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 has made himself some contributions 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 someone else's work. I have therefore finally desided after much hesitation, to take a subject which is quite frankly mathematical, and to give a summary account of the result of some researches which.