Excerpt from Some Famous Problems of the Theory of Numbers, and in Particular Waring's Problem: An Inaugural Lecture Delivered Before the University of Oxford In the second place, I think that a professor should choose, for his inaugural lecture, a subject, if such a subject exists, to which he has made himself some contribution of substance and about which he has something new to say. And about mathematical philosophy I have nothing new to say; I can only repeat what has been said by the men, Cantor and Frege in Germany, Peano in Italy, Russell and Whitehead in England, who have originated the subject and moulded it now into something like a definite form. It would be an insult to my new University to offer it a watered synopsis of some one else's work. I have there fore finally decided, after much hesitation, to take a sub jcet which is quite frankly mathematical, and to give a summary account of the results of some researches which. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.