Shinichi Mochizuki is a number theorist at Kyoto University.
He went to Philip Exeter Academy, one of the most prestigious High Schools in the country, and graduated in a brief two years. He entered Princeton University at age sixteen and left with a Ph. D at 22. He was a full professor by 33, an absurdly young age for academia. And now, this mathematical rock star may have just cracked one of the most important problems in his field.
In short, the abc conjecture — proposed in 1985 — explores the relationships between prime numbers.
It's been described as the most important unsolved problem in Diophantine Analysis, a branch of mathematics that — by working with some of the most simple number systems (like ax + by = 1 or xn + yn = zn) explores some of the deepest relationships in math.
So if you're looking for an instant "real world application," hit the back button — but if you want to see why one equation can tell us so much about how numbers work, read on.