They are vast towers rising out of the jungles of the Amazon basin.

Tepuis, rocky tabletop mountains isolated by hundreds of metres of steep cliffs, form a unique habitat on their tops and inside their maze of caves. Untouched for millions of years, they host a secret world that has evolved in parallel with its surroundings.

Now, the secrets of the ancient tepui are slowly being revealed, thanks to expeditions led by speleologist of the University of Bologna, Italy.

Earlier this month, his team finished an arduous, 40-day expedition to some of the world’s last unexplored caves inside inaccessible tepuis. His team explored Imawarì Yeuta in Venezuela, which has at least 22 kilometres of tunnels, the largest known cave system of its kind.

Ěý

The caves are “a completely different world”, says Sauro. The quartz walls often have a spooky pinkish hue, and organic acids in the water turn the cave streams red.

The speleothems – stalactites and stalagmites – take fantastic forms. Some resemble billowing clouds of smoke; others look like a spray of mineral mushrooms. Exactly how they form is still a mystery.

Many of the peculiar, lumpy, silica speleothems that only occur inside quartzite caves are formed by colonies of microorganisms working together on the bacterial equivalent of a skyscraper.

Most known caves form in limestone – calcium carbonate – which readily dissolves in water.

But the tepui caves run through quartz sandstone, which is less susceptible to water erosion, so caves form much more slowly. Sauro notes that limestone caves form over hundreds of thousands or a few millions of years; his research suggests quartzite caves form over tens of millions of years.

“We don’t have a good idea of how old these caves are,” says , a geographer and cartographer also at the University of Bologna. “There’s nothing we can date inside, it’s all too old. It’s much older than what we expect.”

Caves are like nature’s treasure chests, says de Waele. “They safeguard material from the outside – there’s no wind, no surface erosion,” he says. The tepui caves have been protecting their contents for millions of years. “It’s incredible.”

Sauro says travelling the tepuis’ twists and turns is like taking a trip back in time. Each of his expeditions yields new discoveries. In 2012 the team turned up a never-before-identified . The team has also discovered new species of blind cave fish and bacteria.

Sauro is now focused on better understanding how life evolves in these sunless labyrinths, cut off from the rest of the world. The only way in is via entrances high in the walls or on the mountaintops, which can soar as high as 3000 metres.

The tepuis are isolated by their soaring cliff walls and home to unique species of animals. For example, Mount Roraima tepui is the only known habitat of the Roraima bush toad, a small amphibian that, in the face of danger, curls itself into a ball and rolls away.

The most recent expedition was Sauro’s sixth. The team’s discoveries won’t be released until November, but it’s likely they’ll be able to introduce the world to another crop of previously unknown species.

Microbes that live in those caves are of special interest, says , a clinical microbiologist from the University of Queensland in Brisbane, Australia, who joined two of the expeditions. “Caves harbour chemical compounds and microbes that we don’t know about,” he says.

By comparing these “pristine” bacteria to modern superbugs, Zowawi aims to better understand how pathogens develop resistance to antibiotics. “We hope that will widen our gaze about how those bacteria have evolved,” he says.

His preliminary analyses have already turned up previously unclassified types of bacteria – but it’s too soon to know if they’ll be useful.

There’s so much left to discover, says Sauro. Not only are quartzite caves and what’s hiding inside poorly understood, but individual tepuis can be very different. Each of the hundreds of mountains that dot the landscape developed and evolved independently of the others. “They are like islands in time,” he says.

But it won’t be easy exploring them. You need a helicopter to get to the top, which depends on it being a clear day with minimal wind – in an area that is typically very cloudy and windy. Expeditions require a lot of money and waiting for near-perfect conditions.

Even once they’ve disembarked, the explorers often encounter additional challenges. “They have cracks and canyons, and really rough terrain,” says Sauro.

He is guided by satellite images that detect cave entrances on tepui tops – but those often end up being blocked by rocks and require a nervy descent on ropes. “On most of them, there’s no access without climbing,” says Sauro.

But he is undeterred and is already planning the next expedition for later this year.

