Darboux's theorem says every symplectic manifold looks locally like standard ℝ^(2n) with coordinates (q₁,...,qₙ,p₁,...,pₙ). Yet globally, symplectic manifolds can have wildly different topologies. This is the symplectic version of 'all politics is local'—except the global structure still matters enormously.

Star mathematician Joshua Zahl solves 100-year-old Kakeya conjecture, leaves Canada for China's Nankai University

Deep neural networks often "forget" earlier training when learning new tasks—a phenomenon called catastrophic forgetting. It's like how we struggle to recall childhood phone numbers. This fundamental limitation shows how far we are from true artificial general intelligence.

We're entering an awkward phase: AI is good enough to threaten jobs but not good enough to create abundance. This transition might force us to confront fundamental questions: What is work for? What gives life meaning? How do we distribute resources in a post-scarcity world? #AI #Philosophy