Nathaniel Johnston
@njohnston.ca
Associate Professor of Mathematics at Mount Allison University
Interested in quantum information theory, Conway's Game of Life, recreational mathematics, and mathematics pedagogy.
🔗 https://njohnston.ca/
▶️ https://www.youtube.com/@NathanielMath
Interested in quantum information theory, Conway's Game of Life, recreational mathematics, and mathematics pedagogy.
🔗 https://njohnston.ca/
▶️ https://www.youtube.com/@NathanielMath
Huge shout-out to authors who put humour, even very mild humour, in their papers. You keep me awake.
August 25, 2025 at 8:57 PM
Huge shout-out to authors who put humour, even very mild humour, in their papers. You keep me awake.
New paper published today! "A hierarchy of eigencomputations for polynomial optimization on the sphere", with Benjamin Lovitz: link.springer.com/article/10.1...
A hierarchy of eigencomputations for polynomial optimization on the sphere - Mathematical Programming
We introduce a convergent hierarchy of lower bounds on the minimum value of a real form over the unit sphere. The main practical advantage of our hierarchy over the real sum-of-squares (RSOS) hierarch...
link.springer.com
July 21, 2025 at 5:29 PM
New paper published today! "A hierarchy of eigencomputations for polynomial optimization on the sphere", with Benjamin Lovitz: link.springer.com/article/10.1...
New paper published today! "The factor width rank of a matrix", with Shirin Moein and Sarah Plosker: www.sciencedirect.com/science/arti...
The factor width rank of a matrix
A matrix is said to have factor width at most k if it can be written as a sum of positive semidefinite matrices that are non-zero only in a single k×k…
www.sciencedirect.com
April 3, 2025 at 12:48 PM
New paper published today! "The factor width rank of a matrix", with Shirin Moein and Sarah Plosker: www.sciencedirect.com/science/arti...
Happy belated pi day! Had a midterm in my Vector Calculus class yesterday, so I asked my students to compute some vector line integrals along pi: www.desmos.com/calculator/u...
#ITeachMath #MathsToday
#ITeachMath #MathsToday
Desmos | Graphing Calculator
www.desmos.com
March 15, 2025 at 3:25 PM
Happy belated pi day! Had a midterm in my Vector Calculus class yesterday, so I asked my students to compute some vector line integrals along pi: www.desmos.com/calculator/u...
#ITeachMath #MathsToday
#ITeachMath #MathsToday
Now, two months later, Musk says that "Grok 3 is becoming superhuman" because Grok 3 obtained just as good as solution (i.e., an absolutely terrible non-solution) to this Putnam problem. Unreal.
February 28, 2025 at 8:24 PM
Now, two months later, Musk says that "Grok 3 is becoming superhuman" because Grok 3 obtained just as good as solution (i.e., an absolutely terrible non-solution) to this Putnam problem. Unreal.
I'm teaching Vector Calculus this semester (for the first time, somehow!) and making lecture videos to accompany the course. The first video is now up, with about 3 per week planned (35 to 40 total): www.youtube.com/watch?v=VbDE...
The videos make huge use of @desmos.com
#ITeachMath #EduSky
The videos make huge use of @desmos.com
#ITeachMath #EduSky
Vector Calculus - Lecture 1: Paths and Curves
YouTube video by Nathaniel Johnston
www.youtube.com
January 8, 2025 at 12:43 PM
I'm teaching Vector Calculus this semester (for the first time, somehow!) and making lecture videos to accompany the course. The first video is now up, with about 3 per week planned (35 to 40 total): www.youtube.com/watch?v=VbDE...
The videos make huge use of @desmos.com
#ITeachMath #EduSky
The videos make huge use of @desmos.com
#ITeachMath #EduSky
Happy New Year! Just like every year, there were tons of fantastic discoveries and theorems proved in Conway's Game of Life in 2024. This is a thread for my three favourites (and the context behind them to try to convince you that they're interesting). 🧵
#MathSky
#MathSky
January 1, 2025 at 2:19 AM
Happy New Year! Just like every year, there were tons of fantastic discoveries and theorems proved in Conway's Game of Life in 2024. This is a thread for my three favourites (and the context behind them to try to convince you that they're interesting). 🧵
#MathSky
#MathSky
There's been a bunch of claims (mostly on X) that ChatGPT did great on this year's Putnam math competition. Let's do a thread to talk about it! 🧵
#MathSky
#MathSky
December 20, 2024 at 2:55 AM
There's been a bunch of claims (mostly on X) that ChatGPT did great on this year's Putnam math competition. Let's do a thread to talk about it! 🧵
#MathSky
#MathSky
Reposted by Nathaniel Johnston
It seems like a tradition is emerging here, and it is out duty to maintain it. So here is my part announcing the publication of our review in semidefinite programming for characterizing quantum correlations @dulwichquantum.bsky.social
journals.aps.org/rmp/abstract...
journals.aps.org/rmp/abstract...
