Clippings

“The future historian of science concerned with the development of mathematics in the late nineteenth and the first half of the twentieth century will undoubtedly state that several branches of mathematics are highly indebted to Hilbert’s achievements for their vigorous advancement in that period,” Alfred Tarski has written. “On the other hand, he will have to note, perhaps with some wonder, that the influence of this man appears equally strong and powerful in some other domains which do not owe any exceptionally important results to Hilbert’s own research. An example of this kind is furnished by the foundations of geometry. I am far from underestimating the value of Hilbert’s contributions … in his [Foundations of Geometry], but I think that his most essential merit was the impulse he gave to organized research in this domain. A still more striking example is presented by metamathematics. Occasional considerations in this field preceded Hilbert’s Paris address; the first positive and really profound results appeared before Hilbert started his continuous work in this domain … [and] one does not immediately associate with Hilbert’s name any definite and important metamathematical result. Nevertheless, Hilbert will deservedly be called the father of metamathematics. For he is the one who created metamathematics as an independent being; he fought for its right to existence, backing it with his whole authority as a great mathematician. And he was the one who mapped out its future course and entrusted it with ambitions and important tasks.”