arithmetic progression
The natural numbers, 1, 2, 3, 4, ..., are nice. So what could be nicer than discovering interesting patterns within them? 
This year's Abel Prize goes to Endre Szemerédi for his
"fundamental contributions to discrete mathematics and theoretical
computer science."

The prime numbers are the atoms amongst the integers, and while we know that there are infinitely many of them, there's no general formula that generates them all. Julian Havil looks at a littleknown algorithm that sieves out all primes up to a given number, and which is astonishing in its simplicity.
