The moving power of mathematical invention is not reasoning, but imagination.
--
Quoted in Robert Perceval Graves The Life of Sir William Rowan Hamilton Vol. 3 (1889) p. 219.Augustus De Morgan
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Invention, it must be humbly admitted, does not consist in creating out of void, but out of chaos; the materials must, in the first place, be afforded: it can give form to dark, shapeless substances, but cannot bring into being the substance itself. In all matters of discovery and invention, even of those that appertain to the imagination, we are continually reminded of the story of Columbus and his egg. Invention consists in the capacity of seizing on the capabilities of a subject, and in the power of moulding and fashioning ideas suggested to it.
Mary Wollstonecraft Shelley
Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity. The activity of the intuition consists in making spontaneous judgements which are not the result of conscious trains of reasoning... The exercise of ingenuity in mathematics consists in aiding the intuition through suitable arrangements of propositions, and perhaps geometrical figures or drawings.
Alan Turing
If the system exhibits a structure which can be represented by a mathematical equivalent, called a mathematical model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of mathematical models is termed mathematical programming.
George Dantzig
Now the power of the imagination is a unifying power, hence the force of metaphor; and the poet is the supreme manipulator of metaphor... the world needs the unifying power of the imagination. The two things that give it best are poetry and religion.
R. S. Thomas
He detested objective truths, the burden of argument, sustained reasoning. He disliked demonstrating, he wanted to convince no one. Others are a dialectician's invention.
Emil Cioran
Morgan, Augustus De
Morgan, Frederick E.
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