This monograph has gathered together three extraordinary problems in theoretical physics to be solved exactly. The problems range from the long-standing limit problem of the simple harmonic oscillator in quantum mechanics, the unfolding of a hidden symmetry in the Markovian birth-and-death equations, to the four-hundred-year-old problem of the simple pendulum. Therefore, this monograph is a rare “three-of-a-kind” collection of major essays on seemingly impossible problems in physics.