Perfect numbers were discovered about 2500 years ago, but human intelligence has not revealed much about them. It is not known whether their number is infinite or whether there are any odd perfect numbers. In the early 21st century Reinhard Zumkeller pressed the pedal of his imagination and generalized the perfect numbers. Instead of unsuccessfully searching for proofs for the infinitude of the perfect numbers, the mathematicians started thinking about the Zumkeller numbers and finding interesting things about them. It is now known for certain that there are infinitely many Zumkeller numbers, that some of them are odd, and that out of every 12 consecutive natural numbers at least one is a Zumkeller number.

Elementary, my dear Watson, when you can't go forward and find something about a second thing, you can go sideways and find a third thing about a fourth thing.