who: Maxim Kontsevich
when: when I was a PhD student, and onwards.
why: probably because of my main research interest when I was a PhD student, namely deformation quantization. Also because before moving to (many) other subjects Kontsevich has formulated a lot of very reasonnable conjectures and guessed a lot of possible developpments in the field. Some of them I have been following. Even now, I am still thinking quite often about a few questions he raised .