Mathematician Dr Hannah Fry explores the mystery of maths. It underpins so much of our modern world that it's hard to imagine life without its technological advances, but where exactly does maths come from? Is it invented like a language or is it something discovered and part of the fabric of the universe? It's a question that some of the most eminent mathematical minds have been wrestling with. To investigate this question, Hannah goes head first down the fastest zip wire in the world to learn more about Newton's law of gravity, she paraglides to understand where the theory of maths and its practice application collide, and she travels to infinity and beyond to discover that some infinities are bigger than others.
In this episode, Hannah goes back to the time of the ancient Greeks to find out why they were so fascinated by the connection between beautiful music and maths. The patterns our ancestors found in music are all around us, from the way a sunflower stores its seeds to the number of petals in a flower. Even the shapes of some of the smallest structures in nature, such as viruses, seem to follow the rules of maths. All strong evidence for maths being discovered. But there are those who claim maths is all in our heads and something we invented. To find out if this is true, Hannah has her brain scanned. It turns out there is a place in all our brains where we do maths, but that doesn't prove its invented.
Experiments with infants, who have never had a maths lesson in their lives, suggests we all come hardwired to do maths. Far from being a creation of the human mind, this is evidence for maths being something we discover. Then along comes the invention of zero to help make counting more convenient and the creation of imaginary numbers, and the balance is tilted in the direction of maths being something we invented. The question of whether maths is invented or discovered just got a whole lot more difficult to answer

After the murder of his brother Frank, Al Capone is out for revenge against William Dever and the Chicago police. He plots to kill every undercover cop that was in Cicero on the day of Frank’s death. Before he can set his plan in motion, however, Johnny Torrio returns from Italy and reclaims his control of their criminal empire. Torrio forbids Capone from killing cops, fearing it would spark an all-out war. Despite Capone’s personal loss, Torrio returns to a booming business that’s raking in $10 million a month. However, as Torrio and Capone’s empire grows, it becomes harder to keep smaller factions under control. After a small group of Italian mobsters attacks one of Dean O’Banion’s distilleries, O’Banion blames Torrio and decides to end their business partnership. He announces his retirement to Torrio and offers Torrio an opportunity to buy him out. Torrio meets O’Banion at the Seine Brewery on May 19, 1924, with the buyout money. Chicago police raid the brewery and arrest Torrio while letting O’Banion walk free: O’Banion had set the whole thing up. With prior convictions, Torrio serves a mandatory prison sentence but is first released on bail. He vows to kill O’Banion as payback and gives Capone his blessing to kill O’Banion. Capone spends months planning the hit. Capone knows that catching O’Banion off guard is nearly impossible, so he places an order with O’Banion’s flower shop for nearly $20,000 worth of flowers, knowing that O’Banion personally oversees his biggest arrangements. On November 10, 1924, O’Banion works in his shop preparing the flower delivery. Two of Capone’s men enter the shop and fatally gun O’Banion down. Four days later, Chicago’s most powerful Irish gangster is laid to rest in one of the most lavish funerals Chicago has ever seen. More than two dozen cars are required to transport floral arrangements as a crowd of 10,000 mourns the death of the infamous gangster. Torrio and Capone attend the funeral, infuriating O’Banion’s top lieutenants, Hymie Weiss and Bugs Moran. Chaos breaks out as smaller gangs through the city begin a turf war. It’s the beginning of an era of bloodshed in Chicago known as the Beer Wars. Over 300 people are murdered at a rate of 75 to 100 murders a year.

Go with us on a mathematical mystery tour, a provocative exploration of math's astonishing power across the centuries. We discover math's signature in the swirl of a nautilus shell, the whirlpool of a galaxy, and the spiral in the center of a sunflower. Math was essential to everything from the first wireless radio transmissions to the successful landing of rovers on Mars. But where does math get its power?" Astrophysicist and writer Mario Livio, along with a colorful cast of mathematicians, physicists, and engineers, follow math from Pythagoras to Einstein and beyond, all leading to the ultimate riddle: Is math an invention or a discovery? Humankind's clever trick, or the language of the universe? Whether we think we're good with numbers or not, we all use math in our daily lives. The Great Math Mystery sheds fascinating light on how math works in our brains and ponders the ultimate mystery of why it works so well when decoding the universe.

