A Mathematician is like a Naturalist

An illustrated manifesto

A mathematician is like a naturalist. They travel far away around the world to find the strangest creatures.

They enjoy classifying. Whenever a branch of mathematics is given a classification, mathematicians rejoice.

No one is happier about a list than a mathematician, and what mathematicians like even more than lists, is finding ways to tell a list without listing (or knowing) its elements.

Mathematicians look at the world with two questions always in their minds.

The first one is:

How similar can something be to a tiger, before it is a tiger?

They take measurements and use their classifications to identify creatures they run into. By proving membership to a class, they immediately gain familiarity with the creature. This can be useful in moments of need.

The other question is:

How much of a tiger do I have to see before I can say 'There is a tiger’ ?

At times it is sufficient to check the footprints.

Many creatures look alike, so at times it is necessary to check the footprints.

When mathematicians return from their adventures, they bring home tales of dimensionless points and infinite-dimensional spaces. They often like writing books about their discoveries.

However, the most important job for a mathematician is forever to be amazed by the beauty of it all.