Alice Roberts tries to find out how Stone Age people reached North and South America for the first time. She finds out about an ancient corridor through the Canadian ice sheet that might have allowed the first humans through. Old finds in Chile though point to a whole different route for the first humans making it there.

By our third year, most of us will have learned to count. Once we know how, it seems as if there would be nothing to stop us counting forever. But, while infinity might seem like an perfectly innocent idea, keep counting and you enter a paradoxical world where nothing is as it seems. Mathematicians have discovered there are infinitely many infinities, each one infinitely bigger than the last. And if the universe goes on forever, the consequences are even more bizarre. In an infinite universe, there are infinitely many copies of the Earth and infinitely many copies of you. Older than time, bigger than the universe and stranger than fiction. This is the story of infinity.

Our lifespan is increasing by 2.5 years every decade - and a third of all babies born today can expect to live to 100. But living longer can come at a cost. Old age itself brings with it a range of debilitating illnesses, many of which are the result of accumulating damage during our lifetime. Three diseases in particular have become the main killers in the developed world - cancer, heart disease and dementia. But a revolution in bio-medicine is now offering new hope for the treatment of these ailments, and the potential to extend our lives still further. Methods such as gene editing and stem cell therapies are transforming the way medicine can conquer disease today. "How to Live Longer" counts with the guide of the Nobel laureate Sir Paul Nurse, for whom the big question isn't just what science can do to fix our bodies and extend our lives, but whether it's right to use all the tools and techniques available.

There is a contest each year that can change a young skater's life. There are no pros with million dollar endorsement deals here, just real kids with real lives and everything on the line. This is the story of a few of the best, from France, Brazil and the USA, as they risk everything for a chance of a lifetime. Motivation 3: The Next Generation is a proper follow-up to The Motivation but this time the stakes are so much higher. We're in deep with real kids escaping poverty and violence, crashing in skate-houses or still living with mom. For all of these kids a win at Tampa Am could mean a way out and an opportunity to do what they love for a living-skate.

Last year, just before Thanksgiving, I approached my dad, Leonard Nimoy, about the possibility of working together on a film about Mr. Spock. I had skimmed through some of the books on the making of Star Trek and felt there was so much more to explore about the creation and development of Mr. Spock. And the timing seemed right, as the 50th anniversary of Star Trek the original series was not that far away. Dad agreed that now was the right time, and that he was 100% committed to collaborating with me on this project. He also reminded me that we were (then) just days away from the 50th anniversary of the start of production on 'The Cage,' the original pilot for Star Trek in which dad first appeared as Mr. Spock.

Mathematician Dr Hannah Fry explores the mystery of maths. It underpins so much of our modern world that it's hard to imagine life without its technological advances, but where exactly does maths come from? Is it invented like a language or is it something discovered and part of the fabric of the universe? It's a question that some of the most eminent mathematical minds have been wrestling with. To investigate this question, Hannah goes head first down the fastest zip wire in the world to learn more about Newton's law of gravity, she paraglides to understand where the theory of maths and its practice application collide, and she travels to infinity and beyond to discover that some infinities are bigger than others.
In this episode, Hannah goes back to the time of the ancient Greeks to find out why they were so fascinated by the connection between beautiful music and maths. The patterns our ancestors found in music are all around us, from the way a sunflower stores its seeds to the number of petals in a flower. Even the shapes of some of the smallest structures in nature, such as viruses, seem to follow the rules of maths. All strong evidence for maths being discovered. But there are those who claim maths is all in our heads and something we invented. To find out if this is true, Hannah has her brain scanned. It turns out there is a place in all our brains where we do maths, but that doesn't prove its invented.
Experiments with infants, who have never had a maths lesson in their lives, suggests we all come hardwired to do maths. Far from being a creation of the human mind, this is evidence for maths being something we discover. Then along comes the invention of zero to help make counting more convenient and the creation of imaginary numbers, and the balance is tilted in the direction of maths being something we invented. The question of whether maths is invented or discovered just got a whole lot more difficult to answer