I dreaded each visit, but early on he said that he looked forward to seeing me. Thus the idea of an 'irrational' is deeper than that of an integer; and Pythagoras's theorem is, for that reason, deeper than Euclid's. The writer of these manuscripts was a man of genius. Russell was dismissed from his lectureship, in circumstances of overheated complexity (Hardy was to write the only detailed account of the case a quarter of a century later, in order to comfort himself in another war). A chair or a star is not in the least like what it seems to be; the more we think of it, the fuzzier its outlines become in the haze of sensation which surrounds it; but '2' or '317' has nothing to do with sensation, and its properties stand out the more clearly the more closely we scrutinize it. The Whitehead mathematics may affect astronomy or physics profoundly, philosophy very appreciably—high thinking of one kind is always likely to affect high thinking of another—but it has extremely little effect on anything else. On the other hand a theorem may be essentially superficial and yet quite difficult to prove (as are many 'Diophantine' theorems, i. Its 'tremendous effects' have been, not on men generally, but on men like Whitehead himself. that the series (A) never comes to an end. I cannot remember ever having wanted to be anything but a mathematician