Gottlob Frege (b. 1848–d. 1925) was a German mathematician, logician, and philosopher who is generally regarded as one of the founders of the analytic tradition in philosophy—together with Bertrand Russell, G. E. Moore, and Ludwig Wittgenstein. Frege’s main project was to demonstrate the logicist thesis that arithmetic can be reduced to logic. In attempting to do so, he revolutionized logical theory, creating the first system of modern predicate logic in his first book, Begriffsschrift (1879; the term is often left untranslated: see Main Works). In The Foundations of Arithmetic (Die Grundlagen der Arithmetik, 1884), he offered an informal account of his logicist project, showing how the natural numbers could be defined as extensions of (logically definable) concepts—roughly, what we would now call sets or classes.