Alexander Grothendieck revolutionized mathematics, especially in the period 1958 -- 1970. Our scientific life has been different after he launched his beautiful ideas, mainly in algebraic geometry and number theory. I will say something about the life of Grothendieck (no fiction can improve upon these stories). Then I will discuss some characteristic features of his way of working. We will see some aspects of his correspondence with Serre, and with Mumford. I will illustrate his ideas by analyzing some thoughts. Especially we try to answer the question in the title. We will see some of his big successes, but also see that he could get stuck. Then we see how others carried on his work, but sometimes in a different way: Grothendieck inspired many of us. This might give us a clear picture of the flow of mathematical ideas.