Ěý

Read more: Hunt is on for world’s deepest caves more than 2km underground

Ěý

Ěý

Ěý

“It’s still possible that the deepest cave will be in the Americas, even deeper than the Krubera”

This article appeared in print under the headline “The hunt is on for the deepest cave”

(Image: A First rate Man-of-War driven onto a reef of rocks, floundering in a gale, Reinagle, George Philip/Royal Albert Memorial Museum/Bridgeman Images)

In 2007,ĚýĚýat the US National Oceanic and Atmospheric Administration compiled a catalogue ofĚý. Here are some of the most significant

1498ĚýColumbus recounts how, on his third expedition to the Americas, a giant wave lifts up his boats during the night as they pass through a strait near Trinidad. Supposedly using Columbus’s words, to this day this area of sea is called theĚýBocas del DragĂłnĚý– the Mouths of the Dragon.

1853ĚýThe Annie Jane, a ship carrying 500 emigrants from England to Canada, is hit. Only about 100 make it to shore alive, to Vatersay, an island in Scotland’s Outer Hebrides.

1884ĚýA rogue wave off West Africa sinks the Mignonette, a yacht sailing from England to Australia. The crew of four escape in a dinghy. After 19 days adrift, the captain kills the teenage cabin boy to provide food for the other three survivors.

1909ĚýThe steamship SS Waratah disappears without trace with over 200 people on board off the coast of South Africa – a swathe of sea now known for its high incidence of rogue waves.

1943ĚýTwo monster waves in quick succession pummel the Queen Elizabeth cruise liner as it crosses the North Atlantic, breaking windows 28 metres above the waterline.

1978ĚýThe German merchant navy supertanker MS MĂĽnchen disappears in the stormy North Atlantic en route from Bremerhaven to Savannah, Georgia, leaving only a scattering of life rafts and emergency buoys.

2001ĚýJust days apart, two cruise ships – the Bremen and the Caledonian Star – have their bridge windows smashed by waves estimated to be 30 metres tall in the South Atlantic.

Read more about rogue waves, 9 modern ships they have smashed since 2006, and how we’re fighting to predict them: “Rogue waves: The real monsters of the deep“

AT SOME point in their career every mathematician comes up against the question, is mathematics invented or discovered? The query makes some cranky. The answer doesn’t directly affect their work, after all, and the discussion often leads nowhere useful. Spending time debating the ultimate nature of mathematics takes away from actually doing it.

Some scholars take issue with the terms themselves. In his 2008 essay , Harvard University mathematician Barry Mazur called discovery and invention “those two too-brittle words”. One might be tempted to defuse the question altogether with a merger: perhaps maths involves inventing new relationships between things we have discovered.

It’s a metaphysical query, a nerdy way to ask whether or not some pre-existing truths underlie our existence. Here we bump up against theology. If mathematical ideas are discovered – the Platonist position – then a proof is a real-world encounter with an immortal truth. But then where, exactly, is this ethereal pool of truths? Did prime numbers exist before the big bang?

If, on the other hand, mathematics is invented, then proofs spring from human intelligence a bit like art or law. But then why do mathematicians across time and space always agree on what’s right and wrong?

The question about invention versus discovery flares up every few years, often in a different guise. The latest incarnation concerns something very down to earth: money. In this case, the discovery versus invention question has profound consequences. In fact, there may be no mathematical question with higher stakes. That’s because mathematics powers the algorithms that drive computer software, and software is big business, worth over $300 billion a year to the global economy.

One of the most hotly contested issues in software is whether it should be patentable. At present not all of it can be, because of its dependence on mathematics. Patents are granted for inventions, and most mathematical formulas are deemed to be abstract ideas, not inventions, although the rules vary from country to country; some grant software patents, some don’t. Where patents are granted, they are tantamount to big money.

“Mathematical formulas cannot be patented because they are deemed to be abstract ideas”

Writing in the , David Edwards from the University of Georgia in Athens points out that the debate over patents boils down to the difference between discovery and invention. He argues that because abstract mathematical ideas are regarded as “discoveries”, the system is fundamentally Platonic – and broken.

“There is no economic basis for the distinction between discovery and invention,” he told me. “Economically speaking, the difference between discovery and invention should be done away with.” He argues patents should be granted for every new formula and algorithm, including those that power computer software. Such a change would jump-start innovation. “If math were patentable, then you could have independent groups of mathematicians form a group or small company and support themselves that way,” he says.

His position is extreme, but proponents of software patentability similarly argue that the system fuels growth and rewards people for their work.

