On Imagination (Unsourced)

"A good teacher can inspire hope, ignite the imagination, and instill a love of learning." (Brad Henry)

"An expert problem solver must be endowed with two incompatible qualities, a restless imagination and a patient pertinacity." (Howard W Eves)

"Do not quench your inspiration and your imagination; do not become the slave of your model." (Vincent van Gogh)

"Finding the right answer is important, of course. But more important is developing the ability to see that problems have multiple solutions, that getting from X to Y demands basic skills and mental agility, imagination, persistence, patience." (Mary H Futrell)

"He who has imagination without learning has wings but no feet." (Joseph Joubert)

"Here, where we reach the sphere of mathematics, we are among processes which seem to some the most inhuman of all human activities and the most remote from poetry. Yet it is here that the artist has the fullest scope of his imagination." (Havelock Ellis)

"Imagination, as well as reason, is necessary to perfection in the philosophical mind. A rapidity of combination, a power of perceiving analogies, and of comparing them by facts, is the creative source of discovery." (Sir Humphry Davy)

"Imagination does not breed insanity. Exactly what does breed insanity is reason. Poets do not go mad […] mathematicians go mad." (Gilbert Keith Chesterton)

"Imagination magnifies small objects with fantastic exaggeration until they fill our soul, and with bold insolence cuts down great things to its own size, as when speaking of God." (Blaise Pascal)

"[…] it is impossible to be a mathematician without being a poet in soul […] imagination and invention are identical […] the poet has only to perceive that which others do not perceive, to look deeper than others look. And the mathematician must do the same thing." (Sophia Kovalevskaya)

"Mathematics is the summit of human thinking. It has all the creativity and imagination that you can find in all kinds of art, but unlike art-charlatans and all kinds of quacks will not succeed there." (Meir Shalev)

"No discovery has been made in mathematics, or anywhere else for that matter, by an effort of deductive logic; it results from the work of creative imagination which builds what seems to be truth, guided sometimes by analogies, sometimes by an esthetic ideal, but which does not hold at all on solid logical bases. Once a discovery is made, logic intervenes to act as a control; it is logic that ultimately decides whether the discovery is really true or is illusory; its role therefore, though considerable, is only secondary." (Henri Lebesgue)

"One factor that has remained constant through all the twists and turns of the history of physics is the decisive importance of the mathematical imagination." (Freeman J Dyson)

"Philosophy becomes poetry, and science imagination, in the enthusiasm of genius." (Isaac Disraeli)

"The disclosure of a new fact, the leap forward, the conquest over yesterday’s ignorance, is an act not of reason but of imagination, of intuition." (Charles Nicolle)

"The mathematical works thrall and delight, just like the works of passion and imagination." (Dan Barbilian)

"The mathematician is entirely free, within the limits of his imagination, to construct what worlds he pleases. What he is to imagine is a matter for his own caprice; he is not thereby discovering the fundamental principles of the universe nor becoming acquainted with the ideas of God." (John W N Sullivan)

"The mathematician's best work is art […] a high and perfect art, as daring as the most secret dreams of imagination, clear and limpid. Mathematical genius and artistic genius touch each other." (Gustav Mittag-Leffler)

"The mere formulation of a problem is often far more essential than its solution. To raise new questions, new possibilities, to regard old problems from a new angle, requires creative imagination and marks real advances in science." (Albert Einstein)

"The moving power of mathematical invention is not reasoning but imagination." (Augustus De Morgan)

"There is poetry in science and the cultivation of the imagination is an essential prerequisite to the successful investigation of nature." (Joseph Henry)

"These are among the marvels that surpass the bounds of our imagination, and that must warn us how gravely one errs in trying to reason about infinites by using the same attributes that we apply to finites." (Galileo Galilei)

"We especially need imagination in science. It is not all mathematics, nor all logic, but it is somewhat beauty and poetry." (Maria Mitchell)

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