#mathober day 21: Prime Ring

One ring to contain them all,
one ring to identify them,
one ring to imply them all,
and in the domain bind them.

#mathober2026 #math #abstractalgebra

The PHP security team is giving advance notice of an upcoming security release scheduled for Wed, 21 October 2026 at 14:00 UTC, addresses two critical vulnerabilities, both rated CVSSv4 9.2.

All PHP users are encouraged to prepare so they can upgrade immediately tomorrow. Should details of the vulnerabilities become public, or should evidence of active exploitation appear we will release sooner.

Full details, affected versions, and the fixed versions will be published with the release.

#php

(reposting with alt text)

@pathunstrom A couple of years ago, I was brought in as a moderator to help de-fascist a community that had practically turned into 4chan, in one of the most fundamentally-abuse-attracting and difficult-to-moderate categories of community (privacy/security-related).

The policy was set as "no fascists, no alt-right, nothing that looks like it" and people would either get banned immediately (if clearly intentionally abusive) or get a warning otherwise that they were expected to take seriously (doubling down would be grounds for a ban). Every ban was permanent but revocable if someone showed genuine reflection and commitment to do better - this sometimes took minutes, sometimes months or even longer, sometimes never.

Randos complained for months. "You just call everyone a nazi", "how do you define fascist then", "you're being unreasonable", "the alt right aren't fascists", and so on, and so forth. Without exception, the ones complaining about it the most were the ones who already had a track prior record of being an asshole in different ways. A lot of the bans were the result of brigading attempts from, well, fascists who objected to being pushed out, pretending to be 'new users' and mysteriously immediately knowing about previous bans that happened before they joined.

It took a while, but they eventually gave up. The result was a pleasant community to be in, unusually pleasant for a privacy/security community. I haven't been around there for quite a while now, but my understanding is that it's still a nice place to this day.

"No fascists allowed" works, even under the worst conditions, and the "no, seriously, this is not up for debate, the moderator decides" is a critical component of making it work.

I'm dropping maintainership of the #tic80 nixpkgs package in protest to the maintainer's recent LLM usage in the project.

I'm not going to spend my free time updating the package each time an AI agent decides to make a new release.

Breaks my heart, though. </3

Is a #nixpkgs committer reading along who could approve/merge this PR? https://github.com/NixOS/nixpkgs/pull/576393

(Edit: Now in the merge queue, thanks, @pbsds!)

#mathober day 20: Nice Vector Field

What researching today's prompt feels like:

#mathober2026 #math #differentialgeometry

Did I just write almost 5000 words about why generative "AI" should be resisted, going through every single one of my reasons?

Yes. Because I need this article to exist so I can point people to it.

Enjoy and share widely.

https://estherweidauer.com/articles/why-resist-generative-ai.html

#mathober day 19: Orthic Triangle

find all heights of a triangle, connect their feet: orthic triangle

wear one as a child to straighten your teeth: orthodontic triangle

tool to help you find typos on a page of text: orthographic triangle

common bird classification system: ornithological triangle

seat profile that prevents hurting spines: orthopedic triangle

important doctrines after the great geometric schism: orthodox triangle

keyboard nerds love to type on these: ortholinear triangle

#mathober day 18: Biflecnodal Point

Still traveling, and deprioritizing making big drawings! So here's a haiku! :)

One inflection point
on top of a second one
that's a biflecnode!

#mathober2026 #math #algebraicgeometry

#mathober day 17: Dimension Invariance

A coffee cup is a donut
but certainly not
a napkin
even one with a hole.

No matter how hard you
squish and stretch
R^2 and R^3 can't ever be
homeomorphic.

#mathober2026 #math #algebraictopology

#mathober day 16: Isochronous Curve

There was a YouTuber called Murph
who let marbles race, and observe:
All of them, how sublime,
arrived at the same time
for the track was an isochrone curve.

#mathober2026 #math

#mathober day 15: Irredundant

Here's a game for you: Select some nodes from this graph, so that:

1. All nodes of the graph are either in your set or neighbors of your set (your set is "dominating"), and
2. You can't remove nodes from your set without losing that property (your set is "irredundant").

How small can you make your set? How big? Can you tell why?

#mathober2026 #math #graphtheory

#mathober day 14: Icositetragon

A 24-sided regular polygon, divided into 66 rhombs! Pop art style!

#mathober2026 #math #geometry

#mathober day 13: Standard Map

Imagine a 2D pendulum in zero gravity. Pick an initial angle and momentum. Then, at regular intervals, "kick" the end of the pendulum forward with strength sin(angle). This is a very simple system that exhibits chaotic behavior!

If you place a dot on a diagram after each kick according to the current angle (x-axis) and momentum (y-axis), you get the "standard map". Here is an artist's impression for kick-strength 0.971635!

#mathober2026 #math #chaostheory

I'm in #Mainz and #Wiesbaden for a week! Do I know people here who would show me the local hackspaces or other nerdy places? Also happy about any recommendations for good vegan food, or whatever else to see or do! :)

Obligatorisch: Das wichtige an funktionierende Software ist nicht der Code, sondern Organisation, Absicht und Vertrauen dahinter.

Und das fehlt bei den gesloppten Projekten halt in den allermeisten Fällen. Die werden gebaut für 5 Minutes of Fame. Dann ist der Dopamin Kick weg, und es würde nur extrem viel Arbeit warten

#mathober day 12: Reciprocal Prime Constant

Add up the reciprocals of all primes up to n. How far is this away from ln(ln(n)), as n gets large?

The plot of these two functions reminded me of a bridge. Can you find the constant being visualized here?

#mathober2026 #math #numbertheory

#mathober day 11: Problem of Points

Two players toss coins, and whoever wins 5 rounds first wins the entire pot. But: Someone interrupts the game as one player has won 3 rounds, and the other one 1. How should they split the pot now?

This problem motivated our modern probability theory and the concept of the "expected value".

Here's a "tree" diagram depicting the situation I described. Can you read from it how the players should split the pot?

#mathober2026 #math #probabilitytheory

#mathober day 10: Simple Pole

I learned a lot about complex analysis today! Here's one way to visualize the function f(z) = 1/z, where z is a complex number. The height represents the real part of the result, while the hue represents the "angle" of the complex number.

This particular function has a "pole" at the origin, where it blows up to infinity. It's "simple" (has order 1), because it's "only" a 1/z blow-up. I think a 1/z^2 blow-up would have order 2?

#mathober2026 #math #complexanalysis

In light of the recent news about the 3 dimensional aperiodic monotile (https://arxiv.org/pdf/2609.24779v1) Here an animation of the assembly of the rep-tile it is based on