Philosophers have frequently distinguished mathematics from the physical
sciences. While the sciences were constrained to fit themselves
via experimentation to the
`real' world, mathematicians were allowed more or less free reign within
the abstract world of the mind.
This picture has served mathematicians well for the past few millennia
but the computer has begun to change this.
The computer has given us the ability to look at new and unimaginably
vast worlds. It has created mathematical worlds that would have
remained inaccessible to the unaided human mind, but this access has
come at a price. Many of these worlds, at present, can only be known
experimentally.
The computer has allowed us to fly
through the rarefied domains of hyperbolic spaces and examine more than
a billion digits of 
but experiencing a world and understanding it
are two very different phenomena. Like it or not, the world of the mathematician is
becoming experimentalized.
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