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.
Alice Roberts explores the latest discoveries in the study of human origins, revealing the transformation that has been brought about in this field by genetics. Traditional Palaeoanthropology, based on fossils, is being transformed by advanced genome sequencing techniques. We now know that there were at least four other distinct species of human on the planet at the same time as us - some of them identified from astonishingly well-preserved DNA extracted from 50,000-year-old bones, others hinted at by archaic sections of DNA hidden in our modern genome. What's more, we now know that our ancestors met and interacted with these other humans, in ways that still have ramifications today. Alice uses these revelations to update our picture of the human family tree.
Physicist Jim Al-Khalili travels through Syria, Iran, Tunisia and Spain to tell the story of the great leap in scientific knowledge that took place in the Islamic world between the 8th and 14th centuries. Its legacy is tangible, with terms like algebra, algorithm and alkali all being Arabic in origin and at the very heart of modern science - there would be no modern mathematics or physics without algebra, no computers without algorithms and no chemistry without alkalis. For Baghdad-born Al-Khalili, this is also a personal journey, and on his travels he uncovers a diverse and outward-looking culture, fascinated by learning and obsessed with science. From the great mathematician Al-Khwarizmi, who did much to establish the mathematical tradition we now know as algebra, to Ibn Sina, a pioneer of early medicine whose Canon of Medicine was still in use as recently as the 19th century, Al-Khalili pieces together a remarkable story of the often-overlooked achievements of the early medieval Islamic scientists.
Al-Khalili travels to northern Syria to discover how, a thousand years ago, the great astronomer and mathematician Al-Biruni estimated the size of the earth to within a few hundred miles of the correct figure. He discovers how medieval Islamic scholars helped turn the magical and occult practice of alchemy into modern chemistry. In Cairo, he tells the story of the extraordinary physicist Ibn al-Haytham, who helped establish the modern science of optics and proved one of the most fundamental principles in physics - that light travels in straight lines. Prof Al-Khalili argues that these scholars are among the first people to insist that all scientific theories are backed up by careful experimental observation, bringing a rigour to science that didn't really exist before.
In the last episode, Al-Khalili turns detective, hunting for clues that show how the scientific revolution that took place in the 16th and 17th centuries in Europe had its roots in the earlier world of medieval Islam. He travels across Iran, Syria and Egypt to discover the huge astronomical advances made by Islamic scholars through their obsession with accurate measurement and coherent and rigorous mathematics.He then visits Italy to see how those Islamic ideas permeated into the west and ultimately helped shape the works of the great European astronomer Copernicus, and investigates why science in the Islamic world appeared to go into decline after the 16th and 17th centuries, only for it to re-emerge in the present day. Al-Khalili ends his journey in the Royan Institute in the Iranian capital Tehran, looking at how science is now regarded in the Islamic 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.