This book starts with a brief history of mathematics, and reviews along with the world mathematicians and amateurs the history of mathematics. At the same time, we also stress the deserved fundamental position of China in the history of development of mathematics in the world, so as to fill the void of description of the history of Chinese mathematics in the literature on the history of mathematics written by foreign mathematics history experts. Second is a collection of the full script in English of German mathematician D. Hilbert's Speech at the 2nd International Congress of Mathematicians, and commentaries of the content and progress of the 23 Problems posed by him. Also collected are some of the world's hard mathematical problems that need to be solved. This book also puts forward suggestions to rectify the practices of prevarication and delay of review and publication of the research results of the mathematicians and amateurs amongst the general public. We also analyze the reasons of the slow development of mathematics in China, and expose and criticize the malignant phemena and corruptions existing in the domestic academic and educational fields.