Theory of Martingales

One service mathematics has rc: ndered the Et moi, ", si javait su comment CD revenir, je ny serais point alle. human race. It has put common SCIIJC back Jules Verne where it belongs. on the topmost shelf next to tbe dusty canister 1abdled discarded non- The series is divergent; tberefore we may be sense. able to do sometbing witb it Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: One service topology has rendered mathematical physics . . . ; One service logic has rendered com- puter science . . . ; One service category theory has rendered mathematics . . . . All arguably true_ And all statements obtainable this way form part of the raison detre of this series_ This series, Mathematics and Its ApplicatiOns, started in 1977. Now that over one hundred volumes have appeared it seems opportune to reexamine its scope_ At the time I wrote "Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the tree of knowledge of mathematics and related fields does not grow only by putting forth new branches.