So apparently the geometry department wants a word.
Something about me “defacing” the sacred halls of Euclid with a claim that \(S^2\) doesn’t actually need three coordinates to exist.

Don’t worry — the cameras were rolling.
We’ve got the whole thing: the accusation, the replay, and the quiet moment when everyone realizes the wall was blank all along.

Three PDFs, three acts:

📄 Act I – The Note: On the Minimal Abstract Space Required to Contain \(S^2\)
🔗 https://carlostomas49.github.io/S2-Trilogy/OnMinimalSpaceforS2.pdf

📄 Act II – The Orthodox Reply: No, \(S^2\) Does Not Live in Two Dimensions
🔗 https://carlostomas49.github.io/S2-Trilogy/act2.pdf

📄 Act III – My Answer: On Mistaking a Coordinate System for a Concept
🔗 https://carlostomas49.github.io/S2-Trilogy/act3.pdf

The rest is geometry trying to explain away its own handwriting.

If the language feels dense, that’s fine, grab your nearest 𝐮𝐩𝐩𝐞𝐫-𝐝𝐢𝐯𝐢𝐬𝐢𝐨𝐧 𝐦𝐚𝐭𝐡𝐞𝐦𝐚𝐭𝐢𝐜𝐚𝐥𝐥𝐲-𝐦𝐢𝐧𝐝𝐞𝐝 𝐟𝐫𝐢𝐞𝐧𝐝 and have them walk you through it.
Just make sure that when they’re done, they don’t sound like the person from Act II.

🌀

Because here’s the thing — everyone makes mistakes.
Even the giants who once defined the tone of mathematics itself.
And that’s what makes this moment worth living through: a small correction echoing through a weary decade that’s relearning how to think, together.

A quiet fix to a loud assumption, happening out in the open, in the mid-2020s — post-pandemic, post-certainty — with the chalk dust still hanging in the air.

Stay safe, and cheers 🥂🌍

#Math #Topology #Logic #AI #PhilosophyOfMath #MathHumor #FediverseMath #PostPandemicEra