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| Lê Quỳnh Anh |
Published on Việt Nam News’ monthly edition Outlook Magazine September issue.
Dedicated this article to my mentor Mỹ Hà Nguyễn. Without her support and guidance, I would have never been able to pull it off. I am so blessed.
Mathematician inspires quest for knowledge
The winners of one of the most prestigious awards in the fields of math, Professor Ngô Bảo Châu has been celebrated as a national hero.
By Lê Quỳnh Anh
For a country with a tradition that places great importance on education, the recent awarding of one of the most prestigious awards in mathematics has been seen as extremely encouraging to all Vietnamese students and researchers.
As one of the four winners this year of the Fields Medal, the closest thing the field of math has to the Nobel Prize, Professor Ngô Bảo Châu has also made a nation proud and provided new impetus for efforts to improve Việt Nam’s education system.
The Vietnamese-born and naturalised French mathematician won the award for his work on proving a proposition, or fundamental lemma, that underlies a three-decade effort by mathematicians to link geometry and number theory.
Ten days after Ngô Bảo Châu, a professor at the Université Paris-Sud in Orsay, received the Fields medal, a grand ceremony televised live across the nation was held to welcome the mathematician in Hà Nội.
Speaking to the audience of 4,000 people, the 38-year-old math professor was in high spirits.
“I see the pride sparkle in each young man and woman in this audience, and feel the happiness spread across the country, which in turn magnifies the pride in my soul,” Ngô told the packed auditorium at the Mỹ Đình National Convention Centre.
Winning the Fields award represents years of hard work for Ngô, the first recipient of this medal born and raised in a developing country. Since 1936, the award, named after John Charles Fields, has been given to up to four people every four years by the International Mathematical Union.
In layman’s terms, Ngô’s basic achievement has been to prove what mathematicians refer to as the Fundamental Lemma (FL). It is seen as the key to revealing and understanding a far bigger scientific picture, as it has relevance to the real world, including high-energy physics and computer science. Last year, Ngô’s achievement was selected by Time magazine as one of the 10 top scientific discoveries of 2009.
In the world of figures, a lemma is a proven proposition used as a stepping stone to a larger result, rather than as a statement in itself. There is no formal distinction between a lemma and a theorem, only one of usage and convention.
30-year headache
The Fundamental Lemma that Ngô worked on had been a headache for the mathematical world since 1980 when Canadian mathematician Robert Langlands introduced it in a series of lectures delivered in Paris. It was developed from a larger programme that dated back from 1967 when Langlands, now 73, had a bold vision that different branches of mathematics considered as unrelated actually had intimate, even if hidden, connections. However, no one, including Langlands himself, was able to fully establish the veracity of the theory.
The lemma had sat around for years as different people brainstormed over ways of proving it. Many tried, all failed. Some came close – and the interesting thing about the Fundamental Lemma is that, even before it had been established as a fact, mathematicians supposed it was true to establish other related theorems.
Peter Sarnak, a number theorist at the Institute for Advanced Study at Princeton University in New Jersey said: “It’s as if people were working on the far side of the river waiting for someone to build a bridge across. And now all of a sudden everyone’s work on the other side of the river has been proven.”
In an exclusive e-mailed interview with Outlook, Langlands, now a professor at IAS, explained what had been achieved.
“What is best to emphasise is that Ngô’s achievement has transformed ideas that were latent with possibilities over a period of about 25 years into ideas that we can now, with genuine reasons for optimism, set about transforming into mathematical realities.
“What I have been particularly pleased to see in Ngô is that, in addition to his enormous determination and confidence as well as his technical mastery of the tools of modern algebraic geometry, there is an appreciation of the necessity to master additional techniques from analysis and number theory if one is ever to realise the full possibilities of the Langlands’s programme and the energy, the intelligence, and the willingness to learn them.”
Math columnist for Science News, Julie Rehmeyer, wrote: “Ngô Bảo Châu removed one of the great impediments to a grand, decades-long programme to uncover hidden connections between seemingly disparate areas of mathematics. In doing so, he provided a solid foundation for a large body of theory and developed techniques that are likely to unleash a flood of new results.”
It’s worth noting that it was in 2003 that it first occurred to Ngô “by accident”, as he put it, that a geometric method could provide the solution to the problem. A year later, Ngô and his former thesis advisor in France, Gérard Laumon, actually proved the validity of the Fundamenal Lemma – in one special case. It earned Laumon and him, a research award from the Clay Institute.
After that, Ngô continued to work on the general proof on his own. Ngô told Outlook that he feels grateful for having worked with Laumon on his PhD thesis.
“Professor Laumon helped me progress from a young man fascinated by mathematics into a serious and independent math thinker.”
Ngô recalled his first job interview in France, when he said he was working on the lemma, most of the panel burst out laughing and only a couple, who had also studied the problem, gave incomprehensible smiles.
“Although the strategy was clear, technically, it was still very challenging,” he said. “But I strongly believed that the path I was following would eventually lead me to prove it. If it weren’t me, then it shall be someone else.”Late in 2006, his research seemingly came to a dead end.
Ngô spoke fondly of moving from one great institution to another, first in France, then to the IAS in Princeton and now to the University of Chicago’s Mathematics Department. “It is very helpful to hold regular talks about what you are working on with other colleagues, as it gives you ideas. If I am stuck in a room with a book my research will get nowhere.”
Move to America
In 2006, an invitation to move to America’s Institute for Advanced Study came from Robert Langlands, who was excited when Ngô told him about his work while both were attending a seminar in France.
Unlike the work in Paris, where he had to devote much of his time to teaching, he could spend all his time on research.
The Institute, famous as the academic home of Albert Einstein for 40 years, allows scientists to nurture their talent to the fullest by providing them absolute academic freedom.
