The IUT theory of Shinichi Mochizuki(望月新一) provides revolutionary conceptual non-linear viewpoints and fundamentally change our understanding of number theoretical structures. IUT extends the range of methods in number theory outside traditional ring-theoretical studies. It separates multiplication from addition. It initiates new connections between group theory and number theory and opens a large territory of potential applications, one of which was the abc/Szpiro/Vojta conjectures and another can be a new proof of FLT.
I will discuss some of these aspects. The file of the talk, with many www-links, including a video illustrating one of the main theorems of IUT, is available from https://www.maths.nottingham.ac.uk/personal/ibf/twt.pdf