December 14, 2024 at 4:07 PM
It seems like a tradition is emerging here, and it is out duty to maintain it. So here is my part announcing the publication of our review in semidefinite programming for characterizing quantum correlations @dulwichquantum.bsky.social
journals.aps.org/rmp/abstract...
journals.aps.org/rmp/abstract...
The Putnam math competition happened this past weekend! Made a video of how to work through question A1, which (not surprisingly) was the most "rote" of the bunch. I thought questions A6 and B1 were really neat too. #ITeachMath
www.youtube.com/watch?v=ccu-...
www.youtube.com/watch?v=ccu-...
2024 Putnam Math Competition - Question A1 - Solutions to 2a^n + 3b^n = 4c^n
YouTube video by Nathaniel Johnston
www.youtube.com
December 10, 2024 at 12:27 PM
The Putnam math competition happened this past weekend! Made a video of how to work through question A1, which (not surprisingly) was the most "rote" of the bunch. I thought questions A6 and B1 were really neat too. #ITeachMath
www.youtube.com/watch?v=ccu-...
www.youtube.com/watch?v=ccu-...
It looks like Overleaf's new AI writing tools don't like the notes that I make to myself while writing papers.
December 5, 2024 at 4:21 PM
It looks like Overleaf's new AI writing tools don't like the notes that I make to myself while writing papers.
Had a recent research project where we had to evaluate this hideous sum. Convolution to the rescue! Made a video to talk about how it works (or at least how some similar but simpler sums work):
www.youtube.com/watch?v=aIj6...
www.youtube.com/watch?v=aIj6...
December 5, 2024 at 11:40 AM
Had a recent research project where we had to evaluate this hideous sum. Convolution to the rescue! Made a video to talk about how it works (or at least how some similar but simpler sums work):
www.youtube.com/watch?v=aIj6...
www.youtube.com/watch?v=aIj6...
Overleaf's down, so I'm cancelling research for the day. Everyone go home and play Slay the Spire.
It is my honest opinion that Slay the Spire is one of the greatest games of all time. Greater than infinite replay value — it gets better the more you play.
And please don't say Balatro, that game is pretty good but not as good. Just my opinion.
And please don't say Balatro, that game is pretty good but not as good. Just my opinion.
December 3, 2024 at 2:41 PM
Overleaf's down, so I'm cancelling research for the day. Everyone go home and play Slay the Spire.
Me, a moron: I don't need a local TeX installation, Overleaf works so well and is so easy!
Overleaf: like every online service that exists, goes down from time to time.
Me: shocked Pikachu.
Overleaf: like every online service that exists, goes down from time to time.
Me: shocked Pikachu.
December 3, 2024 at 1:05 PM
Me, a moron: I don't need a local TeX installation, Overleaf works so well and is so easy!
Overleaf: like every online service that exists, goes down from time to time.
Me: shocked Pikachu.
Overleaf: like every online service that exists, goes down from time to time.
Me: shocked Pikachu.
There are lots of standard examples of binary operations that are associative but not commutative (e.g., matrix multiplication). But I don’t know of a better example of the opposite (i.e., commutative but not associative) than Infinite Craft: neal.fun/infinite-cra...
Infinite Craft
An endless crafting game
neal.fun
December 2, 2024 at 10:08 PM
There are lots of standard examples of binary operations that are associative but not commutative (e.g., matrix multiplication). But I don’t know of a better example of the opposite (i.e., commutative but not associative) than Infinite Craft: neal.fun/infinite-cra...
Having links to relevant lecture videos included in the margin of the lecture notes is one of the cooler things I’ve seen. Those are gorgeous.
If you're curious about quantum computing and want to learn the basics, check out the "Quantum Quest" created by me and Michael Walter!
www.quantum-quest.org/material
www.quantum-quest.org/material
The Quantum Quest - Material
www.quantum-quest.org
November 30, 2024 at 11:35 AM
Having links to relevant lecture videos included in the margin of the lecture notes is one of the cooler things I’ve seen. Those are gorgeous.