“I was overwhelmed at first, I mean, who wouldn’t if surrounded by world-renowned figures in the fields of science, not a handful but in a great number,” he said.
Ngô found the power of collective intellectualism highly rewarding. During one of his weekly seminars, he talked about several methods he was thinking of to attack the Fundamental Lemma, one of them turned out to be the subject of research by another Canadian IAS professor, Mark Goresky, who happened to attend the seminar.
“As Goresky was talking about his work, it suddenly struck me as lightning that this could have been the last missing piece of the puzzle,” Ngô recalled when we met him at his parents’ home in Hà Nội two weeks after he received the medal.
It was December 2006. Eureka was just around the corner. Ngô was so shocked, he couldn’t sleep for three days. It took him two more years to construct the 169-page proof, which was then closely checked by other prominent mathematicians until it was declared correct in 2008.
A little bit weary, Ngô Bảo Châu talked to us at his parents’s house.
How it all began
Around the world he is called by his last name Ngô, but in Việt Nam, everyone calls him brother Châu or even uncle Châu.
Ngô Bảo Châu was born in June 1972 in Hà Nội, six months before the notorious Christmas Bombing campaign by the US Air Force over Hà Nội, Hải Phòng and other cities in North Việt Nam.
While Châu’s mother Trần Lưu Vân Hiền, along with many other women and children, evacuated Hà Nội to the safety of the countryside, she returned to the city to give birth to Châu.
His father Ngô Huy Cẩn, had enlisted in the army’s research unit, and was passing through Hà Nội with his contingent when he received the news that his son had just been born. The whole unit agreed to stop by the hospital so that he could hold his newly-born son in his arms for a brief moment before returning to his duties.
In his speech at the Mỹ Đình centre, Châu said, “No one wants to recall hardships and poverty, but I must mention everything that helped bring me to where I am today.
“Since a very small age, I knew that my parents sacrificed what they could eat, what they wore to help provide for my bringing up. Despite their busy working lives, my school studies were always a top priority.”
Châu recalled how his early years at the Thực Nghiệm experimental primary school, where free-speech was encouraged among the young students, helped foster the skills he later needed as a scientist.
The fraternity among the math community in Việt Nam was also a rare and precious gift he said he had treasured.
Châu attended a special class for students who were gifted in math while attending junior and high school. These classes helped foster an eagerness for learning and resolving challenging math problems.
As a student at the age of 16 and again the next year, he won gold medals at the International Mathematics Olympiad held in Australia and Germany.
In 1990, Châu received a scholarship to study mathematics at the Université Pierre et Marie Curie, and two years later moved to the Ecole Normale Superieure in Paris. In 1993, two years before the completion of his undergraduate degree, Châu was recommended by the Dean of Mathematics to Gérard Laumon, an outstanding mathematician at the Université Paris-Sud, to start working on a Ph.D degree.
Many great scientific discoveries are the result of obsession and Châu’s was no exception. It was the Fundamental Lemma that chose Châu rather than the other way around.
Speaking to Outlook from France, Laumon said that he assigned Ph.D theses according to intellectual ability, but he admitted the thesis he gave to Châu on a problem related to the lemma was too difficult. However, he believed that the young Vietnamese could pull it off as “Châu was supposed to be an extremely good student given his recommendation and his outstanding academic records in France”.
It was not an easy task for the “boy from Hà Nội”. For the first three years, he hardly made any progress. “Nevertheless, he never complained and he was working very hard,” Laumon said.
“Finally, in 1996, he had a bright yet incredibly simple idea, one of those ideas that mathematicians can only expect to have once or twice in their whole career,” Laumon said. It was the first breakthrough.
After the brainwave, Châu solved the task his professor had given him in less than six months. A few months later in 1997, he received his PhD and he then was offered a permanent job at the Centre National de la Recherche Scientifique, the largest governmental research organisation in France.
Giving back
After years of study and research abroad, Châu hasn’t forgotten about his homeland.
He joined activities in the movement to encourage children to go to school this month by joining his former classmates from his primary school Thực Nghiệm in the first day to the school this academic year.
It was only a small deed to inspire the younger generation, but since he received the Fields award last month in Hyderabad, India, he has become the new idol of the youth and he says he sees this as a personal responsibility, one that will help push the research work of local academia to the next level.
These ambitious visions are being carried out with the help of local people.
Châu has put aside all his $15,000 in prize money – along with contributions from other donors – to initiate a foundation called “For the Fondness of Learning”, aimed at helping talented but poor students.
“Each student will be paired with a mentor, an experienced senior lecturer to provide them with guidance and support,” he said.
Another ambitious project is to establish a Vietnamese Institute for Advanced Mathematics Study. Its objective is to create a sound working research environment for young Vietnamese mathematicians. It’s like a math camp, where young researchers with innovate ideas will spend six months working closely with mentor professors.
“In modern mathematics, ideas and insights are of crucial importance, but they are not enough. In order to turn them into realities, people need to hone their technical prowess – and this cannot be achieved overnight.”
Châu is moving to Chicago this autumn to take up a professorship at the University of Chicago’s Mathematics Department, where seven other Fields Medallists have worked – or are still working.
“And the University of Chicago is one of the leading institutions in my research field, algebraic geometry,” he said.
He said he likes the vibrant life in a big city because he grew up on Hàng Bài Street, one of the liveliest streets in Hà Nội. Another reason he chose Chicago over Princeton is because he loves jazz, which is abundant in Chicago.
Châu said his journey with Langlands programme seems to never end.
“It’s just like entering another new stage.”
As Langlands himself put it: “I would like to hope that the proof of the fundamental lemma is not the high-point of Ngô’s career and that the best is yet to come.” -VNS
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