Hooked on the Fundamentals

When Professor Ngô Bảo Châu was in sixth grade in Hanoi, his father, a mathematics professor, was dismayed that his son was not advancing fast enough in his subject. By his own admission, Ngô could solve elementary school problems easily enough. But his father saw an ability to do something more. He proved to be right.

Ngô was encouraged to practise and although he initially failed, it was that struggle that attracted him. “I tried very hard and I could feel I was getting better every day. That’s how I got hooked on mathematics,” he said. “It is very gratifying for me to overcome challenges. Sometimes we can’t do it the first time, but the next day we can. I have great fun doing that.”

That persistence led him to win gold medals at two International Mathematical Olympiad competitions in his teens, secure academic posts in both France and the US, and solve one of mathematics’ most difficult problems, which earned him a prestigious Fields Medal.

Professor Ngô is now bringing that spirit to HKU, where he sees an opportunity to build on the existing talent here and create a truly international hub of mathematical excellence.

“I believe Asia will be the future centre of science and mathematics. There are great opportunities to develop mathematics in Hong Kong, the Chinese Mainland, Asia and beyond. I want to be part of that development,” he said.

Signature achievement

Professor Ngô’s greatest achievement was to solve the Langlands Programme, a theoretical framework proposed by Robert Langlands in 1967 that links number theory and group theory but had lacked a proof – a ‘fundamental lemma’ – demonstrating the hidden connections between them.

Langlands and other mathematicians had tried to prove his framework without success, but that challenge intrigued Professor Ngô. In 2002, he began devoting himself to the task and added a twist – applying geometry to the problem – that led him to a solution. Along the way were several ‘aha!’ moments.

The first moment was realising that a geometric shape, called the Hitchin fibration, might indeed help solve the problem – something he was surprised others had not seen. Next, he collaborated with his former adviser, Professor Gérard Laumon, and was struck by a second ‘aha!’ moment while driving on the highway to pick his father up at the airport. “Professor Laumon and I were trying to combine ideas into a new language and suddenly, like a flash, the whole thing appeared very clear in my mind. I almost stopped right there on the highway,” he said.

But the fundamental lemma was not quite nailed down. Professor Ngô continued to work on his own and was almost ready to give up when, in 2007, a chance discussion with mathematician Mark Goresky uncovered an old unpublished notebook containing an equation relevant to Professor Ngô’s work. It was the missing piece to the puzzle. “I probably went two days without sleep after that,” he said – then two years nailing all the pieces down. When he was finished, all other theorems that had been conditional on proof of the Langlands Programme suddenly became unconditional.

The implications have rippled across mathematics, including number theory, representation theory and moduli spaces, reaching certain areas of mathematical physics, and earned him the 2010 Fields Medal, the highest honour for mathematicians under 40. His discovery was also named one of TIME magazine’s Top 10 Scientific Discoveries in 2009.

Making sense of the world

Now, after 18 years in France followed by 18 years in the US (including the last 15 years at the University of Chicago), Professor Ngô is bringing his expertise to HKU, drawn by the desire to be closer to his parents and home country Vietnam and, most importantly, the opportunities in the region.

He is impressed with the quality of HKU’s Department of Mathematics, as well as the commitment from HKU’s senior leadership to establish an institute of mathematics, which he is keen to lead. “Mathematics develops when young and few young mathematicians have the chance to exchange ideas and challenge each other. I want Hong Kong to be the best place in Asia for this vision of mathematics,” he said.

Professor Ngô will be teaching year-long seminars to promote such exchanges among undergraduate and postgraduate students and inviting leaders in the field to visit. “I would love to see collaboration and bonds in mathematics grow in Asia and help other Asian countries to grow, too,” he said.

He is also keen to promote mathematics in K-12 education, having already co-authored a storybook on mathematical concepts in Vietnamese. “Everybody should learn mathematics and be comfortable with a certain level of function, it should not be only for professional mathematicians or done with the help of AI,” he said. “AI can be a great help in some things, but human beings make sense of the world – and mathematics is an essential part of that.”