Source: Alex Lebrun’s website, Jan 2015
Grothendieck continues, providing us with his own interpretation of his work as a mathematician:
If I excelled in the art of the mathematician, this wasn’t so much because of my skills and my determination to solve problems left to me by my predecessors, but rather due to my natural tendency to pick up on crucial issues that nobody else had noticed, or to identify the “best ideas” that were missing (when the new concept hadn’t yet been proposed, no one realized that it was missing) and good formal elaborations which nobody had thought of before.
But more than just simply discovering new questions, ideas, and formal elaborations, my gift lies in the discovery of groundbreaking points of view and this talent has always driven me to introduce and develop completely new topics. And that, I believe, is essentially my contribution to the mathematics of my time.
Grothendieck reveals a lot about himself in the words “I didn’t even realize what I was about to accomplish, it was more like playing a game…” These words remind us of children’s games. In fact, for him, “creation” connects us to the inborn abilities of children who set out to discover the world by playing.
Discovery is a child’s privilege. I mean the small child, the child who is not afraid to be wrong, to look silly, to not be serious, and to act differently from everyone else. He is also not afraid that the things he is interested in are in bad taste or turn out to be different from his expectations, from what they should be, or rather he is not afraid of what they actually are. He ignores the silent and flawless consensus that is part of the air we breathe – the consensus of all the people who are, or are reputed to be, reasonable.
The adult also discovers that he has new eyes, the eyes of a child, in those rare moments when he forgets his fears and his knowledge, when he is eager to learn and look at things or himself with wide-open eyes. [p.127].
Related Resource: the Princeton Companion to Mathematics, 2015