Critics, notably the nonprofit (EFF) in San Francisco, say the current patent system actually stymies innovation, because getting a patent requires years and tens of thousands of dollars.

Another criticism is that hazy wording in software patent laws has given rise to “patent trolls”, predatory companies that purchase old, cheap patents simply to use them to sue other companies for infringement. Trolling cost US companies $29 billion in 2011, according to a from the Boston University School of Law.

The Chicago-based company Soverain Software, for example, has been . It has racked up tens of millions of dollars suing companies including Amazon and Gap over patents for basic online shopping software. The online computer retailer Newegg, sued by Soverain for $2.5 million, fought back – and in January a US District Court in East Texas .

Even if trolls get banished, weak patents exist. The EFF argues that the US Patent Office fails to identify true inventions, resulting in “a flood of bad patents on so-called inventions that are unoriginal, vague, overbroad, and/or so unclear that bad actors can easily use them to threaten all kinds of innovators”. It has found patents issued for such basic tasks as sorting Facebook friends or purchasing a book with a single click – which are neither new nor original inventions. The beneficiaries of the system, they argue, are patent lawyers, not the general public.

Trolls and weak patents highlight the flaws in the current system – and they are keeping attention on the issue. Last month two US politicians introduced legislation that would penalise patent trolls. In the same month the US Patent and Trademark Office hosted two roundtable events – one at Stanford University in California, the other at New York University – to start discussions in the software world about how to improve the quality of patents.

The rallying cry of a good many critics remains “software is mathematics”, meaning that software shouldn’t be patentable. The odds are stacked against them, though – there’s too much money at stake. But if they lose, they can always console themselves that they may have inadvertently helped solve mathematics’ existential crisis.

As the world waits for the next installment of news in the hunt for the Higgs boson, a simple smart phone game encourages players to hide, not hunt, the world’s favourite particle.

Last December, researchers at the Large Hadron Collider at CERN near Geneva, Switzerland, reported that they had seen a hints of the Higgs boson, an elementary but still hypothetical particle that may help explain how mass forms.

Since then, more data has been collected, which could either strengthen or refute the tentative signal. These are due to be presented on 4 July at a , ahead of a hotly anticipated conference in Melbourne, Australia.

The game, , turns the quest on its head. Though physicists still hunt the Higgs, they are the bad guys – the player’s goal is to keep the particle hidden.

Hide that Higgs

Created by of Cambridge, Massachusetts, Agent Higgs depicts the slippery particle as a hapless and immobile secret agent wearing a ridiculous moustache. Other elementary particles also feature, including electrons, muons, other bosons and neutrinos.

Agent Higgs has a simple interface. Players shuffle these particles around a grid, trying to land on – and therefore conceal – the stationary Higgs.

Whether or not you can move a particle to a particular spot, however, is governed by the standard model of physics: our leading explanation of fundamental particles and force. That means electrons can’t approach each other because the electromagnetic force pushes them apart. And when a particle meets its antimatter doppelganger, both of them vanish. As the levels increase, it becomes more difficult to orchestrate the particles and their forces to keep the Higgs hidden.

Be warned: “Agent Higgs” may be addictive. żěè¶ĚĘÓƵ sent a link to the game to several physicists, and at least one is already hooked. “I just wasted 2 hours on a sunny Saturday morning on it,” says of Indiana University in Bloomington, who works on ATLAS, one of the main particle detectors at CERN.

Strong force

She has one gripe with the science however: “An antineutrino meeting an electron should form a W boson – but who cares? It is a fun game and all the different rules certainly add to the fun.”

A former educator at the before going full time as a game designer, Hall has previously designed games about gravity and special relativity. He’s currently expanding Agent Higgs to include quarks and the strong force, which holds quarks together in protons and neutrons, and holds protons and neutrons together in the nuclei of atoms.

“The strong force is not only the toughest one in particle physics to understand, but it will also make for the most difficult game play,” he says.

There’s another major change he may have to consider in the near future: when physicists find the elusive particle – or rule out its existence – will Agent Higgs finally be out, making the game irrelevant? “I don’t know,” Hall says. “I’m going to have to track the progression of current events to see what happens. I’ll have to wait and see.”

The game costs and is designed for smart phones and tablets, although a stripped down version can be played on a computer.

Pi symphony

Copyrighted digits?

Golden music