The mysteries of dark matter and dark energy may be evidence that we don’t fully understand the force of gravity. But when it comes to a force that has been studied mathematically and probed observationally for hundreds of years, what do we still need to learn?

Mathematical mysteries have challenged humanity’s most powerful thinkers and inspired passionate, lifelong obsessions in search of answers. From the strangeness of prime numbers and the nature of infinity, to the turbulent flow of fluids and the geometry of hyperspace, mathematics is our most potent tool for revealing immutable truths.

We once shared the planet with Neanderthals and other human species. Some of our relatives may have had tools, language and culture. Why did we thrive while they perished?

Immanuel Kant, who coined the term genius in the 1700s, defined it as the rare capacity to independently understand concepts that would normally have to be taught by another person. Since then, the spectrum of abilities that we call genius has widened, but pivotal questions remain: What exactly is genius?

This video is part of our Brilliant Breakthroughs series: our new 20-episode mini-series exploring the “Eureka!” moments and proud accomplishments of the greatest scientific minds of our time. Join us …

Does God exist? Could our universe be a simulation? Watch WSF co-founder Brian Greene and evolutionary biologist Richard Dawkins, in a lively discussion on philosophical ideas of atheism, science and religion.