Integer programming is arguably the greatest achievement of applied mathematics. Half of the time, it's what's used to solve real-world problems!
Probabilities have been proven to be a great tool to understand some features of the world, such as what can happen in a dice game. Applied to programming, it has enabled plenty of amazing algorithms. In this article, we discuss its application to the primality test as well as to face detection. We'll also deal with quantum computers, as well as fundamental computer science open problems P=BPP and NP=BQP.
P=NP is probably today's most crucial open problem. Not only is it a very theoretical question in computer science and mathematics, but it also has major implications to real world. Its resolution could revolutionize the world. This article gives the definition and major results of P=NP.