Implicit algebraic surfaces are defined by polynomial equations f(x,y,z) = 0. The Cayley cubic (1869) has 4 nodes — the maximum for a cubic surface. The Kummer quartic has 16 nodes — the maximum for a quartic (Kummer's result, 1864). The Barth sextic has 65 nodes — discovered 1996, maximum known for degree 6. These surfaces arise in algebraic geometry, string theory compactifications, and mirror symmetry. Ray marching finds surface intersections iteratively without analytic inversion.