MathxMatrix on Instagram: "A Hilbert space is essentially a “grown-up” version of Euclidean space. While Euclidean space describes the geometry of the physical world we see (1D, 2D, and 3D), a Hilbert space extends those same rules so they work for any number of dimensions—including infinity. Named after the German mathematician David Hilbert, it is a central concept in modern mathematics and is the primary mathematical “language” used to describe quantum mechanics."

SB Media on Instagram: "In school, we’re taught that parallel lines never meet. But that’s only true on paper or in Euclidean geometry, which assumes a flat, infinite plane. But the universe isn’t flat. It’s curved, warped by mass and energy. And in this non-Euclidean reality, parallel lines don’t behave the way we were taught. In Euclidean space, two lines can run side by side forever without intersecting. But once you enter a curved space (like the surface of a sphere or the warped spacetime a