conjecture: If p(n) divides n!, then
n ∈ { 1,2,3,7,9,10,11,12,14,15,16,17,18,19,20,21,24,28,32,33,39 }.
Verified for n ≤ 2x10^6. See oeis.org/A046668
January 28, 2026 at 12:00 AM
Let p(n) denote the partition function, the number of ways of writing n as the sum of positive integers.
Heffernan-MacHale Conjecture: If p(n) divides n!, then
n ∈ { 1,2,3,7,9,10,11,12,14,15,16,17,18,19,20,21,24,28,32,33,39 }.
Verified for n ≤ 2x10^6. See oeis.org/A046668
Heffernan-MacHale Conjecture: If p(n) divides n!, then
n ∈ { 1,2,3,7,9,10,11,12,14,15,16,17,18,19,20,21,24,28,32,33,39 }.
Verified for n ≤ 2x10^6. See oeis.org/A046668
I'll let someone else write verses for analysis, topology, etc.
January 27, 2026 at 12:40 AM
I'll let someone else write verses for analysis, topology, etc.
Neugebauer on the purpose of historical studies
January 26, 2026 at 6:58 PM
Neugebauer on the purpose of historical studies
To all who teach matrices/linear algebra, I highly recommend vol. 24, issue 1 (Jan. 1993) of The College Mathematics Journal, a special issue dedicated to the teaching of linear algebra. Different ways of interpreting matrix multiplication is one of the themes of the issue.
Teaching matrix mult, noticed that I mentally pick up the rows in the first and align them with the columns in the second before multiplying and adding, realised that that is actually the wrong way round: it makes more sense to pick up the columns in the second and align with the rows in the first.
January 25, 2026 at 5:49 PM
To all who teach matrices/linear algebra, I highly recommend vol. 24, issue 1 (Jan. 1993) of The College Mathematics Journal, a special issue dedicated to the teaching of linear algebra. Different ways of interpreting matrix multiplication is one of the themes of the issue.
In a new file, I typed "Let", then was distracted by family and dog for several minutes. Now I am staring at the page and wondering what in the mathematical world I was going to let.
January 23, 2026 at 7:37 PM
In a new file, I typed "Let", then was distracted by family and dog for several minutes. Now I am staring at the page and wondering what in the mathematical world I was going to let.
AI Overview:
* Michael had a lot of work he was supposed to be doing but he instead spent time on Bluesky
* He will regret his choices but that will not be a new experience for him
* Michael had a lot of work he was supposed to be doing but he instead spent time on Bluesky
* He will regret his choices but that will not be a new experience for him
January 19, 2026 at 6:39 PM
AI Overview:
* Michael had a lot of work he was supposed to be doing but he instead spent time on Bluesky
* He will regret his choices but that will not be a new experience for him
* Michael had a lot of work he was supposed to be doing but he instead spent time on Bluesky
* He will regret his choices but that will not be a new experience for him
I finally found the file I was looking for. It was inside a subsubfolder named "April 23" which is inside a subfolder named "Sept 19", which is inside a folder named "Dec 17".
Which is exactly where you would expect the file to be, of course.
Which is exactly where you would expect the file to be, of course.
January 19, 2026 at 4:45 PM
I finally found the file I was looking for. It was inside a subsubfolder named "April 23" which is inside a subfolder named "Sept 19", which is inside a folder named "Dec 17".
Which is exactly where you would expect the file to be, of course.
Which is exactly where you would expect the file to be, of course.
Me, writing a grant proposal:
...because of a fruitful collaboration...
Wait, I already used "fruitful" two sentences earlier and it sounds better there. What are some synonyms for "fruitful"? How about:
...because of a fecund collaboration...
That sounds so awful that I'm tempted to use it
...because of a fruitful collaboration...
Wait, I already used "fruitful" two sentences earlier and it sounds better there. What are some synonyms for "fruitful"? How about:
...because of a fecund collaboration...
That sounds so awful that I'm tempted to use it
January 18, 2026 at 3:02 AM
Me, writing a grant proposal:
...because of a fruitful collaboration...
Wait, I already used "fruitful" two sentences earlier and it sounds better there. What are some synonyms for "fruitful"? How about:
...because of a fecund collaboration...
That sounds so awful that I'm tempted to use it
...because of a fruitful collaboration...
Wait, I already used "fruitful" two sentences earlier and it sounds better there. What are some synonyms for "fruitful"? How about:
...because of a fecund collaboration...
That sounds so awful that I'm tempted to use it
Usenet, specifically rec.arts.int-fiction
Okay, let's get nostalgic
What was the VERY FIRST online platform that you became addicted to posting on?????