This episodes the nature of the cosmos on the micro and atomic scales, using the Ship of the Imagination to explore these realms. Tyson describes some of the micro-organism that live within a dew drop, demonstrating parameciums and tardigrades. He proceeds to discuss how plants use photosynthesis via their chloroplasts to convert sunlight into chemical reactions that convert carbon dioxide and water into oxygen and energy-rich sugars. Tyson then discusses the nature of molecules and atoms and how they relate to the evolution of species. He uses the example set forth by Charles Darwin postulating the existence of the long-tongued Morgan's sphinx moth based on the nature of the comet orchid with pollen far within the flower. He further demonstrates that scents from flowers are used to trigger olfactory centers in the brain, stimulating the mind to threats as to aid in the survival of the species. Tyson narrates how Greek philosophers Thales and Democritus postulated that all matter was made up of combinations of atoms in a large number of configurations, and describes how carbon forms the basic building block for life on earth due to its unique chemical nature. Tyson explains on the basic atomic structure of protons, neutrons, and electrons, and the nature of nuclear fusion that occurs in most stars. He then discusses the existence of neutrinos that are created by these nuclear processes in stars, and that detecting such sub-atomic particles which normally pass through matter require subterranean facilities like the Super-Kamiokande that were used to detect neutrinos from the supernova SN 1987A in the Large Magellanic Cloud before light from the explosion were observed due to their ability to pass through matter of the dying sun. Tyson compares how neutrinos were postulated by Wolfgang Pauli to account for the conservation of energy from nuclear reactions in the same manner as Darwin's postulate on the long-tongued moth. Tyson concludes by noting that there are neutrinos from the Big Bang still existing in the universe but due to the nature of light, there is a "wall of infinity" that cannot be observed beyond.

Written and presented by David Attenborough, who said: 'One of the most wonderful things about filming plants is that you can reveal hidden aspects of their lives, you can capture the moment as one plant strangles another, and as they burst into flower. But whilst time-lapse photography allows you to see things that no human being has ever seen before". David begins his journey inside the magnificent Palm House, a unique global rainforest in London. Here, he explores the extraordinary plants that are so well adapted to wet and humid environments and unravels the intimate relationships between wet zone plants and the animals that depend on them. It was in the wet zones of the world that plants first moved on to land and in the Waterlily House David reveals how flowers first evolved some 140 million years ago. Watching a kaleidoscope of breath-taking time-lapses of these most primitive of flowers swelling and blooming in 3D, he is able to piece together the very first evolutionary steps that plants took to employ a wealth of insects to carry their precious pollen for the first time. David discovers clues to answer a question that even had Charles Darwin stumped: how did flowering plants evolve so fast to go on to colonise the entire planet so successfully?

Bladderwort utricularia is a pond-dweller that is among the fastest known, its traps snapping shut in less than a millisecond. As the seasons change, David demonstrates how plants operate on a different time scale to us; how they modify their lives according to the time of year. We discover insects’ hidden links with plants, both as pests and pollinators. UV-sensitive 3D cameras reveal the invisible alter-ego of plants and their flowers’ mesmerizing patterns; a parallel-dimension of strange colours and stunning patterns through which plants communicate with them. With the aid of visual effects, David steps among the swirling vortices of plant scent; communication signals with which plants are inextricably plugged in to the natural world. And using a tuning fork, he demonstrates how plants and insects can even communicate with music. As autumn envelopes the Gardens, fungi reveal themselves not as the enemies of plants but their vital allies. In Kew’s atmospheric Fungarium, David discovers a specimen that has the power of mind control and another that lives underground where it has grown to be so big it can be counted as the largest single organism on the planet. It is 6 times bigger than Kew Gardens itself.