This statement is false. Think about it, and it makes your head hurt. If it’s true, it’s false. If it’s false, it’s true. In 1931, Austrian logician Kurt Gödel shocked the worlds of mathematics and philosophy by establishing that such statements are far more than a quirky turn of language: he showed that there are mathematical truths which simply can’t be proven.
“The infinite! No other question has ever moved so profoundly the spirit of man,” said David Hilbert, one of the most influential mathematicians of the 19th century. A subject extensively studied by philosophers, mathematicians, and more recently, physicists and cosmologists, infinity still stands as an enigma of the intellectual world.
Black holes are gravitational behemoths that dramatically twist space and time. Recently, they’ve also pointed researchers to a remarkable proposal—that everything we see may be akin to a hologram.
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.
In the future, a woman with a spinal cord injury could make a full recovery; a baby with a weak heart could pump his own blood. How close are we today to the bold promise of bionics—and could this technology be used to improve normal human functions, as well as to repair us?
The inflationary theory of cosmology, an enduring theory about our universe and how it was formed, explains that just after the Big Bang, the universe went through a period of rapid expansion. This theory has been critical to understanding what’s going on in the cosmos today.
It’s an old question: What is consciousness? Today, sophisticated brain imaging technologies, clinical studies, as well as the newfound ability to listen to the whisper of even an individual nerve cell, are bringing scientists closer than ever to the neurobiological basis of consciousness.
For all we understand about the universe, 96% of what’s out there still has scientists in the dark. Astronomical observations have established that familiar matter—atoms—accounts for only 4% of the weight of the cosmos. The rest—dark matter and dark energy—is invisible to our telescopes.