The Pythagorean Theorem is simple: x2 + y2 = z2. In this form, the equation can be solved. But what if the 2 is replaced with any positive integer greater than 2? Would the equation still be solvable? More than 300 years ago, amateur mathematician Pierre de Fermat said no, and claimed he could prove it. Unfortunately, the book margin in which he left this prophecy was too small to contain his thinking. Fermat's Last Theorem has since baffled mathematicians armed with the most advanced calculators and computers. Andrew Wiles methodically worked in near isolation to determine the proof for this seemingly simple equation.

Homer's The Odyssey ranks amongst the most famous epics ever written. Follow its archetypal hero, Odysseus, as he sets sail on a twenty-year journey to return home from battle to reclaim his wife and kingdom. It's a timeless tale of adventure, filled with mythological beasts, vengeful gods, and enchanting seductresses. But could it have actually happened? Underwater divers have uncovered remains that date back thousands of years and may be a direct link to the story of Odysseus.

The series concludes by delving into the world of satirical maps. How did maps take on a new form, not as geographical tools, but as devices for humour, satire or storytelling? Graphic Artist Fred Rose perfectly captured the public mood in 1880 with his General Election maps featuring Gladstone and Disraeli, using the maps to comment upon crucial election issues still familiar to us today. Technology was on the satirist's side with the advent of high-speed printing allowing for larger runs at lower cost. In 1877, when Rose produced his 'Serio Comic Map of Europe at War', maps began to take on a new direction and form, reflecting a changing world. Rose's map exploited these possibilities to the full using a combination of creatures and human figures to represent each European nation. The personification of Russia as a grotesque-looking octopus, extending its tentacles around the surrounding nations, perfectly symbolised the threat the country posed to its neighbours.

Journey Through Space gives you an astronaut's eye view of the wonders of the universe, featuring imagery and specially-created animations based upon images from NASA and the European Space Agency and presented here on 720p HD. Your journey begins in Earth orbit and takes you past our moon and neighboring planets, before venturing into deep space for a stunning interstellar tour.

The simple act of making an apple pie is extrapolated into the atoms and subatomic particles (electrons, protons, and neutrons) necessary. Many of the ingredients necessary are formed of chemical elements formed in the life and deaths of stars (such as our own Sun), resulting in massive red giants and supernovae or collapsing into white dwarfs, neutron stars, pulsars, and even black holes. These produce all sorts of phenomena, such as radioactivity, cosmic rays, and even the curving of spacetime by gravity. Cosmos Update mentions the supernova SN 1987A and neutrino astronomy.

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.