The years 1825-1918 were bloody and traumatic, a period when four tsars tried - and failed - to deal with the growing pressure for constitutional reform and revolution. In 1861, millions of enslaved serfs were freed by the Tsar-Liberator, Alexander II. But Alexander paid the ultimate penalty for opening the Pandora's box of reform when he was later blown up by terrorists on the streets of St Petersburg. Elsewhere, there was repression, denial, war and - in the case of the last tsar, Nicholas II - a fatalistic belief in the power of God, with Nicholas's faith in the notorious holy man Rasputin being a major part in his undoing. Lucy Worsley also details the chilling murder of Nicholas and his family in 1918, and asks whether all of this horror have been avoided.

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.

Over one billion Christians look to Rome, more than half of all Christians on the planet. But how did a small Jewish sect from the backwoods of 1st-century Palestine, which preached humility and the virtue of poverty, become the established religion of western Europe - wealthy, powerful and expecting unfailing obedience from the faithful? Amongst the surprising revelations, Professor MacCulloch tells how confession was invented by monks on a remote island off the coast of Ireland, and how the Crusades gave Britain the university system. Above all, it is a story of what can be achieved when you have friends in high places.

Atheist and scientist Richard Dawkins visits England, America and Israel interveiwing prominant people of faith; Islamic, Hasidic Jews, and the new Christian sects popping up throughout the world, and expressing his view of the extent to which this fanaticism has degraded our civilisation, and will continue to degrade it. "The God Delusion" explores the unproven beliefs that are treated as factual by many religions and the extremes to which some followers have taken them. Dawkins opens the programme by describing the "would-be murderers ... who want to kill you and me, and themselves, because they're motivated by what they think is the highest ideal." Dawkins argues that "the process of non-thinking called faith" is not a way of understanding the world, but instead stands in fundamental opposition to modern science and the scientific method, and is divisive and dangerous.

Fancisco Pizarro hoped to find great riches in the land of the Inca when he set off on his third voyage to the new world in 1527. Travel back in time with Michael Wood and learn how Pizarro ransomed the life of a king for a room full of gold and silver. Trough letter and drawings from the 16th century and film from modern-day south America, discover this remarkable story of greed, faith, dishonor and valor.

With optional Hebrew subtitles. This episode explores how the spread of the Enlightenment brought ghetto walls around Europe crashing down and allowed Jews to join the wider fabric of modern life in Europe in unprecedented ways. This Jewish renaissance saw Giacomo Meyerbeer and Felix Mendelssohn to establish the enduring tradition for Jewish musical prodigies. However the integration of Jewish talent into the mainstream of European culture and commerce eventually stirred up ancient prejudice, expressed in the new fashion of Romantic nationalism and the pseudo-science of anti-semitism.