A human mission to Mars is technologically feasible, but hugely expensive requiring enormous financial and political commitments. A creative solution to this dilemma would be a one way human mission to Mars in place of the manned return mission that remains stuck on the drawing board. Our proposal would cut the costs several fold but ensure at the same time a continuous commitment to the exploration of Mars in particular and space in general. It would also obviate the need for years of rehabilitation for returning astronauts, which would not be an issue if the astronauts were to remain in the low gravity environment of Mars. We envision that Mars exploration would begin and proceed for a long time on the basis of outbound journeys only. A mission to Mars could use some of the hardware that has been developed for the Moon program. One approach could be to send four astronauts initially, two on each of two space craft, each with a lander and sufficient supplies, to stake a single outpost on Mars. A one way human mission to Mars would not be a fixed duration project as in the Apollo program, but the first step in establishing a permanent human presence on the planet. The astronauts would be re supplied on a periodic basis from Earth with basic necessities, but otherwise would be expected to become increasingly proficient at harvesting and utilizing resources available on Mars. Eventually the outpost would reach self sufficiency, and then it could serve as a hub for a greatly expanded colonization program. There are many reasons why a human colony on Mars is a desirable goal, scientifically and politically. The strategy of one way missions brings this goal within technological and financial feasibility. Nevertheless, to attain it would require not only major international cooperation, but a return to the exploration spirit and risk taking ethos of the great period of Earth exploration, from Columbus to Amundsen, but which has nowadays being replaced with a culture of safety and political correctness...