G. H. Hardy Quotes (1877-1947)

“A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.”

“A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.”

“I can remember Bertrand Russell telling me of a horrible dream. He was in the top floor of the University Library, about A.D. 2100. A library assistant was going round the shelves carrying an enormous bucket, taking down book after book, glancing at them, restoring them to the shelves or dumping them into the bucket. At last he came to three large volumes which Russell could recognize as the last surviving copy of Principia Mathematica. He took down one of the volumes, turned over a few pages, seemed puzzled for a moment by the curious symbolism, closed the volume, balanced it in his hand and hesitated …”

“Mathematicians have constructed a very large number of different systems of geometry, Euclidean or non-Euclidean, of one, two, three, or any number of dimensions. All these systems are of complete and equal validity. They embody the results of mathematicians' observations of their reality, a reality far more intense and far more rigid than the dubious and elusive reality of physics. The old-fashioned geometry of Euclid, the entertaining seven-point geometry of Veblen, the space-times of Minkowski and Einstein, are all absolutely and equally real. ...There may be three dimensions in this room and five next door. As a professional mathematician, I have no idea; I can only ask some competent physicist to instruct me in the facts.”

“In his insight into algebraical formulae, transformation of infinite series, and so forth, that was most amazing. On this side most certainly I have never met his equal, and I can compare him only with Euler or Jacobi.”

“Hardy was a great internationalist who worked with foreign mathematicians, visiting them, encouraging them to visit him and settling some, including Besicovitch, in England. There were some major probability figures in Hardy’s network: George Pólya (1887-1985) of Zürich, Norbert Wiener (1894-1964) of MIT and Harald Cramér (1893-1985) of Stockholm-appropriately Wiener and Cramér first met when visiting Hardy in 1920.”

“In 1933 Landau was dismissed from his [University of Göttingen] chair on the grounds of his race. An important colleague... Ludwig Bieberbach ...wrote the following lines in a treatise on Personality structure and mathematical creativity: "In this way... the ultimate reason behind the courageous rejection which the students at Göttingen University meted out to a great mathematician, Edmund Landau, was that his un-German style in research and teaching had become intolerable to German sensitivities. A people which has seen how alien desires for dominion are gnawing at its identity, how enemies of the people are working to impose their alien ways on it, must reject teachers of a type alien to it." The English mathematician Godfrey H. Hardy... responded to Bieberbach... "There are many of us, many English and many Germans, who said things during the (First) War which we scarcely meant and are sorry to remember now. Anxiety for one's own position, dread of falling behind the rising torrent of folly, determination at all costs not to be outdone, may be natural if not particularly heroic excuses. Prof. Bieberbach's reputation excludes such explanation for his utterances; and I find myself driven to the more uncharitable conclusion that he really believes them true."”

“To illustrate to what extent Hardy and Littlewood in the course of the years came to be considered as the leaders of recent English mathematical research, I may report what an excellent colleague once jokingly said: 'Nowadays, there are only three really great English mathematicians: Hardy, Littlewood, and Hardy-Littlewood.'”

“Hardy in his thirties held the view that the late years of a mathematician's life were spent most profitably in writing books; I remember a particular conversation about this, and though we never spoke of the matter again it remained an understanding.”