【Abstract】In 1900 David Hilbert stated his famous 23 Mathematical problems. In the tenth of them he asked to find an algorithm for deciding for arbitrary Diophantine equation whether it has solutions or not. In 1970 the speaker made the last step in the proof of the impossibility of such an algorithm.In the talk I shall present the history of this negative solution and the main technical result obtained for proving it.This result has numerous interesting corollaries, including  the undecidability of many other decision problems. Some of such results will be presented in the talk.

【个人简介】Yuri Matiyasevich 是世界著名的俄罗斯数学家与计算机科学家，主要研究领域是数理逻辑，可计算理论与数论。在1970年，Matiyasevich证明了一般整系数多项式方程是否有整数解问题是不可判定的，从而解决了希尔伯特第十问题。Matiyasevich教授现为俄罗斯Steklov数学研究所数理逻辑实验室主任与圣彼得堡数学会会长。2008年当选俄罗斯科学院院士，2014年当选欧洲科学院院士。1980年获得俄罗斯科学院颁发的Markov数学奖，1997年获得德国洪堡研究奖，1970年法国尼斯举办的数学家大会邀请报告人。