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.

The key to understanding the universe seems to be understanding its smallest components. But the quantum realm bears little resemblance to the universe we know. Image a particle that can be many places at the same time and communicate changes instantly across vast distances, even to the other side of the Universe. Shrinking down billions of times, into the realm of atoms and sub-atomic particles, takes us into a bizarre world of paradoxes and multiverses. Explore with us quantum physics and the potential applications in computer science.

Professor Jim Al-Khalili investigates the most accurate and yet perplexing scientific theory ever - quantum physics. At the beginning of the 20th century scientists were led into the hidden workings of matter, into the sub-atomic building blocks of the world around us. They discovered phenomena unlike any encountered before - a realm where things can be in many places at once, where chance and probability call the shots and where reality appears to only truly exist when we observe it. Albert Einstein hated the idea that nature, at its most fundamental level, is governed by chance. Jim reveals how, in the 1930s, Einstein thought he'd found a fatal flaw in quantum physics because it implies that sub-atomic particles can communicate faster than light in defiance of the theory of relativity. In the 1960s the scientist John Bell showed there was a way to test if Einstein was right and quantum mechanics was actually mistaken. Jim repeats this critical experiment - with shocking results.

On a trip to the fortified Moroccan village of Ait-Ben-Haddou in the Atlas Mountains, Professor Brian Cox reveals how by watching the stars' motion across the night sky, it is quite natural for man to think he is at the centre of everything. That view was held for many ages, but innate human curiosity has eventually led to an understanding of mankind's true place in space and time, and an appreciation that Earth is not a focal point but a mere particle of rock in a possibly infinite expanse of space, 13.8 billion years from the beginning of the universe.

While scientists have previously theorised about a “Big Crunch” where the universe retracts back to its original size, the discovery of Dark Matter and Dark Energy has placed that hypothesis on the backburner. Some astronomers now believe that if Dark Matter offsets Dark Energy then as the universe slowly expands, stars will gradually fade, running out of fuel and leading to a dark, cold and lifeless universe. Others hypothesise a much more violent end where Dark Energy continues to expand the universe at a greater and greater speed. Stronger than gravity, Dark Energy would pull apart everything down to the fundamental particles – the universe’s very fibres. While the universe’s end may be 50 billion years away, great leaps in science will continue to alter how we believe the universe was formed – and how it will end.

Einstein's world-shaking Theory of Relativity says that time travel is perfectly possible -- if you're going forward in time. Finding a way to travel backwards requires breaking the speed of light, which so far seems impossible. But now, strange-but-true phenomena such as quantum nonlocality (where particles instantly teleport across vast distances) may give us a way to make the dream of traveling back and forth through time a reality. Step into a time machine and rewrite history, bring loved ones back to life, control our destinies. But if succeed, what are the consequences of such freedom? Will we get trapped in a plethora of paradoxes and multiple universes that will destroy the fabric of the universe?