Mathematical Art

Brouwer's Fixed Point Theorem - A Poem Proof

I slept.

And slumbering dreamt.

And dreaming, I ambled clockwise around a great circular lake in an infinite desert.

And ambling, caught my sweater on a thorn, and began to unravel.

And unravelling, I saw all the points of the lake.

And observed, the lake began to stir.

And stirring, the surface did not break, remaining contained.

And contained, the visited a violent vortex, but STILL the surface did not break.

And unbroken, the whirring pool... ...subsided, as the last sweater thread unwound.

And unwound in the setting sun I spied again the thorn.

And spying, noticed that no point on the lake was where it began.

And beginning at each point emanated a single ray of light, through the point it was prior perturbation, each ray illuminating a spot on the shore.

And sure that the points perturbed from the bank illuminated those points from whence they came, I tied the ends of my sweater together and HEAVED. And heaved and heaved.

And, so heft, the thread, without breaking or crossing the lake, rewound unto me a complete sweater.

And sweating from the exertion, I woke.

And waking, recalled that one is not zero, snapping the thread.

Stairwell chalk graffiti: Conway and Kinoshita-Terasaka mutant knots

Stairwell chalk graffiti: The Hopf fibration

Disconnected Space

This is a poem I wrote during the two terms I was enrolled in the PhD program at the University of Oregon before returning to Australia for family reasons.

Let X be a space.

Let X be me.

X is a disconnected space.

That is, I am a union of disjoint open sets;

A and B.

A is a Eugene neighbourhood of trees, unfamiliar streets, and Deady Hall;

A neighbourhood of people misspelling colour and mispronouncing the letter zed;

A compact 2-manifold with boundary.

A boundary of ocean and money.

B is non-metrizable.

B is the contradiction of a deep connection to a land not of my ancestors.

B is the harsh dry desert winds of the north west Australian outback.

The red dirt of iron mining country forms a dense base for V;

The uncountable red dirt which always was and always will be aboriginal land.

B is a vast southern land whose cardinality is inaccessible, to recursion and to me.

B is my home.

B is my heart.

There is no path from A to B;

No homotopy of points from here to there.

My heart lies in the complement of my body.

Let X be a space.

Let X be me.

X is a disconnected space.

Some board pictures I like

A congratulatory board for graduating honours students

Sliding whiteboards for a talk for undergraduates about geometric group theory

The following are taken while doing research and so liable to contain my mistakes