It is a mistake to think that because the poles, the Moon and Mount Everest have been conquered, the excitement and adventure that was once the hallmark of human exploration at home on Earth is over. In fact, the far corners beckon as never before, and the deep unknown calls out to men and women of courage and curiosity to reach out and make it familiar territory.

Some witty physicist posed the question, “What’s left to be discovered in physics?” and answered himself like this: “Maybe nothing, probably almost everything, can’t say for sure, no one’s yet discovered what we don’t know.” And so it goes with dozens of subjects. There is an abundance of challenges out there and much knowledge that we do not have and cannot even perceive as yet. But there is a lot to chew over to keep our minds fertile and our feet itchy.

Take, as a first step, the idea of climbing Mount Gangkhar Puensum in the Kingdom of Bhutan. It is the highest and most difficult unclimbed mountain in the world, standing at almost 25 000 feet above sea level. Many have tried to conquer it, but none have succeeded. Now, the degree of difficulty has been added to by a 2003 ban on mountaineering, a religious stricture because the people of Bhutan are devout Buddhists and the mountain has religious significance for them. The lure of doing what has never been done before will no doubt prevail in the end, however, and some as-yet embryonic mountaineer will gain fame and perhaps fortune thereby.

There is, on our Earth, much remaining wilderness waiting to be thoroughly explored, some doable, some not so. The Darien Gap is one of the most forbidding and not recommended for holidays or casual pleasure jaunts. It straddles part of the narrow neck of land that connects the two Americas. It is the bit between Panama and Colombia, and few people have even heard of it. The land of the Gap is a very wet, very muddy rainforest whose inhabitants include any number of deadly insects and animals that simply cannot be avoided. There are no towns as we know them, and few roads. Footpaths crisscross the boggy wetland, but they are said to be used only for transporting drugs, which makes them even more hazardous than the abundance of spiders and snakes.

A similar challenge is to be found in Brazil in a sizeable chunk of land called the Javari Valley, which, at more than 33 000 square miles, is somewhat bigger than Austria. It is home to a number of indigenous tribes that still live in a kind of protected seclusion, screened on purpose from the modern world. The ‘valley’ recently became famous, or rather infamous, when a British journalist and a Brazilian expert on indigenous peoples were murdered while trying to protect the locals from drug traffickers, illegal loggers and miners. The attractions of the valley are manifold; apart from still being an almost pristine rainforest, it is home to many scarcely documented people whom we would do well to learn more about.

At another end of the world, in New Zealand, it is said there are equally impressive bits of unexplored land and scores of peaks to climb for the first time. The authorities there are always helpful, however, and all legitimate applications are quickly dealt with. Best of all, though, is that in New Zealand the modern explorer has nothing to fear from drug lords and unknown ferocious tribes.

High on the list of places to go for unexplored majesty and jaw-dropping astonishment is Vietnam’s Hang Sơn Đoòng cave. Called a cave, it is rather more of an underground country or province. Nearly 10 kilometres long, the complex has a flowing river running through its 38 000 cubic meters. It was discovered in 2009, and vigorous exploration is still going on. The cave’s interior is described as being so roomy that you could easily fit an entire New York block inside, including skyscrapers. More impressively, you could fly a Jumbo jet through it without the wings touching the sides.

In the realm of mystery, history and archaeology there are projects enough to fill many volumes. Three have an especially strong pull if current newspaper attention is a yardstick.

The first is the search for MH370, the airliner that went missing on a flight from Kuala Lumpur to Beijing in 2014 and has held the world spellbound ever since. Three or four identified pieces of it have surfaced on Indian Ocean island beaches, but the plane is still missing and the full story remains unknown. Like Titanic, the mystery screams to be uncovered, and like Dr Ballard, who found Titanic, the finder of MH370 is surely in for a lifetime reward.

A more ancient historical mystery that engages us still is how on earth people with apparently slender technical resources managed to move massive stone blocks as often and as easily as they seem to have done. One such block that still sits in the quarry where it was cut in Baalbek, Lebanon, more than 2 000 years ago, weighs 1 650 tonnes. At the time Baalbek went by the name of Heliopolis, City of the Sun, a busy outpost of the Roman empire. The quarry is well-known as the source of other gigantic blocks, one in particular of over 1 000 tonnes known as ‘The Stone of the Pregnant Woman,

Archaeologists say the block left behind was never moved because in the end it was too big. But can we believe that where a block of 1 200 tonnes was cut and moved not long before, one 400 tonnes heavier was beyond their technology? We need an architectural or building industry Rosetta Stone to more accurately decipher some of the many hidden hieroglyphs that may unlock that secret too.

Huge stone blocks, minutely cut to be fitted together and then carted up some desperately rugged terrain by their Inca builders at Machu Picchu, add much to this same mystery, and there are many archaeologists who believe that if we solve the, one we stand a fair chance to solve them all.

The only difficulty about all these targets is to isolate and define them before you ever set out. Then, with all the equipment now available, it’s just a matter of perseverance and money. A lot of it.