Imagination in Mathematics

"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)

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

"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 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)

"An expert problem solver must be endowed with two incompatible qualities, a restless imagination and a patient pertinacity.” (Howard W Eves, “In Mathematical Circles”, 1969)

“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)

"One of the most fundamental notions in mathematics is that of number. Although the idea of number is basic, the numbers themselves possess both nuance and complexity that spark the imagination." (Edward B Burger, “Exploring the Number Jungle”, 2000)

"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 whole of Mathematics consists in the organization of a series of aids to the imagination in the process of reasoning." (Alfred North Whitehead, “A Treatise on Universal Algebra”, 1898)

“The structures of mathematics and the propositions about them are ways for the imagination to travel and the wings, or legs, or vehicles to take you where you want to go.” (Scott Buchanan, ”Poetry and Mathematics”, 1962)