Explorer VS Adventurer

As Ursula K. LeGuin writes in The Dispossessed, a novel in which a man returns to Earth for the first time from an anarchist colony: “The explorer who will not come back or send back his ships to tell his tale is not an explorer, only an adventurer.”

 Mathematics as Exploration

Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere.

 Mathematicians Must be Adventurers

There is no thing as a man who does not create mathematics and yet is a fine mathematics teacher. Textbooks, course material—these do not approach in importance the communication of what mathematics is really about, of where it is going, and of where it currently stands with respect to the specific branch of it being taught. What really matters is the communication of the spirit of mathematics. It is a spirit that is active rather than contemplative—a spirit of disciplined search for adve...

 Happenings: Impermanent, Impromptu Art

In this context of achievement-and-death, artists who make Happenings are living out the purest melodrama. Their activity embodies the myth of nonsuccess, for Happenings cannot be sold and taken home; they can only be supported. And because of their intimate and fleeting nature, only a few people can experience them. They remain isolated and proud. The creators of such events are adventurers too, because much of what they do is unforseen. They stack the deck that way.