Most people get cold feet or the jitters if you mention these creatures to them. I would agree theorems are scary things! But what do they look like?

Well here is what I've been able to come up with so far:

Theorems: (The main species of mathematica theoria) This creature can generally be found standing on hilltops throwing large boulders at passersby. Sometimes also referred to as golems or basilisks.

Lemmas: (Subspecies mathematica lemmia) These small furry creatures can often be found scuttling down the corridors of your local mathematics department. They come in yellow, green and a kind of purply colour. Often seen throwing themselves off rooftops in large groups.

Propositions: (Subspecies mathematica minutae) These tiny creatures are surprisingly agile and get very aggressive when cornered, beware! They are quite difficult to trap and quite often suffer from the left-up-to-the-reader syndrome.

Corollaries: (Subspecies mathematica corolloria) These creatures are generally blue-eyed with sweet smiles and very sharp teeth which cut through flesh like straight razors. They are four legged, hairless and quite ubiquitous.

Postulates: (Subspecies mathematica postularia) These creatures resemble a cross between a rock hyrax and a bush pig. They can often be found hanging on to bushes in arid semi-desert climates whistling to eachother.

The last story, Mathenauts written by Norman Kagan in a collection of "Tales of Mathmatical Wonder" (also titled "Mathenauts") compiled by Rudy Rucker deals with just such a concept....

In the story the mathematical theories occupy a position in some "space", not your ordinary 4-dimensional space we're used to, oh no, this space is defined by the relationship linking mathmatical objects (theorems) together. The story deals with the concept that this space has an objective reality and if all theories can have a coordinate in this meta-space of theories, then it is possible to create a "ship" that can navigate it way through this space, to find new theories and lemmas in uncharted waters.

To be able to survive a voyage in this craft takes a pilot six years of "Brill" conditioning, a Ph.D. in pure maths, and a psychic ecology provided "ordinary" passengers to provide a mapping for the "mathenaut" to chart a course home....

Imagine your universe mapped onto a new reality as the outlandish theories of topology warp reality into new forms, or projected into multi-dimensional worlds, or reduced to flatland. The first such ships simply disapeared from our universe, to wander the infinite mathematical spaces.

How about theories that subsume other theories, feed off them, grow and evolve and look at your projection into their world hungrily?

Quite a good short story, and I'm sure has some philosphical merit.

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