The next time someone claims that we “know how LLMs work”, ask them to explain how they perform arithmetic. If they don’t know (they won’t), maybe sharing this post will make them understand their profound epistemological error.

Prime numbers above 3 cannot live in positions divisible by 3. That single arithmetic fact forces every prime into exactly six positions on a nine point circle. Those six positions split into two perfect triangles. Two triangles on a circle is a Star of David. The math drew it with no symbol in mind.The same framework keeps producing ancient shapes. The exponential decay function that describes time in this system draws a pyramid. The three-fold vortex symmetry draws a triskelion. The Fibonacci

The Hidden Geometry of FractionsEvery reduced fraction a/b in [0,1] is born from the Stern-Brocot mediant rule:a/b ⊕ c/d = (a+c)/(b+d).The animation wraps each fraction around a disk by θ = 2πa/b, while its visible scale follows the Ford-circle law rₐ⧸ᵦ = 1/(2b²). The glowing backdrop is a denominator-resonance field built from phases qθ, weighted by Euler’s totient φ(q), which counts the reduced residue classes modulo q.As new Stern-Brocot fractions appear, they inject heat into that same denom