Abstract
Do you know the area of a triangle? Do you know how to construct all right triangles with rational sides? If you know both, then try to solve a problem raised by Arabs over 1040 years ago: find a method to determine a positive integer n to be the area of a rational right triangle. Such a number is called a congruent number. Is 1 a congruent number? What about 5 or 7? After 1000 years, we still could not solve this problem. But we know it will follow from another unsolved problem which has a prize US$1,000,000.
About the speaker
Prof Shou-Wu Zhang received his PhD from Columbia University in 1991. He was a member of the Institute for Advanced Study in Princeton and an Assistant Professor at Princeton University from 1991 to 1996. He has been tenured at Columbia University since 1996 and at Princeton University since 2011.
Prof Zhang’s research areas include number theory and arithmetic algebraic geometry. He is on the editorial boards of the Journal of Algebraic Geometry, Journal of Differential Geometry, and Science in China, among other publications.
Prof Zhang was an invited speaker of the International Congress of Mathematicians at Berlin in 1998 and was awarded a Morningside Gold Medal of Mathematics in the same year by the International Congress of Chinese Mathematicians for his work on the Bogomolov conjecture and Gross-Zagier formula. He was a Sloan Research Fellow, a Guggenheim Fellow, a L.-K. Hua Chair Professor at Chinese Academy of Sciences, a Changjiang Chair Professor at Tsinghua University, and a Prize Fellow at Clay Mathematical Institute. In 2011, he was elected Fellow of the American Academy of Arts and Sciences.
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