Sir William Rowan Hamilton

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Sir William Rowan Hamilton MRIA
(3 August 1805 - 2 September 1865) [1]
was an Irish mathematician.
He worked in both pure mathematics and mathematics for physics.

He made important contributions to optics, classical mechanics and algebra.
Although Hamilton was not a physicist–he regarded himself as
a pure mathematician–his work was of major importance to physics,
particularly his reformulation of Newtonian mechanics,
now called Hamiltonian mechanics.

This work has proven central to the modern study of classical field theories
such as electromagnetism, and to the development of quantum mechanics.

In pure mathematics, he is best known as the inventor of quaternions.

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Hamiltonian mechanics
can be used to describe simple systems such as a bouncing ball,
a pendulum or an oscillating spring in which energy changes from kinetic to potential
and back again over time, its strength is shown in more complex dynamic systems,
such as planetary orbits in celestial mechanics.[3]
The more degrees of freedom the system has, the more complicated its time evolution is
and, in most cases, it becomes chaotic.