Only two people will ever know what it was like to move up the last few hundred feet of Mount Everest's southeast ridge for the first time in human history. From what these two revealed afterwards of their personalities, they will have kept their emotions well under control. Their fellow climbers, Tom Bourdillon and Charles Evans, had come within an hour's climb of the summit the day before, and lived. The weather had stayed fine. Their oxygen equipment was working smoothly. Their confidence in their own stamina was high, and their hunch - that they had nothing to fear but frostbite, oedema and fear itself - proved accurate.

The conquest of Everest by Edmund Hillary and Tenzing Norgay on May 29, 1953, was a transcendent event; singular, spectacular and inspirational. It was also hard to beat for sheer simplicity. Climbing ropes and supplemental oxygen apart, this was nothing more nor less than an epic feat of walking. But the courage that took it to the summit, and the matter-of-fact conviction that what looked possible in theory was also doable in practice, were qualities that Tenzing and Hillary shared with every true pioneer. Chuck Yeager needed them to light the engine of his Bell X-1 rocketplane and break the sound barrier in 1947 in defiance of the respectable myth that the barrier was intrinsically unbreakable. Squadron Leader Andy Green defied similar scepticism exactly half a century later, this time in a jet-powered car. Ferdinand Magellan, Roald Amundsen, Yuri Gagarin and Neil Armstrong all, likewise, entered legend for matching their peers and predecessors, then taking a step farther.

Their spirit lives on. There are six billion people on the planet and no age has a monopoly on bravery or curiosity. So where can the instinct to explore still find expression? As it happens, no human has yet crossed Antarctica in the southern winter. Although the bathyscaphe Trieste has plumbed the Challenger Deep, seven miles beneath the Pacific, there may be pockets of jungle in Brazil or Borneo as yet unseen by human eyes, and new species to discover there. But if so, the pockets will be small. There is no point in denying that the obvious, iconic challenges Earth poses to adventurers have been surmounted. Had they not been, Sir Ranulph Fiennes would not be attempting Everest (again) this year, but something higher. Dame Ellen Macarthur would not be retracing old routes round the world but finding new ones. There was a golden age of exploration, and it is over.

Some may respond as Francis Fukuyama responded to the fall of the Berlin Wall - by announcing the end of the quest for the new, just as he announced the end of history. A bleaker defeatism would be hard to imagine. In the final episode of David Attenborough's seminal Life on Earth series, which he devoted to homo sapiens, he called us “compulsive communicators”. We are. But we are also compulsively inquisitive, and restless. When humans lose the urge to roam they will have lost a large part of their humanity.

The wave of euphoria triggered by the first Moon landings subsided more than a generation ago. Ever since, talk of new frontiers has been infected by a sense of cliché. Yet the fact is that as a species we need them, and only the wilfully blind could fail to see them at every turn. Intellectual frontiers are no less real for being intangible. They continue to thwart even the most heroic efforts to unlock the mysteries of the atom, the cosmos, the human brain and human history. Does the Higgs Bosun particle exist? The truth is that we have no idea. What happens to consciousness in sleep? How, in heaven's name, did Stonehenge get there?

We have theories, but no answers. The search for them counts emphatically as exploration, but it does not have to substitute for the old-fashioned kind that Vasco da Gama would have recognised. Nor do explorers have to know exactly what they seek to have a reason to depart. “Because it's there” will always be the best justification. And so, cost what it may, to Mars - not because there might be signs of life there, but out of simple human curiosity. It may seem impossible, but so, for centuries, did Everest.