Even 2,000 years after his death, General Hannibal's battle strategies are still studied today. But of all his military feats, perhaps his greatest was leading his massive Carthaginian army of men and three-dozen elephants across the Alps and into the heartland of Rome in 218 B.C. Until now, the route they took has been a matter of dispute, but thanks to modern-day technology, geomorphologist Bill Mahaney and microbiologist Chris Allen believe they've accurately traced this ancient journey.

Dr Hannah Fry explores a paradox at the heart of modern maths, discovered by Bertrand Russell, which undermines the very foundations of logic that all of maths is built on. These flaws suggest that maths isn't a true part of the universe but might just be a human language - fallible and imprecise. However, Hannah argues that Einstein's theoretical equations, such as E=mc2 and his theory of general relativity, are so good at predicting the universe that they must be reflecting some basic structure in it. This idea is supported by Kurt Godel, who proved that there are parts of maths that we have to take on faith.
Hannah then explores what maths can reveal about the fundamental building blocks of the universe - the subatomic, quantum world. The maths tells us that particles can exist in two states at once, and yet quantum physics is at the core of photosynthesis and therefore fundamental to most of life on earth - more evidence of discovering mathematical rules in nature. But if we accept that maths is part of the structure of the universe, there are two main problems: firstly, the two main theories that predict and describe the universe - quantum physics and general relativity - are actually incompatible; and secondly, most of the maths behind them suggests the likelihood of something even stranger - multiple universes.
We may just have to accept that the world really is weirder than we thought, and Hannah concludes that while we have invented the language of maths, the structure behind it all is something we discover. And beyond that, it is the debate about the origins of maths that has had the most profound consequences: it has truly transformed the human experience, giving us powerful new number systems and an understanding that now underpins the modern world.

On April 20, 2010, the Deepwater Horizon oil rig exploded in the Gulf of Mexico. It killed 11 workers and caused the worst oil spill in American history. The explosion still haunts the lives of those most intimately affected, though the story has long ago faded from the front page.
At once a fascinating corporate thriller, a heartbreaking human drama and a peek inside the walls of the secretive oil industry, 'The Great Invisible' is the first documentary feature to go beyond the media coverage to examine the crisis in depth through the eyes of oil executives, survivors and Gulf Coast residents who experienced it first-hand and then were left to pick up the pieces while the world moved on.

The big blue is the world's greatest wilderness, far from shore and many kilometres deep. It's a vast marine desert where there is little to eat and nowhere to hide. Yet it's home to some of the biggest and most spectacular creatures on earth. This episode reveals what it takes to survive in this savage and forbidding world. We witness feats of incredible endurance, moments of high drama and extraordinary acts of heart-wrenching self-sacrifice. Every animal in the big blue must find their own unique way to survive. Sperm whales have the largest brains in the world. They live for 80 years, and we are only now beginning to learn the extraordinary complexity of their language of clicks - thought to coordinate the whole family in everything from childcare to hunting. With special pressure-proof cameras, we witness record-breaking feats of endurance as they hunt for squid a kilometre down into the abyss. Only recently have we begun to solve the mystery of where baby turtles disappear to in their early years. They leave the crowded waters of the coast and head to the open ocean, where they use floating debris like logs as life rafts. Here they remain until adulthood, adrift on the high seas in relative safety away from coastal predators. Over half of all animals in the open ocean drift in currents. Jellyfish cross entire oceans feeding on whatever happens to tangle with their tentacles. The jelly-like Portuguese man-of-war can harness sail power to fish with its deadly tentacles. Sometimes there is a brief explosion of food in this marine desert, but ocean hunters must be fast to make the best of this bonanza. We witness super pods of up to 5,000 spinner dolphins racing to herd vast shoals of lanternfish, briefly caught at the surface where it is thought they spawn. New aerial footage reveals, for the first time, the truth to a centuries-old sailors' legend of the 'boiling seas' - the spectacular feeding frenzy of 90kg tuna and dolphins smashing through the lantern fish shoals turning the sea white with foam.

More than 2,000 years ago, the thriving city of Petra rose up in the bone-dry desert of what is now Jordan. An oasis of culture and abundance, the city was built by wealthy merchants whose camel caravans transported incense and spices from the Arabian Gulf. They carved spectacular temple-tombs into its soaring cliffs, raised a monumental Great Temple at its heart, and devised an ingenious system that channeled water to vineyards, bathhouses, fountains, and pools. But following a catastrophic earthquake and a slump in its desert trade routes, Petra's unique culture faded and was lost to most of the world for nearly a thousand years. Now, in a daring experiment, an archaeologist and sculptors team up to carve an iconic temple-tomb to find out how the ancient people of Petra built their city of stone. Meanwhile, scientists using remote sensors and hydraulic flumes uncover the vast city and its sophisticated water system. The race is on to discover how these nomads created this oasis of culture in one of the harshest climates on Earth.

Dr Michael Mosley traces the sinister ways the experimental psychology has used to try to control our minds. He finds that the pursuit of mind control has led to some truly horrific experiments and left many casualties in its wake. Extraordinary archive captures what happened - scientists systematically change the behaviour of children; law abiding citizens give fatal electric shocks; a gay man has electrodes implanted in his head in an attempt to turn his sexuality. Michael takes a hallucinogenic drug as part of a controlled experiment to try to understand how its mind-bending properties can change the brain. This is a scientific journey goes to the very heart of what we hold most dear - our free will, and our ability to control our own destiny.