brilliant mathematicians, whose genius has profoundly affected us, but which tragically drove them insane and eventually led to them all committing suicide. Georg Cantor, the great mathematician whose work proved to be the foundation for much of the 20th-century mathematics. He believed he was God's messenger and was eventually driven insane trying to prove his theories of infinity. Ludwig Boltzmann's struggle to prove the existence of atoms and probability eventually drove him to suicide.

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.

A visit to arguably the most famous archipelago on Earth, the Galapagos. It's home to a myriad of bizarre and unique creatures, endemic to these islands - but how did they get here and what is the key to these extraordinary islands that allows them to thrive? The programme reveals that this key holds not just the secret to life here, but also to how Darwin was able to leave with the ideas that would revolutionise biology.

A stellar explosion, the supernova is the sensational death of a star. It can shine as bright as 100 billion Suns and radiate as much energy as the Sun would emit over 10 billion years. Jets of high-energy light and matter are propelled into space and can cause massive Gamma Ray Bursts and emit intense X-ray radiation for thousands of years. Astronomers believe that this process creates the very building blocks of planets, people and plants. Meet the world's leading Supernova hunters, and take a look at recorded supernovas throughout history.

1916. The war is raging in Europe and stretches from the trenches in France to the Italian Alps and the Balkans, and beyond to the gates of the Eastern world. The conflict becomes industrial, and millions of shells rain down on the battlefields; Verdun and the Somme are the deadliest battles in this second year of the war. Who can stop this infernal machine?

The Cave of Swallows in Mexico is a 400m vertical shaft, deep enough to engulf the Empire State Building. The Lechuguilla cave system in the USA is 193km long and 500m deep with astonishing crystal formations hanging from its chambers. Although often overlooked, caves are remarkable habitats with equally bizarre wildlife. Cave angel fish cling to the walls behind cave waterfalls with microscopic hooks on their flattened fins. Cave swiftlets navigate by echo-location and build nests out of saliva. The Texas cave salamander has neither eyes nor pigment. Unique access to a hidden world of stalactites, stalagmites, snotites and troglodytes brings a wealth of surprises.