Even Russell's biographer, the philosopher Ray Monk, no admirer of Russell's personal snobbery, characterised his work on the philosophy of mathematics as intense, august and incontestably great and acknowledged, in the preface to the second volume of his biography, that he is one of the indisputably great philosophers of the twentieth century. Russell's influence on individual philosophers is singular, especially in the case of Ludwig Wittgenstein, who was his student between 1911 and 1914. Wittgenstein had an important influence on Russell as he himself discusses in his "My Philosophical Development". He led him, for example, to conclude, much to his regret, that mathematical truths were purely tautological truths, however it is doubtful that Wittgenstein actually held this view, which he discussed in relation to logical truth, since it is not clear that he was a logicist when he wrote the Tractatus. What is certain is that in 1901 Russell's own reflections on the issues raised by the paradox that takes his name Russell's paradox, led him to doubt the intuitive certainty of mathematics. This doubt was perhaps Russell's most important 'influence' on mathematics, and was spread throughout the European universities, even as Russell himself laboured (with Alfred North Whitehead) in an attempt to solve the Paradox and related paradoxes, such as Burali-Forti. As Stewart Shapiro explains in his "Thinking About Mathematics", Russell's attempts to solve the paradoxes led to the ramified theory of types, which, though it is highly complex and relies on the doubtful axiom of reducibility, actually manages to solve both syntactic and semantic paradoxes at the expense of rendering the logicist project suspect and introducing much complexity in the PM system. Philosopher and logician F.P. Ramsey would later simplify the theory of types arguing that there was no need to solve both semantic and syntactic paradoxes to provide a foundation for mathematics. The philosopher and logician George Boolos discusses the power of the PM system in the preface to his "Logic, logic & logic", stating that it is powerful enough to derive most classical mathematics, equating the power of PM to that of Z, a weaker form of set theory than ZFC (Zermelo-Fraenkel Set theory with Choice). In fact, ZFC actually does circumvent Russell's paradox by restricting the comprehension axiom to already existing sets by the use of subset axioms. Russell wrote (in "Portraits from Memory", 1956) of his reaction to Gödel's 'Theorems of Undecidability':  Evidence of Russell's influence on Wittgenstein can be seen throughout the "Tractatus", which Russell was instrumental in having published.