The On-Line Encyclopedia of Integer Sequences (OEIS) is hiring someone to manage the crazy number of sequences that it has to review. If you're a US resident with a math PhD, give it a look! Applications due Jan. 25, 2025.
neilsloane.com/doc/OEIS.ME....
neilsloane.com/doc/OEIS.ME....
November 25, 2024 at 6:33 PM
The On-Line Encyclopedia of Integer Sequences (OEIS) is hiring someone to manage the crazy number of sequences that it has to review. If you're a US resident with a math PhD, give it a look! Applications due Jan. 25, 2025.
neilsloane.com/doc/OEIS.ME....
neilsloane.com/doc/OEIS.ME....
I wrote a review of Jane Hawkins' new book "The Mathematics of Cellular Automata", which is now online.
tl;dr: It would be fun to teach a CA course from this book to students who have already taken Real Analysis.
www.tandfonline.com/doi/full/10....
tl;dr: It would be fun to teach a CA course from this book to students who have already taken Real Analysis.
www.tandfonline.com/doi/full/10....
November 25, 2024 at 12:18 PM
I wrote a review of Jane Hawkins' new book "The Mathematics of Cellular Automata", which is now online.
tl;dr: It would be fun to teach a CA course from this book to students who have already taken Real Analysis.
www.tandfonline.com/doi/full/10....
tl;dr: It would be fun to teach a CA course from this book to students who have already taken Real Analysis.
www.tandfonline.com/doi/full/10....
Fun fact: my advanced linear algebra textbook has a page about exactly this! Screenshot attached.
November 22, 2024 at 10:49 AM
Fun fact: my advanced linear algebra textbook has a page about exactly this! Screenshot attached.
Back making math videos! #ITeachMath #EduSky
I'm teaching calculus this semester, so I'm filling in some of the gaps in my calculus playlist. Animations made with #Manim.
www.youtube.com/watch?v=Afc4...
I'm teaching calculus this semester, so I'm filling in some of the gaps in my calculus playlist. Animations made with #Manim.
www.youtube.com/watch?v=Afc4...
Constrained optimization: how to find the maximal area of a Norman window
YouTube video by Nathaniel Johnston
www.youtube.com
November 21, 2024 at 2:51 PM
Back making math videos! #ITeachMath #EduSky
I'm teaching calculus this semester, so I'm filling in some of the gaps in my calculus playlist. Animations made with #Manim.
www.youtube.com/watch?v=Afc4...
I'm teaching calculus this semester, so I'm filling in some of the gaps in my calculus playlist. Animations made with #Manim.
www.youtube.com/watch?v=Afc4...
Reposted by Nathaniel Johnston
Little known fact: the Bloch Sphere is named after a famous Swedish physicist Felix Sphere.
November 20, 2024 at 10:08 PM
Little known fact: the Bloch Sphere is named after a famous Swedish physicist Felix Sphere.
What are everyone's favourite instructional and/or weird examples to illustrate how much weirder functions of 2 variables can be than functions of 1 variable? ♾️
I'll start with two of my favourites (1/3).
I'll start with two of my favourites (1/3).
November 20, 2024 at 1:36 PM
What are everyone's favourite instructional and/or weird examples to illustrate how much weirder functions of 2 variables can be than functions of 1 variable? ♾️
I'll start with two of my favourites (1/3).
I'll start with two of my favourites (1/3).
Does anyone on #MathSky / #ITeachMath have a favourite way to illustrate and/or motivate mixed 2nd partial derivatives of 2-variable functions?
November 18, 2024 at 10:55 AM
Does anyone on #MathSky / #ITeachMath have a favourite way to illustrate and/or motivate mixed 2nd partial derivatives of 2-variable functions?
Recent paper with Sarah Plosker about Laplacian integral graphs is now published! Open access: www.sciencedirect.com/science/arti...
Laplacian {−1,0,1}- and {−1,1}-diagonalizable graphs
A graph is called Laplacian integral if the eigenvalues of its Laplacian matrix are all integers. We investigate the subset of these graphs whose Lapl…
www.sciencedirect.com
November 17, 2024 at 11:43 PM
Recent paper with Sarah Plosker about Laplacian integral graphs is now published! Open access: www.sciencedirect.com/science/arti...