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\begin{document}
\title{Preface to a Compendium of Mathematical Superheroism}%
\author{Daniel Mathews}%
\maketitle
In the beginning was mathematics. Mathematics may precede us, but is
revealed to us by the great. As long as there has been mathematics
with us, there have been the great. Greatness produces mathematics;
mathematics produces greatness; mathematics is greatness. And the
mathematical superhero personifies the zenith of this greatness.
Who are they? Where do they come from? What is their purpose? What
do they do? Why? And why do they all have such bad fashion sense?
They were not called upon. They were not crowned in glory. They were
not elected, selected, or appointed to the job. They were not born
with a silver spoon; even though some were born through the fourth
dimension. Some were discreet; but others were continuous. Some were
straightlaced; but others are a little more knotty.
For the mathematical superhero is a complex
character.\footnote{\emph{Complex}? Get it? 5 points for
appreciating the mathematical pun. \emph{Character}? Get it? 30
points for this one.} The mathematical superhero is a function of
many variables.\footnote{10 points.} The mathematical superhero is
just one element in a free associative group.\footnote{15 points.}
The mathematical superhero knows no boundaries\footnote{10 points.}
--- something of a closed manifold.\footnote{40 points.} The mathematical superhero, in
the end, though there are variations,\footnote{20 points.} solves
the problem, and with minimal energy\footnote{20 points.} ---
something of a geodesic.\footnote{Bonus 50 points for your knowledge
of differential geometry!} He or she may be rather
twisted,\footnote{10 points.} may be rather tangled,\footnote{30
points.} but transforms well under change of variables\footnote{10
points.} --- something of a tensor, really.\footnote{50 points.} The
mathematical superhero comes in many varieties\footnote{30 points.}
--- is often stalked\footnote{40 points.} --- but is always enough to foil any evil
scheme\footnote{30 points --- bonus 50 points if you know the
definition of a scheme!} from any point in the
spectrum,\footnote{Minus 200 points for knowing way too much
algebraic geometry!} from the most generic\footnote{Minus 500 points
more, this is getting ridiculous.} to the most
maximal.\footnote{Minus 50 points.}
No, greatness was thrust upon them. Their geekiness knew no bounds,
and they revelled in things other than sport. Their intellects
overtook them, and could only express itself in strange and bizarre
outgrowths: spiky-haired protrusions, strange capes and outrageous
socks and sandals. And in matters linguistic, a tendency --- or
rather, an irresistible compulsion --- to pun relentlessly and
atrociously on mathematical terms, well beyond any reasonable
limit.\footnote{Oh yes, beyond any reasonable limit: 20 points.}
They could not help themselves; they could not avoid it; that would
be an infinite descent.\footnote{20 points.} Powered with coffee
--- the product of the cup\footnote{50 points. (No, not for `product', but for `cup product'.)}
--- more bad mathematical puns have been made than was ever thought
possible, and mathematical harmony has been restored to the universe
time and time again.
For not everyone can be a mathematical superhero. Not everyone can
make terrible mathematical puns as consistently and as appallingly.
Not everyone can save the world from a maniacal
physicist/economist/vice-chancellor/(insert your least favourite
non-mathematical person here) with an evil and suitably twisted and
ridiculous plan to take over the world --- or, much the same thing,
the mathematics department. Not everyone can be so utterly inept at
every facet of human endeavour other than world-saving heroism. Not
everyone refers to a donut as 'genus-1 nutrition'. And not everyone
is so comfortable with Cauchy's formulation of continuity as to be
named after its essential variables. Yes, the world needs
mathemagicians to look up to. Yes, even if they arise from the
demented vision of a twisted author in the rather obscure genre of
mathematical comics.
But we should not go too far. We should not put these heroes on a
pedestal. For in a sense, the mathematical superhero is everywoman
and everyman. Is there not really, deep in our hearts, a
mathematical superhero in all of us? We need to unlock our
potential, remove our cutoff functions, and drink too much coffee.
We must disgorge ourselves of all selfishness, avarice, and fashion
sense. We must rail against injustice, iniquity, and inelegance. We
must take action, when necessary, and apply our knowledge to the
real world, sometimes, when we really have to, and physicists or
engineers will not do it for us.
In this humble collection, you will see some of the finest examples
of mathematical superheroes ever produced. You will be taken to
heights of superhero magnificence greater than $N$, for any
given $N>0$. So let us proceed.
\bigskip
--- Daniel Mathews, 8/10/05, Stanford, USA
\newpage
{ \center \huge Results}
\begin{itemize}
\item
400+: You are truly one of the great. You have \emph{more brains
than the basket behind a guillotine}, and \emph{more sexual allure
than a hyperbolic attractor}.
\item
300--400: You are almost there. Try wearing socks and sandals more
often. You might even like to get yourself a cape or a
\emph{super}visor.
\item
200--300: You are well on your way. You should read more comics
about the exploits of mathematical superheroes. Lucky, then, that
you are reading this. But please refrain from battling any but the
most minor villains. You will need yet to obtain \emph{more power
than a quintic (5)}.
\item
100--200: Above average. You have potential, but you have much to
learn in our ways. Yes, there is a mathematical superhero inside
you. But you will need to obtain a \emph{transcendental extension in
all fields} first.
\item
50--100: You have yet to make an impression in the world of
mathematical superheroism, but yet you can succeed. You have made a
start, but there is a long way to go. Your first task is to become
\emph{more caffeinated than a convoy of long-haul truck drivers} and
\emph{more poised than a stable 2-cycle}.
\item
0--50: Perhaps you would be better leaving the crazed physicists and
economists and vice-chancellors to others.
\item
Less than 0: You know way too much algebraic geometry. \emph{Shame
on you!}
\end{itemize}
\end{document}