直觉是发明的根源。“没有作何一个创造性行为能离开直觉活动”(凯德洛夫语)。科学表明:很多重大科学发现都得益于直觉。数学发现也不例外。实践表明,直觉能力的强弱,直接影响着解题能力的提高。 1 直觉猜想,探索思路在数学研究里面,先猜想后证明,几乎是一条规律。虚数的发现、四元数代数的创立、n维空间的引进, Intuition is the root of invention. “No creative activity can leave the intuitive activity ” (Kedlov). Science shows that many major scientific discoveries benefit from intuition. Mathematical findings are no exception. Practice shows that the strength of intuition, a direct impact on the improvement of problem-solving skills. 1 intuition guess, explore ideas in mathematical research, the first guess after proving, is almost a law. The discovery of imaginary numbers, the establishment of quaternion algebra, the introduction of n-dimensional space,