Mathematicians create by acts of insights and intuition. Logic then sanctions the conquests of intuition.
Morris KlinePsychologically, the teaching of abstractions first is wrong. Indeed, a thorough understanding of the concrete must precede the abstract.
Morris KlineActually, most mathematics courses do not teach reasoning of any kind. Students are so baffled by the material that they are obliged to memorize in order to pass examinations.
Morris KlineEvery paper published in a respectable journal should have a preface by the author stating why he is publishing the article, and what value he sees in it. I have no hope that this practice will ever be adopted.
Morris KlinePerhaps the best reason for regarding mathematics as an art is not so much that it affords an outlet for creative activity as that it provides spiritual values. It puts man in touch with the highest aspirations and lofiest goals. It offers intellectual delight and the exultation of resolving the mysteries of the universe.
Morris Kline