Welcome to the 252nd Carnival of Mathematics! This post brings together submissions and other posts from the mathy web. Thanks all for participating.
Let's start with the number: 252
- Divisors: 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252
- Prime factorization: 252 = 2² × 3² × 7
- 36 weeks = 252 days
- From Wikipedia 252 is:
- a practical number
- a refactorable number
- a hexagonal pyramidal number
- in the Mian-Chowla sequence
- the number of points on the surface of a cuboctahedron of radius five in the face-centered cubic lattice
- "252 is the standard assumption for number of trading days per year. 52 weeks*5 days/week, minus a few holidays." - Aaron Soley
- "There are 252 unique ways of selecting 4 different squares from a 4x4 square grid equivalent under rotations and reflections." - Foldster
- There are 252 ways to choose 5 from 10 (play here):
Pages and Posts
Visually Beautiful & Creative Math
- Turtles and polynomials — Math is a Creative Space dives into math with beautiful animations and visuals
- 3-body problem fractal — Non-Euclidean dreamer creates a mesmerizing fractal from physics.
- Polyhedra inside polyhedra — PolyhedronGuy handcrafted a series of nested polyhedra
- From Pentagons to Pentagrams — The Azimuth blog
- The Great Icosahedron — The Azimuth blog
- I Found a Seashell in the Middle of the Desert — Hawzen made a tool to model sea shells with code and explanation.
- Mucking about with Riley's shift — John Golden explores playful mathematics.
- Red and Black Knights — Numberphile.
- Rubik's Cube and Ridiculous Numbers — Numberphile explores the mathematics of permutation puzzles.
- OEIS A395531 — A new sequence just added! Christian Lawson-Perfect posts about it on Mathstodon with discussion.
Deep dives and open problems
- Easy Random Trees — Rigorous Nonsense explores Catalan numbers and random tree generation using Richard P. Stanley's book Catalan Numbers.
- Sigma Algebra vs Topology: Epic Smackdown — A face-off between two fundamental structures.
- The Unsolved Lollipop Problem — Numberphile investigates a deceptively simple problem.
- Cotes Harmonic Means Theorem in Geometry — Theorem of the Day features this elegant result.
- Inverse Cube Force Law — The Azimuth blog on quantum mechanics and forces.
- Freiman's Constant — The Azimuth blog explores a constant from additive combinatorics.
- The Spectrum of the Rainbow and the Benefits of Blue Sky Research — ThatsMaths on why fundamental research matters.
- Calendar Problems — Karen Campe shares monthly puzzles.
- Newton Diameters — John D. Cook on a classical tool in algebraic geometry.
- Two Researchers Are Rebuilding Mathematics from the Ground Up — Quanta Magazine on foundational work in topology.
The Journey, Not Just the Destination
- Math Moments — Amanda Hinton's reflective post.
- Mathematical Memoirs: The Transversal Invariant — Eric Asaah shares a window into how mathematics happens:
"I wrote this more like a mathematical memoir than a formal paper because I wanted to preserve the actual process: the wrong turns, the lazy shortcuts, the pattern hunting, the visual confusion, and the moment where the structure suddenly became obvious. The final result gives a very fast invariant filter for a class of SAT parallel-transversal problems, but honestly the interesting part for me was watching a routine exam question slowly turn into something structural."
LLMs & Mathematics
- Did AI Just "Solve" Math?(youTube link) — Cal Newport investigates the hype and reality.
- A Recent Experience with ChatGPT 5.5 Pro — Gower's Weblog reflects on LLMs in academic settings
- Who Verifies the Verifier? — Alex Korbonits
- Happy 2026 Women in Maths Day! — Plus.Maths celebrates women mathematicians.
- My Hundred Friends Campaign: Update #1 — Natural Maths shares progress on an exciting book.
- Mathematics for Ladies: Poems on Women in Science — Mathateca's +Resource Blog reviews Jessy Randall's collection with poetry snippets.
- Double Maths First Thing: Issue 5A
- Talking Maths in… Coventry Transport Museum
- Formalizing Fermat workshop — Xena invites the community to formalize Fermat's Last Theorem in Lean.
Posts with some History
And to close this post, I'd like to thank Joe Crawford and Mike Kupietz for making fractal kitty animations! (Mike's is here with many colors)
See the Pen Fractal Kitty Experiment by Joe Crawford (@artlung) on CodePen.