No, no, not not the politician Hamilton-- the scientist Hamilton. They do use a pretty awesome homemade acapella cover of the first song from the play Hamilton to do it, though. It's arranged well and diversely cast, too, Check it out!
So what did William Rowan Hamilton discover? He discovered quaternions, which are an extension of complex numbers: rather than just one number (i) that equals -1 when squared, these use thee (i,j,k). Also in that formula, multiplication is no longer commutative (the order in which things are multiplied matters, so a times b is not the same as b times a). They can be used to represent rotations.