弗吉尼亚州(Virginia)托马斯·杰斐逊科技高中(Thomas Jefferson High School for Science and Technology)的高等数学课教师乔纳森·奥斯本(Jonathan Osborne)教过许多聪明学生,然而,亚当·阿迭沙尔(Adam Ardeishar)更胜一筹。
奥斯本记得阿迭沙尔曾问他一个关于“我们如何真的确知泰勒级数(Taylor series)在某一区域内收敛”这种尖锐的高等数学微积分问题。他说,“我教这门课十年,从来不曾对有些原理为什么成立有过这么深的思考”。
奥斯本的这位优秀学生和其他五名美国青少年在2018年国际奥林匹克数学竞赛(International Mathematical Olympiad)中,为美国再次赢得冠军(英文)。这是自2015年以来,美国队(Team USA)第三次获得国际奥数比赛冠军。
美国队队员来自全美各地的公立和私立中学。参加在罗马尼亚举行的2018年国际奥林匹克数学竞赛的六名队员年龄为16岁到19岁。他们是:阿迭沙尔、安德鲁·顾(Andrew Gu)、文森特·黄(Vincent Huang)、詹姆斯·林(James Lin)、迈克尔·任(Michael Ren)和米赫·辛加尔(Mihir Singhal)。他们都是从美国数学协会(Mathematical Association of America)组织的一系列地区和全国竞赛中脱颖而出,而后又参加了美国数学协会在麻省理工学院(Massachusetts Institute of Technology)举办的夏令营集训。
领导夏令营集训的是自2013年以来担任美国队教练的卡内基·梅隆大学(Carnegie Mellon University)数学教授罗博深(Po-Shen Loh)。美国数学协会一些会员将美国近年连连夺冠归功于他的指导。
数学协会负责人迈克尔·皮尔森(Michael Pearson)说,罗博深“非常有活力,有他自己的风格”。
2016年,罗博深开始邀请其他国家的数学队(英文)参加夏令营。今年,有来自10个国家的20名参赛学生与美国和加拿大的60名学生一道,接受了一个月的2018年奥数竞赛训练。
美国队17岁的米赫·辛加尔表示,结识其他国家的同学使美国队受益。辛加尔在竞赛中获得个人金牌。
他说,“他们有不同的视角。不同国家有不同的解决问题方式。”
这种好奇心和合作精神也是皮尔森希望传授给美国数学学生和到美国来的其他学生的。
他说,“我们希望显示,虽然我们能够、也将会在某些场合竞争,但我们愿意合作并且在国际数学界之间搭桥,从而让各地都提高水平。”
Jonathan Osborne teaches many intelligent students in his advanced math classes at Thomas Jefferson High School for Science and Technology in McLean, Virginia, but Adam Ardeishar was something more.
Osborne said he remembered when Ardeishar asked “a pointed question about how we knew for certain that a Taylor series converged in a given region,” he said, referring to a concept used in advanced calculus. “I had never thought so deeply about exactly why certain things are true in my 10 years of teaching this class.”
Osborne’s star student and five other American teenagers are the reigning champions of the 2018 International Mathematical Olympiad. For the third time since 2015, Team USA took home first place at the competition that stands as the global benchmark for excellence in youth mathematics. The teammates hail from public and private secondary schools across the United States.
Ardeishar, Andrew Gu, Vincent Huang, James Lin, Michael Ren and Mihir Singhal represented the United States at the 2018 International Mathematical Olympiad in Romania after excelling at a series of rigorous regional and national competitions that the Mathematical Association of America organized.
The six secondary school students, ranging in age from 16 to 19, attended an intensive summer camp the association hosted at the Massachusetts Institute of Technology.
Po-Shen Loh, professor of mathematics at Carnegie Mellon University, has led the camp since taking over as coach of Team USA in 2013. Several members of the association credit Loh’s teaching for the United States’ current winning streak.
“Po is very energetic and he has his own style,” says Michael Pearson, director of the association.
In 2016, Loh began inviting members of other countries’ teams to attend the camp. This year, 20 competitors from 10 countries spent a month training for the 2018 Olympiad alongside 60 students from the United States and Canada.
The American team benefited from getting to know the students from other countries, says Mihir Singhal, a 17-year-old teammate who earned a gold medal for his individual performance at the Olympiad.
“They had different perspectives,” he says. “In different countries, there is a different style of approaching a problem.”
This is the kind of curiosity and collaboration that Pearson wants to instill in America’s math students and the students of other countries who come to study here.
“We want to demonstrate that while we can and will compete in certain contexts, we want to collaborate and build bridges between the international mathematical community so we can raise standards everywhere.”