https://andrewmccalip.com/space-datacenters #OrbitalDataCenters #SpaceTech #MathHumor #Innovation #CosmicQuest #HackerNews #ngated
This complex number book is based on the innovative work of deriving the imaginary unit and Euler formula from first principles. Complex numbers formed from imaginary numbers have widespread applications, but have remained puzzling to many learners. The work opens up the opportunity to explore, extend and share with the general public the newly gained comprehensive understanding of complex numbers for the thorough demystificatio, popularization and empowerment to broader educational levels.
Why formalize mathematics - more than catching errors I read a good post by one of the authors of the Isabelle theorem prover, that got me thinking. The author, Lawrence Paulson, observed that most math proofs are trivial, but writing them (preferably with a proof assistant) is a worthwhile activity, for reasons similar to safety checklists - โNot every obvious statement is true.โ As I have been a bit obsessed with doing formalized mathematics, this got me thinking about why I am excited to spend many hours recently writing formalized proofs in Lean for exercises from Taoโs Real Analysis (along with this recent attempt to write a companion to Riehlโs Category Theory In Context). On a very personal level, I just like math, computers and puzzles, and writing Lean proofs feels like doing all three at once. But I do believe formalization is important beyond nerd-snipping folks like me.
So apparently the geometry department wants a word.
Something about me โdefacingโ the sacred halls of Euclid with a claim that \(S^2\) doesnโt actually need three coordinates to exist.
Donโt worry โ the cameras were rolling.
Weโve 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:
๐ Act I โ The Note: On the Minimal Abstract Space Required to Contain \(S^2\)
๐ https://carlostomas49.github.io/S2-Trilogy/OnMinimalSpaceforS2.pdf
๐ Act II โ The Orthodox Reply: No, \(S^2\) Does Not Live in Two Dimensions
๐ https://carlostomas49.github.io/S2-Trilogy/act2.pdf
๐ Act III โ My Answer: On Mistaking a Coordinate System for a Concept
๐ https://carlostomas49.github.io/S2-Trilogy/act3.pdf
The rest is geometry trying to explain away its own handwriting.
If the language feels dense, thatโs fine, grab your nearest ๐ฎ๐ฉ๐ฉ๐๐ซ-๐๐ข๐ฏ๐ข๐ฌ๐ข๐จ๐ง ๐ฆ๐๐ญ๐ก๐๐ฆ๐๐ญ๐ข๐๐๐ฅ๐ฅ๐ฒ-๐ฆ๐ข๐ง๐๐๐ ๐๐ซ๐ข๐๐ง๐ and have them walk you through it.
Just make sure that when theyโre done, they donโt sound like the person from Act II.
๐
Because hereโs the thing โ everyone makes mistakes.
Even the giants who once defined the tone of mathematics itself.
And thatโs what makes this moment worth living through: a small correction echoing through a weary decade thatโs relearning how to think, together.
A quiet fix to a loud assumption, happening out in the open, in the mid-2020s โ post-pandemic, post-certainty โ with the chalk dust still hanging in the air.
Stay safe, and cheers ๐ฅ๐
#Math #Topology #Logic #AI #PhilosophyOfMath #MathHumor #FediverseMath #PostPandemicEra
Idea: A quarterly math magazine with the most amazing mathematical analysis, the most confusing page layouts, and the most ridiculous line graphs ever conceived called "Jacobi Magazine"