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Math. Here’s a gem from Ramanujan relating pi, a natural logarithm, and the golden ratio. (Can you find the golden ratio?)

Math. Rubik's Cube for higher-dimensional aliens. By Tom Beddard, Tom Beddard, sub.blue, Used with permission.

Fractal are wondrous patterns or objects that echo themselves across size scales. Each fragment, when magnified, reveals the same essence as the whole—a self-similar symphony of form.

→ Your mind and consciousnesses in a nutshell. Credit: thehighestofthemountains.com/brainmaps.php. I didn’t upload this image to 𝕏. I’m pointing to an image residing in the 𝕏 stream of “nickyoungMD” (Jun 17, 2024).

→ Mathematics and the Mind. Credit: I didn’t upload this image to 𝕏. I’m pointing to an image residing in the 𝕏 stream of “Simon Kuestenmacher”, 𝕏 ID “simongerman600” (Jul 7, 2025).

Math, physics, geometry, architecture. This is mathematical physicist Roger Penrose, standing on floor with Penrose tiling. Source: tinyurl.com/ajw6dexd

I asked AI: "Given the current usage of Windows 10, along with current trends, how many people do you estimate will be using Windows 10 one year from now?" Grok: 120–150 million Gemini: 280–420 million ChatGPT: 350–500 million

In order to enroll my PC in the Extended Security Updates (ESU) program for Windows 10, using the $30 paid option, must my PC be logged into a Microsoft account instead of a local account to complete the enrollment? I asked 3 AIs for an answer: 1. Grok: YES. You'll need to sign

Math. This is an amusing coincidence. Gelfond's Constant.

Astronomy. Imagine the joy of explaining this image to Newton, Galileo, Copernicus, and Kepler. Nebula NGC 6357: Cathedral to Massive Stars. Source: apod.nasa.gov/apod/ap160327.…

Today, I asked Grok to draw an array of famous people. Here is the result. How many can you identify? How many are real people?

Math. Physics. Ripples. Waves. Propagation. By dave, beesandbombs.tumblr.com/post/164268518…, Used with permission.

Highway Humor. Highway Engineer Prank: The "zero-choice" interchange. By Randall Munroe, xkcd.com/253/, cc by-nc 2.5

Mathematics. Geometry. Tiling. "Nesting Kisrhombille Tessellation-Based Geometry and Forsythia Fractal." [Select image to reveal the full piece.] By John Greene, github.com/johnalexanderg…, Used with permission.

Math, Chess, and Beyond. Doesn't this illustration provoke the imagination? Source: C. D. A. Evans and Joel David Hamkins, "Transfinite game values in infinite chess," arxiv.org/abs/1302.4377

Math. Shiver. 7 is the only prime number that is followed by a cube number.

Math. This is an example of a paper loaded with impressive-looking formulations. → What paper can you find that is loaded with even more impressive symbols and formulations? Source: logicandanalysis.org/index.php/jla/…, CC BY 3.0

Physics, mathematics, science, history. "Everything is interesting if you go into it deeply enough." ~American physicist Richard Feynman (1918–1988), Omni interview, "The Smartest Man in the World" (1979)

Physics. Mathematics. Reality. Universe. Stephen Wolfram's "Theory of Everything" is free online, as a 448-page PDF. Here is a sample figure, to intrigue you (p. 31). Source: arxiv.org/abs/2004.08210

The year is 1887. I like this figure from "Report on the Radiolaria" because it has a strong mathematical resonance. The creatures' shapes, radial symmetry, and intricate lattice-like structures mirror mathematical concepts like polyhedra, fractals, or tessellations. Art and