Mathematics and Conjecture (1 volume) discusses the methods of argumentation through many famous conjectures in ancient times, and expounds the author's point of view: we should not only learn argumentative reasoning, but also learn perceptual reasoning, thus enriching people's scientific thinking and improving dialectical thinking ability. The examples in Mathematics and Conjecture (1 volume) involve not only mathematics, but also physics. The book is divided into two volumes, the first volume is induction and analogy in mathematics, the second volume is perceptual reasoning mode, and this volume is the first volume, which mainly tells various examples of perceptual reasoning in mathematics. Mathematics and Conjecture (1 volume) can be read by teachers and students of university mathematics department, middle school mathematics teachers, mathematics researchers and mathematics enthusiasts.