This year the Abel Prize is awarded to John Tate "for his vast and lasting impact on the theory of numbers". It seems a good idea to present at least one aspect of his work to illustrate aspects which lead to the decision for this prestigious prize in 2010. I will sketch some personal memories which may show his pioneering ideas in creating new tools, his modesty and his wit. John Tate proved beautiful theorems. He created many new "tools", and this is perhaps his greatest influence on modern mathematics. As it is not possible to give a survey of his achievements, we will explain one example: the way Tate considered the concept of a /period lattice /and replaced this by a / Tate module. /This new method enabled Tate to describe endomorphisms, a theorem later vastly generalized by Faltings. It provided tools for new proofs, such as Wiles´ proof of Fermat´s last theorem (which we will not discuss). It also gave rise to a much more general conjecture, unproven up to now, with intriguing relations with the Hodge conjecture. Following Tate, we have the feeling we are on the right track. -- The mathematical half of the lecture will be understandable for a broad mathematical audience, no special prerequisites are necessary.