# Hamilton: The Mathematical Musical

I had an idea to write a musical about a man who lived about 200 years ago and made profound contributions that affect our everyday lives to this very day, although his story remains relatively unknown. But when I revealed that this man’s name was Hamilton, I was accused of plagiarism!

That’s so unfair–with all due respect to Lin-Manuel Miranda, *nobody* has written a musical about William Rowan Hamilton, the 19th century Irish mathematician. Today, April 1st 2021, I’m sharing parts of three songs from this highly original musical.

William Rowan Hamilton was a child prodigy in mathematics, linguistics, physics, and astronomy.

# William Rowan Hamilton

How does the 4th of 9 children, son of a solicitor Scotsman, dropped in the middle of a forgotten

spot in Talbots Castle in a town that’s smaller

grow up to be a hero and a scholar?

The mathematician on a mission, sent away by his father

got a lot farther by working a lot harder

by being a lot smarter by climbing up the rungs

by thirteen, he knew a dozen tongues.

Well the word got around they said this kid has knowledge

took up a collection just to send him to Trinity College.

Get your education don’t forget from whence you came. And the world is gonna know your name.

What’s ya name, man?

William Rowan Hamilton.

My name is William Rowan Hamilton.

And there’s a million things I haven’t done.

But just you wait, just you, wait.

Hamilton was a pioneer in graph theory, the branch of mathematics concerning connections between things. Every time your UPS or DoorDash or Amazon driver makes a series of deliveries to different locations, that’s a Hamiltonian Path, and the deliveries are more efficient thanks to Hamilton’s work.

# I’m Not Throwing Away My Path

I am not throwing away my path!

I am not throwing away my path!

Hey yo, I’m just like my graph

I’m multiply connected, don’t laugh

And I’m not throwing away my path!

I’m ‘a get a scholarship to Trinity College

I prob’ly shouldn’t brag, but I got the fire and

I’m the Royal Astronomer of Ireland

Only eighteen but my mind is older

These Dublin streets get colder, I pledge

Ev’ry vertex, ev’ry edge

I have learned to manage, I don’t have disciples

I walk these graphs in cycles

But I am not throwing away

My path

I am not throwing away

My path

Hamilton invented the quaternion number system, which can be used to represent the position of objects in three-dimensional space, the direction they are pointing, and most importantly the way they rotate. This number system is used today in computer graphics–Buzz Lightyear and Woody are described by quaternions–and in video games such as Assassin’s Creed and Kerbal Space Program. Quaternions are used by industrial robots that have several arm joints that must all rotate in smooth unison. And NASA uses quaternions to accurately chart the flight paths of spacecraft through the solar system.

# The Vector Where it Happened

The quaternion emerges as an unprecedented multiplicative pearl

A system he can rotate however he wants

The del operator emerges with div, grad, and curl

And here’s the pièce de résistance:

No other numbers are in

The vector where it happened

The vector where it happened

The vector where it happened

No other numbers are in

The vector where it happened

The vector where it happened

The vector where it happened

No one really knows what **i**, **j**, and **k** mean

The math is so clean

How they depict a scene

We just assume that it happens

But no other numbers are in

The vector where it happens.