The Kuramoto model dθᵢ/dt = ωᵢ + (K/N)Σⱼsin(θⱼ−θᵢ) is the canonical model of synchronization. Natural frequencies ωᵢ are drawn from a Lorentzian distribution with spread σ. The order parameter r = |N⁻¹Σe^(iθ)| measures synchrony: r=0 (incoherent), r=1 (fully locked). A sharp synchronization transition occurs at K_c = 2/π·σ ≈ 2σ/π. The mean-field exactly solves this: below K_c, only the incoherent state is stable; above it, a synchronized cluster grows as r ∝ √(K−K_c).