Stephen Hawking is the most famous scientist on the planet. But behind the public face lies an argument that has been raging for almost 30 years. Has he been wrong for the last 30 years? Hawking shot to fame in the world of physics when he provided a mathematical proof for the Big Bang theory. This theory showed that the entire universe exploded from a singularity, an infinitely small point with infinite density and infinite gravity. Hawking was able to come to his proof using mathematical techniques that had been developed by Roger Penrose. These techniques were however developed to deal not with the beginning of the Universe but with black holes". Science had long predicted that if a sufficiently large star collapsed at the end of its life, all the matter left in the star would be crushed into an infinitely small point with infinite gravity and infinite density – a singularity. Hawking realised that the Universe was, in effect, a black hole in reverse. Instead of matter being crushed into a singularity, the Universe began when a singularity expanded to form everything we see around us today, from stars to planets to people. Hawking realised that to come to a complete understanding of the Universe he would have to unravel the mysteries of the black hole and its paradoxes

Dark energy - the mysterious force that is unexpectedly causing the universe's expansion to speed up. The effects of dark energy were discovered in 1998 but physicists still don't know what it is. Worse, its very existence calls into question Albert Einstein's general theory of relativity - the cornerstone of modern physics. The hunt for the identity of dark energy is on". Experiments on earth and in space generate data that might provide a clue, but there are also hopes that another Einstein might emerge - someone who can write a new theory explaining the mystery of the dark energy.

One of the Universe's most enduring mysteries is Time Travel. In this episode, we explore the possibilities. Discover why Time Travel into the future is unavoidable in the Einsteinian world of Relativity. As for the past... the laws of physics do not tell us it's impossible, but the bizarre consequences of going into the past and altering the future make for mind-bending science. Finally, we go for the future by traveling to the nearest star, 4.3 light years away... in only 45 days. Our destination may be an Earth-like planet; a planet scientists are now hunting for, and may find in the next 3 to 4 years.

Is Time Travel Possible? Stephen Hawking explores the world's favourite scientific 'what if?' He explores all the possibilities, warping the very fabric of time and space as he goes. From killing your grandfather to riding a black hole, we learn the pitfalls and the prospects for a technology that could quite literally, change everything.

Explore the myths, misconceptions, truths & amazing mysteries of our unique universe. Could life exist on Mars? Is time travel possible & does Einstein's theory of relativity support it?

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.