Nathaniel Johnston

@njohnston.ca

361 Followers 124 Following

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

A screenshot of a math paper.
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.
The cover of the book "Conway's Game of Life: Mathematics and Construction"
An infinite still life in Conway's Game of Life, made up of alternating rows of alive and dead cells.
Three gliders colliding so as to create a lightweight spaceship in Conway's Game of Life.
The "phoenix 1" oscillator in Conway's Game of Life.
A screenshot of ChatGPT's method of finding the solution to problem A6: computing small values.
A screenshot of ChatGPT finding the correct solution to problem A6.
Problem A6 from the 2024 Putnam math competition, which asks for a formula for the determinant of a certain matrix.
A screenshot of ChatGPT writing several paragraphs of introductory text, most of which is irrelevant or unhelpful.
A screenshot of ChatGPT writing a gibberish proof.
A screenshot showing ChatGPT solving a problem via "experimentation with small cases".
Problem B1 from the 2024 Putnam math competition, which says "Let n and k be positive integers. The square in the i-th row and j-th column of an n-by-n grid contains the number i+j-k. For which n and k is it possible to select n squares from the grid, no two in the same row and column, such that the numbers contained in the selected squares are exactly 1, 2, ..., n?"
A screenshot of a Tweet that says someone instructed ChatGPT to act as though it's writing the Putnam competition, causing ChatGPT to write more "rigorous" solutions.
Problem B3 from the 2024 Putnam math competition, which says "Let r(n) be the n-th smallest positive solution to tan(x)=x, where the argument of tangent is in radians. Prove that 0 < r(n+1) - r(n) - pi < 1/((n^2+n)*pi) for n >= 1."
A screenshot of a Tweet claiming that OpenAI o1 scored between 80/120 and 90/120 on the Putnam math competition.
A screenshot of a Tweet claiming that OpenAI o1 scored in the top 1%-2% of participants in the Putnam math competition.
A screenshot of Overleaf recommending that I correct "How the hell to do this?" to "How else can we do this?"
A formula that says "0 if n is odd, 2^(2m-n) * (m choose n) * (n choose n/2) if n is even"
An alternating double sum of a product of 4 binomial coefficients.
A FoxTrot comic strip in which one character complains about not knowing how to solve a linear system, but when presented the exact same linear system in the context of shopping solves it immediately.
A screenshot of overleaf.com giving a "Error: Server Error" message.
The logo of the On-Line Encyclopedia of Integer Sequences.
The front cover of the book "The Mathematics of Cellular Automata" by Jane Hawkins.
A screenshot of a textbook page that describes how to solve semidefinite programs analytically by first solving them numerically, and then using the Inverse Symbolic Calculator to turn that numeric solution into an analytic one, which can then be verified via duality.