Discovery in Mathematics (1975-1999)

"Here is one way to look at physics: the physicists are men looking for new interpretations of the Book of Nature. After each pedestrian period of normal science, they dream up a new model, a new picture, a new vocabulary, and then they announce that the true meaning of the Book has been discovered." (Richard Rorty, "Philosophy as a Kind of Writing", 1978)

"Mathematicians do not agree among themselves whether mathematics is invented or discovered, whether such a thing as mathematical reality exists or is illusory." (Albert L Hammond, "Mathematics - Our invisible culture", 1978)

"A mathematician’s work is mostly a tangle of guesswork, analogy, wishful thinking and frustration, and proof, far from being the core of discovery, is more often than not a way of making sure that our minds are not playing tricks." (Gian-Carlo Rota, 1981)

"For the great majority of mathematicians, mathematics is […] a whole world of invention and discovery - an art. The construction of a new theorem, the intuition of some new principle, or the creation of a new branch of mathematics is the triumph of the creative imagination of the mathematician, which can be compared to that of a poet, the painter and the sculptor." (George F J Temple, "100 Years of Mathematics: a Personal Viewpoint", 1981)

"In the initial stages of research, mathematicians do not seem to function like theorem-proving machines. Instead, they use some sort of mathematical intuition to ‘see’ the universe of mathematics and determine by a sort of empirical process what is true. This alone is not enough, of course. Once one has discovered a mathematical truth, one tries to find a proof for it." (Rudy Rucker, "Infinity and the Mind: The science and philosophy of the infinite", 1982)

"To experience the joy of mathematics is to realize mathematics is not some isolated subject that has little relationship to the things around us other than to frustrate us with unbalanced check books and complicated computations. Few grasp the true nature of mathematics - so entwined in our environment and in our lives." (Theoni Pappas, "The Joy of Mathematics" Discovering Mathematics All Around You", 1986)

"There is one qualitative aspect of reality that sticks out from all others in both profundity and mystery. It is the consistent success of mathematics as a description of the workings of reality and the ability of the human mind to discover and invent mathematical truths." (John D Barrow, "Theories of Everything: The quest for ultimate explanation. New", 1991)

"One of the lessons that the history of mathematics clearly teaches us is that the search for solutions to unsolved problems, whether solvable or unsolvable, invariably leads to important discoveries along the way." (Carl B Boyer & Uta C Merzbach, "A History of Mathematics", 1991)

"One of the deepest problems of nature is the success of mathematics as a language for describing and discovering features of physical reality." (Peter Atkins, "Creation Revisited" 1992)

"Practically everyone can understand and enjoy mathematics and appreciate its role in modem society. More generally, I feel that we develop only a small part of our potential, not only in mathematics but also in art, carpentry, cooking, drawing, singing, and so on. We close up too soon. Each of us can reach a higher level than we imagine if we are willing to explore the world and ourselves." (Sherman K Stein, "Strength in Numbers: Discovering the Joy and Power of Mathematics in Everyday Life", 1996)

"The controversy between those who think mathematics is discovered and those who think it is invented may run and run, like many perennial problems of philosophy. Controversies such as those between idealists and realists, and between dogmatists and sceptics, have already lasted more than two and a half thousand years. I do not expect to be able to convert those committed to the discovery view of mathematics to the inventionist view." (Paul Ernst, "Is Mathematics Discovered or Invented", 1996)

"There is no end to discoveries in mathematics just as there is no end to the mystery of the universe. Both are boundless. Hence mathematics is not so much a body of knowledge as a way of thought with inexhaustible possibilities." (Karma V Mital, "Understanding Mathematics And Computers", 1997)

"Mathematics is a product - a discovery - of the human mind. It enables us to see the incredible, simple, elegant, beautiful, ordered structure that lies beneath the universe we live in. It is one of the greatest creations of mankind - if it is not indeed the greatest." (Keith Devlin, "Life By the Numbers", 1998)