Singularities within equations are common ... question is that of a more fundamental one. How does a mathematical singularity exist in our reality? How does one of the most massive objects ...

What Hawking ended up with were descriptions of black holes that could boil themselves out of existence, and equations that ... an infinitely small point - a singularity Black holes radiate ...

He came up with an innovative equation called the Ricci flow that ... and a milestone for the mathematical community. But in 2010, Dr. Perelman turned down the Millennium Prize.