On Principles (Unsourced)

 "A small error in the beginning (or in principles) leads to a big error in the end (or in conclusions)." (ancient axiom)

"A theory of physics is not an explanation; it is a system of mathematical oppositions deduced from a small number of principles the aim of which is to represent as simply, as completely, and as exactly as possible, a group of experimental laws." (Pierre-Maurice-Marie Duhem)

"It [science] has as its highest principle and most coveted aim the solution of the problem to condense all natural phenomena which have been observed and are still to be observed into one simple principle, that allows the computation of past and more especially of future processes from present ones. [...] Amid the more or less general laws which mark the achievements of physical science during the course of the last centuries, the principle of least action is perhaps that which, as regards form and content, may claim to come nearest to that ideal final aim of theoretical research." (Max Planck)

"No mathematical exactness without explicit proof from assumed principles – such is the motto of the modern geometer." (George Bruce Halsted)

"The aim of every science is foresight (prevoyance). For the laws of established observation of phenomena are generally employed to foresee their succession. All men, however little advanced make true predictions, which are always based on the same principle, the knowledge of the future from the past." (Auguste Compte)

"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 most general law in nature is equity - the principle of balance and symmetry which guides the growth of forms along the lines of the greatest structural efficiency." (Herbert Read)

"[…] the mathematician learns early to accept no fact, to believe no statement, however apparently reasonable or obvious or trivial, until it has been proved, rigorously and totally by a series of steps proceeding from universally accepted first principles." (Alfred Adler)

"There is a great difference between the spirit of Mathematics and the spirit of Observation. In the former, the principles are palpable, but remote from common use; so that from want of custom it is not easy to turn our head in that direction; but if it be thus turned ever so little, the principles are seen fully confessed, and it would argue a mind incorrigibly false to reason inconsequentially on principles so obtrusive that it is hardly possible to overlook them." (Blaise Pascal)

"There is no law of physics that does not lend itself to most economical derivation from a symmetry principle. However, a symmetry principle hides from view any sight of the deeper structure that underpins that law and therefore also prevents any immediate sight of how in each case that mutability comes about." (John A Wheeler)

"We consider it a good principle to explain the phenomena by the simplest hypothesis possible." (Ptolemy)

"What makes a great mathematician? A feel for form, a strong sense of what is important. Möbius had both in abundance. He knew that topology was important. He knew that symmetry is a fundamental and powerful mathematical principle. The judgment of posterity is clear: Möbius was right." (Ian Stewart)