Terence Tao

But over time, people realized that this was actually a really fundamental concept.

Hamilton eventually, in the 19th century, reformulated Newton's laws of physics into what's called Hamiltonian mechanics.

where the energy, which is now called the Hamiltonian, was the dominant object.

Once you know how to measure the Hamiltonian of any system, you can describe completely the dynamics, like what happens to all the states.

It really was a central actor, which was not obvious initially.

And this helped, actually, this change of perspective really helped when quantum mechanics came along.

Because the early physicists who studied quantum mechanics, they had a lot of trouble trying to

adapt their Newtonian thinking because everything was a particle and so forth to quantum mechanics because everything was a wave.

It just looks really, really weird.

Like you ask, what is the quantum vision if it was MA?

And it's really, really hard to give an answer to that.

But it turns out that the Hamiltonian, which was so

secretly behind the scenes in classical mechanics, also is the key object in quantum mechanics.

There's also an object called Hamiltonian.

It's a different type of object.

It's what's called an operator rather than a function.

But again, once you specify it, you specify the entire dynamics.

So there's something called Schrodinger's equation.

that tells you exactly how quantum systems evolve once you have the Hamiltonian.

So side by side, they look completely different objects.