"As an operation, multiplication by i x i has the same effect as multiplication by -1; multiplication by i has the same effect as a rotation by a right angle, and these interpretations […] are consistent. […] Although the interpretation by means of rotations proves nothing, it may suggest that there is no occasion for anyone to muddle himself into a state of mystic wonderment over nothing about the grossly misnamed ‘imaginaries’." (Eric T Bell, "Gauss, the Prince of Mathematicians", 1956)
"The word ‘imaginary’ is the great algebraical calamity, but it is too well established for mathematicians to eradicate. It should never have been used. Books on elementary algebra give a simple interpretation of imaginary numbers in terms of rotations. […] Although the interpretation by means of rotations proves nothing, it may suggest that there is no occasion for anyone to muddle himself into a state of mystic wonderment over nothing about the grossly misnamed ‘imaginaries’." (Philip E B Jourdain, "The Nature of Mathematics" in [James R Newman, "The World of Mathematics" Vol. I, 1956])
"It is common knowledge today that in general a symmetry principle (or equivalently an invariance principle) generates a conservation law. For example, the invariance of physical laws under space displacement has as a consequence the conservation of momentum, the invariance under space rotation has as a consequence the conservation of angular momentum." (Chen-Ning Yang, "The Law of Parity Conservation and Other Symmetry Laws of Physics", [Nobel lecture] 1957)
"A transformation by translation has the effect of moving the origin to a new position without changing the directions of the axes. A transformation by rotation has the effect of turning the axes through an angle about the origin as a pivot, but without changing the position of the origin. Either transformation may be effected by itself, or both may be effected jointly; although, in such case, the rotation is normally performed first and the translation second." (William L Schaaf, "Analytic Geometry; a college course guide", 1962)
"When either the translation or the rotation transformations are applied to an equation, they change the coordinates of all points in the plane (except the origin in the case of a rotation). These transformations actually move the axes with relation to the curve, but they do not alter the shape of the curve represented by the original equation and by the transformed equation. Beside this constant or unvarying feature, i.e., the preservation of the geometric form of the curve, there are also certain algebraic expressions whose values remain unchanged in both equations. Mathematical forms which are preserved or do not vary when other changes take place are called invariants." (William L Schaaf, "Analytic Geometry; a college course guide", 1962)
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