Quotes & Sayings About Riemann

The best that Gauss has given us was likewise an exclusive production. If he had not created his geometry of surfaces, which served Riemann as a basis, it is scarcely conceivable that anyone else would have discovered it. I do not hesitate to confess that to a certain extent a similar pleasure may be found by absorbing ourselves in questions of pure geometry. — Albert Einstein

It is well known that geometry presupposes not only the concept of space but also the first fundamental notions for constructions in space as given in advance. It only gives nominal definitions for them, while the essential means of determining them appear in the form of axioms. The relationship of these presumptions is left in the dark; one sees neither whether and in how far their connection is necessary, nor a priori whether it is possible. From Euclid to Legendre, to name the most renowned of modern writers on geometry, this darkness has been lifted neither by the mathematicians nor the philosophers who have laboured upon it. — Bernhard Riemann

Riemann found that in four spatial dimensions, one needs a collection of ten numbers at each point to describe its properties. — Michio Kaku

No mathematician should ever allow him to forget that mathematics, more than any other art or science, is a young man's game. ... Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty. There have been men who have done great work later; ... [but] I do not know of a single instance of a major mathematical advance initiated by a man past fifty. ... A mathematician may still be competent enough at sixty, but it is useless to expect him to have original ideas. — G.H. Hardy

Does anyone believe that the difference between the Lebesgue and Riemann integrals can have physical significance, and that whether say, an airplane would or would not fly could depend on this difference? If such were claimed, I should not care to fly in that plane. — Richard Hamming

If only I had the Theorems! Then I should find the proofs easily enough. — Bernhard Riemann

Even today, I am in total awe of the following wondrous chain of ideas and interconnections. Guided throughout by principles of symmetry, Einstein first showed that acceleration and gravity are really two sides of the same coin. He then expanded the concept to demonstrate that gravity merely reflects the geometry of spacetime. The instruments he used to develop the theory were Riemann's non-Euclidean geometries-precisely the same geometries used by Felix Klein to show that geometry is in fact a manifestation of group theory (because every geometry is defined by its symmetries-the objects it leaves unchanged). Isn't this amazing? — Mario Livio

Riemann conjecture, — Gregory Benford

The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method-more daring than anything that the history of philosophy records-of Lobachevsky and Riemann, Gauss and Sylvester. Indeed, mathematics, the indispensable tool of the sciences, defying the senses to follow its splendid flights, is demonstrating today, as it never has been demonstrated before, the supremacy of the pure reason. — Nicholas Murray Butler

If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven? — David Hilbert

Riemann concluded that electricity, magnetism, and gravity are caused by the crumpling of our three-dimensional universe in the unseen fourth dimension. Thus a "force" has no independent life of its own; it is only the apparent effect caused by the distortion of geometry. By introducing the fourth spatial dimension, Riemann accidentally stumbled on what would become one of the dominant themes in modern theoretical physics, that the laws of nature appear simple when expressed in higher-dimensional space. He then set about developing a mathematical language in which this idea could be expressed. — Michio Kaku

In Riemann, Hilbert or in Banach space Let superscripts and subscripts go their ways. Our symptotes no longer out of phase, We shall encounter, counting, face to face. — Stanislaw Lem

I have tried to avoid long numerical computations, thereby following Riemann's postulate that proofs should be given through ideas and not voluminous computations. — David Hilbert

It would be very discouraging if somewhere down the line you could ask a computer if the Riemann hypothesis is correct and it said, 'Yes, it is true, but you won't be able to understand the proof.' — Ronald Graham

The greatest problem for mathematicians now is probably the Riemann Hypothesis. — Andrew Wiles

Near Shepherd's Bush two thousand Beta-Minus mixed doubles were playing Riemann-surface tennis. — Aldous Huxley

It wouild be very discouraging if somewhere down the line you could ask a computer if the Riemann hypothesis is correct and it said, 'Yes, it is true, but you won't be able to understand the proof.' John Horgan. — Ronald Graham

Shut up about Leibniz for a moment, Rudy, because look here: You - Rudy - and I are on a train, as it were, sitting in the dining car, having a nice conversation, and that train is being pulled along at a terrific clip by certain locomotives named The Bertrand Russell and Riemann and Euler and others. And our friend Lawrence is running alongside the train, trying to keep up with us - it's not that we're smarter than he is, necessarily, but that he's a farmer who didn't get a ticket. And I, Rudy, am simply reaching out through the open window here, trying to pull him onto the fucking train with us so that the three of us can have a nice little chat about mathematics without having to listen to him panting and gasping for breath the whole way. — Neal Stephenson