Do other worlds tremble and heave with geological life? On Mars, we found a volcano to dwarf Mount Everest. On the moons of the giants our understanding of volcanoes was changed forever.

This four-part British television series outlines aspects of the history of mathematics. Written and presented by University of Oxford professor Marcus du Sautoy, it is a co-production between the Open University and the BBC. In the first episode, Marcus du Sautoy in Egypt uncovers use of a decimal system based on ten fingers of the hand and discovers that the way we tell the time is based on the Babylonian Base 60 number system. In Greece, he looks at the contributions of some of the giants of mathematics including Plato, Archimedes and Pythagoras, who is credited with beginning the transformation of mathematics from a counting tool into the analytical subject of today. A controversial figure, Pythagoras’ teachings were considered suspect and his followers seen as social outcasts and a little be strange and not in the norm. There is a legend going around that one of his followers, Hippasus, was drowned when he announced his discovery of irrational numbers. As well as his work on the properties of right angled triangles, Pythagoras developed another important theory after observing musical instruments. He discovered that the intervals between harmonious musical notes are always in whole number intervals.

After filming for three years, Planet Earth finally captures the shy Mongolian gazelle. Only a handful of people have witnessed its annual migration. Don't miss the bizarre-looking Tibetan fox, captured on film for the first time. Over six weeks the team follow a pride of 30 lions as they attempt to hunt elephants. Using the latest night vision equipment, the crew film the chaotic battles that ensue at close quarters.

There are 200 million insects for each of us. They are the most successful animal group ever. Their key is an armoured covering that takes on almost any shape. Darwin's stag beetle fights in the tree tops with huge curved jaws. The camera flies with millions of monarch butterflies which migrate 2000 miles, navigating by the sun. Super slow motion shows a bombardier beetle firing boiling liquid at enemies through a rotating nozzle. A honey bee army stings a raiding bear into submission. Grass cutter ants march like a Roman army, harvesting grass they cannot actually eat. They cultivate a fungus that breaks the grass down for them. Their giant colony is the closest thing in nature to the complexity of a human city.

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.