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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

105 Posts366 Follower124 Folgt
Nathaniel Johnston@njohnston.ca · 3w ago

It seems the rush to use ChatGPT Sol to solve all our open problems has hit quantum information theory. A problem from the field that has been open for 25 years was just solved 3 times, by 3 separate groups, in 2 days: arxiv.org/abs/2607.23416 arxiv.org/abs/2607.24309 arxiv.org/abs/2607.24479

A partial-trace matrix inequality and Werner-state distillability

Motivated by the equivalent partial-trace formulations of Werner-state distillability [P. Costa Rico, Lett. Math. Phys. 115, 47 (2025); S.-Y. Qi et al., Phys. Rev. A 110, 012406 (2024)], we prove a bi...

arxiv.org

Nathaniel Johnston@njohnston.ca · last mo.

New preprint with Sarah Plosker and my student, Luis Varona: "Enumeration of Laplacian integral and {-1,0,1}-diagonalizable graphs" (description in replies) arxiv.org/abs/2607.06336

Enumeration of Laplacian integral and {-1,0,1}-diagonalizable graphs

A graph with Laplacian matrix $L$ is called Laplacian integral if the eigenvalues of $L$ are all integers, and it is called $\{-1,0,1\}$-diagonalizable if $L$ has a full set of eigenvectors with entri...

arxiv.org

Nathaniel Johnston@njohnston.ca · last yr.

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

Nathaniel Johnston@njohnston.ca · last yr.

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.

Luis Batalha: None of the top 500 contestants in the 2025 Putnam competition fully solved this problem. Grok 3 (Think) found the solution in ~8 minutes. Elon Musk: Grok 3 is becoming superhuman.
Nathaniel Johnston@njohnston.ca · 2y ago

To see why this line of reasoning falls flat to me, let's look at its answer to this year's question A6. If you don't want to read the technical details of the question, all that really matters here is that the question asks you to compute a formula for something.

Problem A6 from the 2024 Putnam math competition, which asks for a formula for the determinant of a certain matrix.
Nathaniel Johnston@njohnston.ca · 2y ago

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

Nathaniel Johnston@njohnston.ca · 2y ago

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.

A screenshot of overleaf.com giving a "Error: Server Error" message.
Nathaniel Johnston@njohnston.ca · 2y ago

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).