What was the VERY FIRST online platform that you became addicted to posting on?????
January 16, 2026 at 11:37 PM
Usenet, specifically rec.arts.int-fiction
This grant agency's records say that my degree is a Doctor of Pharmacy. I didn't realize I was part of Big Pharma.
January 15, 2026 at 4:13 PM
This grant agency's records say that my degree is a Doctor of Pharmacy. I didn't realize I was part of Big Pharma.
"One Proof To Rule Them All is too much to ask" is a sentence I didn't think I would type in an email today but here we are.
January 13, 2026 at 9:06 PM
"One Proof To Rule Them All is too much to ask" is a sentence I didn't think I would type in an email today but here we are.
"The proof is well known and can be found in [3], but for the sake of completeness and to make this paper self-contained, we will plagiarize [3] here."
January 12, 2026 at 8:11 PM
"The proof is well known and can be found in [3], but for the sake of completeness and to make this paper self-contained, we will plagiarize [3] here."
"I turn with terror and horror from this lamentable scourge of continuous functions with no derivatives" -- Charles Hermite in a letter to Thomas Stieltjes, 20 May 1893
Nowhere differentiable functions have entered the chat
January 12, 2026 at 2:33 AM
"I turn with terror and horror from this lamentable scourge of continuous functions with no derivatives" -- Charles Hermite in a letter to Thomas Stieltjes, 20 May 1893
Everything is linear
In its own way
Cuz if you zoom in close enough
The curviness almost goes away
In its own way
Cuz if you zoom in close enough
The curviness almost goes away
January 12, 2026 at 2:04 AM
Everything is linear
In its own way
Cuz if you zoom in close enough
The curviness almost goes away
In its own way
Cuz if you zoom in close enough
The curviness almost goes away
And of course if you can add, subtract, divide by 2, and have a big enough table of squares, you can find any product you want: xy = ((x + y)^2 - x^2 - y^2)/2
In high school, I didn't realize we could actually use difference of two squares to help us with mental math. Here's how we can apply this.
January 10, 2026 at 5:51 PM
And of course if you can add, subtract, divide by 2, and have a big enough table of squares, you can find any product you want: xy = ((x + y)^2 - x^2 - y^2)/2
So strange to see Hilbert with hair and without his glasses
January 10, 2026 at 5:46 PM
So strange to see Hilbert with hair and without his glasses
I don't use Academia dot Edu (ugh!) but this bit in my junk mail happened to catch my eye just before I deleted it:
"On January 9, 2026, we'll be sunsetting the AI Assistant and transitioning back to the regular Academia . edu experience."
"On January 9, 2026, we'll be sunsetting the AI Assistant and transitioning back to the regular Academia . edu experience."
January 5, 2026 at 8:23 PM
I don't use Academia dot Edu (ugh!) but this bit in my junk mail happened to catch my eye just before I deleted it:
"On January 9, 2026, we'll be sunsetting the AI Assistant and transitioning back to the regular Academia . edu experience."
"On January 9, 2026, we'll be sunsetting the AI Assistant and transitioning back to the regular Academia . edu experience."
You can't have metempsychosis without psychosis
January 3, 2026 at 2:34 AM
You can't have metempsychosis without psychosis
Willy Wonka and the Chocolate Factory (1971).
I was 7.
The famous boat ride scene didn't bother me at all. I thought that part was funny. Rather, the scenes where the Bad Kids were getting their comeuppances were too intense for me.
I was 7.
The famous boat ride scene didn't bother me at all. I thought that part was funny. Rather, the scenes where the Bad Kids were getting their comeuppances were too intense for me.
Name 1 movie from your childhood you were way too young to watch.
December 29, 2025 at 1:30 AM
Willy Wonka and the Chocolate Factory (1971).
I was 7.
The famous boat ride scene didn't bother me at all. I thought that part was funny. Rather, the scenes where the Bad Kids were getting their comeuppances were too intense for me.
I was 7.
The famous boat ride scene didn't bother me at all. I thought that part was funny. Rather, the scenes where the Bad Kids were getting their comeuppances were too intense for me.
I really wanted a French monic baguette, but they were all out
December 25, 2025 at 4:46 PM
I really wanted a French monic baguette, but they were all out
Reading a paper citing work of mine from 2007. Every sentence of the author's summary has me responding "wait, what? I did?"
December 22, 2025 at 2:32 AM
Reading a paper citing work of mine from 2007. Every sentence of the author's summary has me responding "wait, what? I did?"
You're against the Pythagorean Theorem? How hyperbolic of you.
December 21, 2025 at 6:54 PM
You're against the Pythagorean Theorem? How hyperbolic of you.