\documentclass{Article}
\title{Mathematical Haiku}
\author{Daniel Mathews}
\begin{document}
\maketitle
\begin{verse}
Maths haikus are hard \\
All the words are much too big \\
Like homeomorphic. \\
\end{verse}
Some observations on abstract algebra... \\
\begin{verse}
Fields, groups, semirings \\
Who remembers which with which? \\
Pesky axioms! \\
\end{verse}
\begin{verse}
Fields can add, subtract \\
And multiply and divide \\
But not by zero \\
\end{verse}
\begin{verse}
Rings are just like fields \\
except for the division \\
Well, you know... kind of \\
\end{verse}
\begin{verse}
Module is to ring \\
as vector space is to field. \\
What analogy! \\
\end{verse}
\subsection*{A proof that $\sqrt{2}$ is irrational}
\begin{verse}
Suppose rational \\
Let fraction be p on q \\
hcf is 1 \\
\end{verse}
\begin{verse}
Square both sides and so \\
$\frac{p^2}{q^2} = 2$ \hfil Read: p squared on q squared is 2 \\
then multiply out. \\
\end{verse}
\begin{verse}
But then p's even... \\
... But then q's even! Bang! wow! \\
Like freakout! Pigs fly! \\
\end{verse}
\begin{verse}
Woe, too much to take. \\
So now spare a moment few. \\
Poor Pythagoras \\
\end{verse}
Firstly, an introduction to Lebesgue integration... (more on this later)... \\
\begin{verse}
Countable subset \\
G-delta $\mu$-measurable \\
Yeah! Lebesgue's the man! \\
\end{verse}
How cool is maths?
\begin{verse}
Maths is really cool \\
Really really really cool \\
I like it alot \\
\end{verse}
And now for my work on topology...
\begin{verse}
Group presentation \\
Quotient space by inclusions \\
Van Kampert is cool \\
\end{verse}
\begin{verse}
Continuity: \\
Open pre-image open \\
Or by epsilons. \\
\end{verse}
\begin{verse}
A Mobius strip \\
Is not orientable \\
Idea for boob tube.
\end{verse}
\begin{verse}
Orientable: \\
Bug walking along surface \\
Not turned upside-down \\
\end{verse}
...And my treatment of field extensions and ruler-and-compass
constructions...
\subsection*{An ode to constructability in triumvirate of Haiku}
\begin{verse}
Ruler and compass \\
Degree of field extension \\
Must be power of 2. \\
\end{verse}
\begin{verse}
Squaring the circle! \\
Ha ha you stupid doofus! \\
$\pi$ transcendental! \\
\end{verse}
\begin{verse}
Duplicating cube? \\
$[\mathcal{Q} (\sqrt[3]{2}):\mathcal(Q)]$ \hfil Read: 'Q cube root of two to Q' \\
Degree three, not two! \\
\end{verse}
\end{document}