On Theorems (1970-1979)

“In many cases a dull proof can be supplemented by a geometric analogue so simple and beautiful that the truth of a theorem is almost seen at a glance.” (Martin Gardner, “Mathematical Games”, Scientific American, 1973)

“The world is anxious to admire that apex and culmination of modern mathematics: a theorem so perfectly general that no particular application of it is feasible.” (George Pólya, “A Story With a Moral”, Mathematical Gazette 57 (400), 1973) 

 „For hundreds of pages the closely-reasoned arguments unroll, axioms and theorems interlock. And what remains with us in the end? A general sense that the world can be expressed in closely-reasoned arguments, in interlocking axioms and theorems.“ (Michael Frayn, „Constructions“, 1974)

“Mathematics does not grow through a monotonous increase of the number of indubitably established theorems, but through the incessant improvement of guesses by speculation and criticism.” (Imre Lakatos, "Proofs and Refutations", 1976)

“The esthetic side of mathematics has been of overwhelming importance throughout its growth. It is not so much whether a theorem is useful that matters, but how elegant it is.” (Stanislaw Ulam “Adventures of a Mathematician”, 1976)

“At the heart of mathematics is a constant search for simpler and simpler ways to prove theorems  and solve problems.” (Martin Gardner, “Aha! Insight”, 1978)

 “A good theorem will almost always have a wide-ranging influence on later mathematics, simply by virtue of the fact that it is true. Since it is true, it must be true for some reason; and if that reason lies deep, then the uncovering of it will usually require a deeper understanding of neighboring facts and principles.” (Ian Richards, “Number theory”, 1978)

„[...] despite an objectivity about mathematical results that has no parallel in the world of art, the motivation and standards of creative mathematics are more like those of art than of science. Aesthetic judgments transcend both logic and applicability in the ranking of mathematical theorems: beauty and elegance have more to do with the value of a mathematical idea than does either strict truth or possible utility.“ (Lynn A Steen, „Mathematics Today: Twelve Informal Essays“, 1978)

See also:
Theorems I, II, III, IV, V, VI, VIII, IX, X
Proofs I, II, III, IV, V,. VI, VII, VIII, IX