Super quick computers and advanced mathematical formulas have taken over trading on the financial markets from human beings -algorithms- which seem to have a life of their own. The only ones who understand the system in any way are its architects, the algorithm developers. Haim Bodek is one such algo-developer. After finding some strange wrongdoings he set out on a personal crusade against this elusive system". The machinery behind our financial markets, consisting of mathematical models, data centers and miles and miles of fiber optic cables, is disguised by technological complexity and secrecy. The builders of this financial system are a new breed of Wall Street employees -quants- mathematicians and physicists who are responsible for a technological revolution. Haim Bodek is a quant; he specialized in artificial intelligence and worked for Goldman Sachs. He knows the system from the inside, he helped build it. Haim Bodek was invited to tell his story at the "Battle of the Quants" - a recurring event where quants discuss high-frequency trading, amongst other things. Bodek wrote an algorithm for trading machines that would generate guaranteed income - a money machine that weathered the financial meltdown of 2008. But then from one day to the next the algorithm stopped working.

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.

When ancient architects completed construction on the Great Pyramid at Giza, they left behind the greatest riddle of the engineering worldâ€”how did builders lift limestone blocks weighing an average of two and a half tons 480 feet up onto the top of the Pyramid? For centuries, adventurers and Egyptologists have crawled through every passageway and chamber of the Pyramid, measuring and collecting data in an attempt to determine how it was built. For the first time, a revolutionary theory argues that the answer may be inside the Pyramid. Architect Jean-Pierre Houdin and Egyptologist Bob Brier use 3-D software to unlock the secret.

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.

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.

Writing itself is 5,000 years old, and for most of that time words were written by hand using a variety of tools. The Romans were able to run an empire thanks to documents written on papyrus. Scroll books could be made quite cheaply and, as a result, ancient Rome had a thriving written culture. With the fall of the Roman Empire, papyrus became more difficult to obtain. Europeans were forced to turn to a much more expensive surface on which to write: Parchment. Medieval handwritten books could cost as much as a house, they also represent a limitation on literacy and scholarship.

No such limitations were felt in China, where paper had been invented in the second century. Paper was the foundation of Chinese culture and power, and for centuries how to make it was kept secret. When the secret was out, paper mills soon sprang up across central Asia. The result was an intellectual flourishing known as the Islamic Golden Age. Muslim scholars made discoveries in biology, geology, astronomy and mathematics. By contrast, Europe was an intellectual backwater.

That changed with Gutenbergâ€™s development of movable type printing. The letters of the Latin alphabet have very simple block-like shapes, which made it relatively simple to turn them into type pieces. When printers tried to use movable type to print Arabic texts, they found themselves hampered by the cursive nature of Arabic writing. The success of movable type printing in Europe led to a thousand-fold increase in the availability of information, which produced an explosion of ideas that led directly to the European Scientific Revolution and the Industrial Revolution that followed.

No such limitations were felt in China, where paper had been invented in the second century. Paper was the foundation of Chinese culture and power, and for centuries how to make it was kept secret. When the secret was out, paper mills soon sprang up across central Asia. The result was an intellectual flourishing known as the Islamic Golden Age. Muslim scholars made discoveries in biology, geology, astronomy and mathematics. By contrast, Europe was an intellectual backwater.

That changed with Gutenbergâ€™s development of movable type printing. The letters of the Latin alphabet have very simple block-like shapes, which made it relatively simple to turn them into type pieces. When printers tried to use movable type to print Arabic texts, they found themselves hampered by the cursive nature of Arabic writing. The success of movable type printing in Europe led to a thousand-fold increase in the availability of information, which produced an explosion of ideas that led directly to the European Scientific Revolution and the Industrial Revolution that followed.