Frases de G. H. Hardy
G. H. Hardy
Data de nascimento: 7. Fevereiro 1877
Data de falecimento: 1. Dezembro 1947
Godfrey Harold Hardy foi um matemático inglês.
É conhecido principalmente na teoria dos números e análise matemática. De 1931 a 1942 foi Professor Sadleiriano de Matemática Pura na Universidade de Cambridge.
Publicou o livro autobiográfico A mathematician's Apology , defendendo o valor da matemática pura e da dimensão estética da matemática. Foi escrito no final de sua vida, quando não mais se sentia capaz de produzir "matemática criativa". Seu amigo e biógrafo, C. P. Snow, afirmou na introdução que preparou para a edição do livro que era um "livro de tristeza enorme", o "testamento de um artista criativo".
Seu relacionamento profissional com o matemático indiano Srinivasa Ramanujan e os seus trabalhos publicados em 1914 o tornaram célebre. Hardy imediatamente reconheceu Ramanujan como um aluno de destaque, por seus raciocínios inovadores, e a partir disso, Hardy e Ramanujan começaram a trabalhar conjuntamente. Em uma entrevista feita por Paul Erdős a Hardy, quando Hardy foi questionado sobre qual seria a sua grande contribuição para a matemática, sem hesitar, disse que foi Ramanujan. Ele denominou a parceria de "o único incidente romântico na sua vida".
Citações G. H. Hardy
„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.
The function of a mathematician, then, is simply to observe the facts about his own intricate system of reality, that astonishingly beautiful complex of logical relations which forms the subject-matter of his science, as if he were an explorer looking at a distant range of mountains, and to record the results of his observations in a series of maps, each of which is a branch of pure mathematics.... Among them there perhaps none quite so fascinating, with quite the astonishing contrasts of sharp outline and shade, as that which constitutes the theory of numbers.“
— G. H. Hardy
"The Theory of Numbers," Nature (Sep 16, 1922) Vol. 110 https://books.google.com/books?id=1bMzAQAAMAAJ p. 381
„... there is probably less difference between the positions of a mathematician and of a physicist than is generally supposed, [... ] the mathematician is in much more direct contact with reality. This may seem a paradox, since it is the physicist who deals with the subject-matter usually described as ‘real’, but [... ] [a physicist] is trying to correlate the incoherent body of crude fact confronting him with some definite and orderly scheme of abstract relations, the kind of scheme he can borrow only from mathematics.“
„Bradman is a whole class above any batsman who has ever lived: if Archimedes, Newton and Gauss remain in the Hobbs class, I have to admit the possibility of a class above them, which I find difficult to imagine. They had better be moved from now on into the Bradman class.“
— G. H. Hardy
Quoted by C. P. Snow in his introduction to reprints of the book.
„A painter makes patterns with shapes and colours, a poet with words. A painting may embody an ‘idea’, but the idea is usually commonplace and unimportant. In poetry, ideas count for a good deal more; but, [... ] the importance of ideas in poetry is habitually exaggerated: '... Poetry is not the thing said but a way of saying it.' [In poetry, ] the poverty of the ideas seems hardly to affect the beauty of the verbal pattern.“
„He could remember the idiosyncrasies of numbers in an almost uncanny way. It was Littlewood who said that every positive integer was one of Ramanujan's personal friends. I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."“
— G. H. Hardy
Ch. I : The Indian mathematician Ramanujan.