The course consists of three parts, each focusing on one of the most famous mathematical problems, Fermat’s Last Theorem(about 350 years ago and proved in 1994), Riemann’s Hypothesis(about 150 years ago and still not proved or disproved) and Poincare Conjecture(about 110 years ago and proved in 2004). The Fermat’s Last Theorem was stated by the most famous nonprofessional French mathematician Fermat that the equation x^n+y^n=z^n has no solutions of positive integers for all n>2. This was not proved for over 350 yeas until 1994 when the British mathematician Wiles gave a proof known as the most important achievement of mathematics during the whole 20th century. The Riemann’s hypothesis was conjectured by the famous German mathematician Riemann in 1859 that the so-called Riemann theta function 1+2^s+3^s+...+n^s+... has all its nontrivial zeros on the line Re(s)=0.5. This hypothesis is regarded as the number 1 question in mathematics and is still unknown whether it is true or false. The Poincare conjecture was stated as a question in 1904 by the famous French mathematician, physist and philosopher Poincare as he studied the topics of the shape of our universe. This conjecture was proved in 2004 by Russian mathematician Perelman, who refused the highest mathematical medal-Fields medal and an award of one million dollars for the first solver of one of seven million dollars problems, two among which are Poincare conjecture and Riemann’s hypothesis. The most famous mathematician S.T.Yau said that if Poincare conjecture were the Yellow river, the Goldbach conjecture is only a small brook, a beautiful brook. This course aims to make students to know some theorems about prime numbers and several concise proofs and bright ideas; to understand the logic of the formation of mathematical theories and to apply mathematics to the real world; most importantly, to get a feeling of the struggling history of mathematical heroes and to make themselves a wonderful struggling lives. | 
