In the attempt to make scientific discoveries, every problem is an opportunity, and the more difficult the problem, the greater will be the importance of its solution.

Even in places like Senegal, beginning in the early 20th century, there were major breakthroughs in public health, and life expectancy began to rise.

Carolyn Porco shares exciting new findings from the Cassini spacecraft's recent sweep of one of Saturn's moons, Enceladus. Samples gathered from the moon's icy geysers hint that an ocean under its surface could harbor life.

Our societies now spend two, three, four percent of GDP to invest systematically in new discovery, in science, in technology, to fuel the pipeline of brilliant inventions which illuminate gatherings like this.

I'm hoping we can, for example, use that even to get Wolfram Alpha to routinely do invention and discovery on the fly, and to find all sorts of wonderful stuff that no engineer and no process of incremental evolution would ever come up with.

At TEDxNASA, planetary scientist Joel Levine shows some intriguing and puzzling new discoveries about Mars craters full of ice, traces of ancient oceans, and compelling hints at the presence, sometime in the past, of life. He makes the case for going back to Mars to find out more.

The relatively few copies of Archimedes' written work that survived through the Middle Ages were an influential source of ideas for scientists during the Renaissance, while the discovery in 1906 of previously unknown works by Archimedes in the Archimedes Palimpsest has provided new insights into how he obtained mathematical results.