The universe began with a massive expansion, billions and billions of years ago, and it continues to expand with every passing second. The idea that the universe, and man's very existence, began with a "Big Bang" is no longer a topic of debate among most scientists--it is essentially taken as fact.

Survival of the fittest: Raw competition? Intense cooperation? Both are essential. Interactions between and within species are among the most powerful evolutionary forces on Earth, and understanding them may be a key to our own survival.

Scorched by their proximity to the sun, Mercury and Venus are hostile worlds; one gouged with craters from cosmic collisions and the other a vortex of sulphur, carbon dioxide and acid rain. Prime examples of planets gone awry, do they serve as a warning for ominous scenarios that might someday threaten Earth?

Shocking new evidence has convinced some of the world's greatest physicists that the universe is a hologram. Using cutting-edge technology, they investigate the secrets of black holes and space-time to build the case for this game-changing discovery.

The holographic principle is a supposed property of quantum gravity that states that the description of a volume of space can be thought of as encoded on a lower-dimensional boundary to the region like a gravitational horizon. First proposed by Gerard 't Hooft, it was given a precise string-theory interpretation by Leonard Susskind.

The holographic principle was inspired by black hole thermodynamics, which conjectures that the maximal entropy in any region scales with the radius squared, and not cubed as might be expected. In the case of a black hole, the insight was that the informational content of all the objects that have fallen into the hole might be entirely contained in surface fluctuations of the event horizon.

The holographic principle is a supposed property of quantum gravity that states that the description of a volume of space can be thought of as encoded on a lower-dimensional boundary to the region like a gravitational horizon. First proposed by Gerard 't Hooft, it was given a precise string-theory interpretation by Leonard Susskind.

The holographic principle was inspired by black hole thermodynamics, which conjectures that the maximal entropy in any region scales with the radius squared, and not cubed as might be expected. In the case of a black hole, the insight was that the informational content of all the objects that have fallen into the hole might be entirely contained in surface fluctuations of the event horizon.

But in the 19th century, maths is turned on its head when new types of geometry are invented. No longer is the kind of geometry we learned in school the final say on the subject. If maths is more like a game, albeit a complicated one, where we can change the rules, surely this points to maths being something we invent - a product of the human mind. To try and answer this question, Hannah travels to Halle in Germany on the trail of perhaps one of the greatest mathematicians of the 20th century, Georg Cantor. He showed that infinity, far from being infinitely big, actually comes in different sizes, some bigger than others. This increasingly weird world is feeling more and more like something we've invented. But if that's the case, why is maths so uncannily good at predicting the world around us? Invented or discovered, this question just got a lot harder to answer.