Inventing GPS, Carbon nanotube computer, Steven Strogatz and Monty Lyman discuss calculus and skin

Global Positioning System, or GPS is perhaps the best known of the satellite navigation systems, helping us find our way every day. Back in the 1970's Bradford Parkinson and Hugo Fruehauf were two of the inventors who miniaturised atomic clocks and launched them in Earth orbit satellites. This was part of the US Department of Defense's plan to track ships and aircraft and guide targeted missiles. In the intervening years, Brad and Hugo had no idea just how far the civilian applications of GPS would go. Alongside Richard Schwartz and James Spilker, they have just been awarded the prestigious the Queen Elizabeth Prize for Engineering. The age of silicon chip based computing could be coming to an end. Difficulties in shrinking silicon transistors, or switches, into ever smaller processors led researchers at MIT to search for alternative semiconducting materials to replace them. Cue carbon nanotubes, tubes of carbon atoms many tens of thousands of times narrower than a human hair. Electrical engineer Max Shulaker and his team have overcome spaghetti-like tangles of CNTs and varying levels of conductivity to create a 16bit processor. He says that rather than a straight forward replacement to silicon, the initial hope is that CNT chip technology can be added to existing silicon wafers. Steven Strogatz and Monty Lyman have been shortlisted for the Royal Society Insight Investment Science Book Prize this year. In "Infinite Powers", Professor of applied maths at Cornell University, Steven Strogatz tells Adam Rutherford the story of calculus and why his book has a warning saying "this book is dangerous, it will make you love mathematics!" And in "The Remarkable Life of the Skin" Dr. Monty Lyman takes Claudia Hammond on an intimate journey across our surface. They discuss advances in skin treatments, new research on the importance of our diet and our skin and the vital role our largest organ plays in our lives. Producer - Fiona Roberts Presenter - Gareth Mitchell