Prompt
                                        
                                            Create a realistic portrait of William Rowan Hamilton, a middle-aged Irish mathematician, physicist, and astronomer from the 19th century, sitting in a study with papers, quills, and mathematical instruments around him, wearing formal attire, with a thoughtful expression, and a hint of a chalkboard or blackboard with mathematical equations in the background, incorporating elements that reflect his contributions to quaternions, Hamiltonian mechanics, and optics.