While reading The Princeton companion to Mathematics Timothy Gowers choose not to list alive mathematicians in the last part but I think it's important to know about them. Recently I've read about Alexander Grothendieck, Jean Pierre Serre, Sir Michael Atiyah, Vladimir Arnold and Robert Wisbauer. It was very interesting and enlightening, I am reading La Clef des Songes by Alexander Grothendieck, watched this lecture by Vladimir Arnold, read an advice to a young mathematician by Sir Michael Atiyah on the Princeton companion to Mathematics, and I usually read Terence Tao's personal blog.
I'd like you to point me to more contemporary mathematicians and readings to know their work, as Abel said one should learn from the masters and being a beginner mathematician it's not clear what one should read to achieve that.