`The poet's eye, in a fine frenzy rolling,
Doth glance from heaven to earth, and earth to heaven,
And as imagination bodies forth the forms of things unknown
The poet's pen turns them to shapes, and gives to airy nothing
A local habitation and a name.'
Theseus in `A Midsummer Night's Dream', Act V, Scene 1, by William Shakespeare
I like to view this quotation as giving Shakespeare's own views, and also
to suggest it as giving an indication of one role of the mathematician, in
searching out new worlds, as did Alexander Grothendieck to a great degree.
See also `mathoetic mode'.
Link to some work of Alexander Grothendieck
We can also see how a sculptor may use the imagination, as in John Robinson's work.
Teaching and Popularisation page