"This is a major step forward," Andrews told New Scientist. "We would not have expected that the crank would have been the right answer to so many of these congruence theorems." But again, it was not clear why prime numbers showed these patterns - until Mahlburg proved the crank can be generalised to all primes. He likens the problem to a gymnasium full of people and a "big, complicated theory" saying there is an even number of people in the gym. Rather than counting every person, Mahlburg uses a "combinatorial" approach showing that the people are dancing in pairs. "Then, it's quite easy to see there's an even number," he says.
Not really. I don't understand it very well (this is number theory) myself and I certainly couldn't explain it to FR, unfortunately.