"William Rowan Hamilton was the greatest mathematician Ireland has ever produced."
Hamilton made a huge breakthrough; an analogy (identity), between mechanics and optics, the science of light. His discovery was amazing. It was a surprise when he discovered that mechanics (the study of moving bodies) and optics (the geometry of light rays) were connected, and an even bigger surprise when he discover that they were the same! This led to the formal setting used by mathematicians and mathematical physicists today. It is used not only in mechanics and optics but in quantum theory too. It is called Hamiltonian systems. What they do is derive the equations of motion of a mechanical system from a single quantity (the total energy). This is now called the Hamiltonian of the system. The equations that result from this involve the position of the parts of the system as well as the speed at which they are moving, also known as the momentum of the system. The equations do not depend on the choice of coordinates which is a great feature.
"Beauty is truth, at least in mathematics. And here the physics is both beautiful and true."
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