
AsianScientist (Jan. 23, 2015) – Mathematics is one of the oldest sciences, making connections in patterns and ideas that are surprisingly pervasive in nature. The ancient Egyptians used the mathematical constant pi to build the Great Pyramids of Giza more than four thousand years ago. Not long after, the ancient Greeks broke ground on number theory by using a simple ruler and compass to solve the quadratic equation that we now learn about in high school.
All these stories and more were shared by Professor Ngô Bảo Châu, professor of physics at the Vietnam National Institute of Mechanics and the University of Chicago, during his plenary lecture at the Global Young Scientists Summit (GYSS@one-north 2015) on Wednesday at Singapore’s Nanyang Technological University.
It was in 2010 that Ngô was awarded the prestigious Fields Medal, given to the most brilliant mathematicians under the age of 40. Ngô won for his ingenious proof of the fundamental lemma, a conjecture in number theory that is part of the Langlands Program.
Ngô humbly noted that his and Robert Langlands’ contributions were preceded by more than thousands years of mathematical deconstruction by the Egyptians and the Greeks.
“Number theory is the oldest part of science,” Ngô said. “It asks very simple questions that have, in fact, been asked since antiquity. It was realized that more mathematical tools are needed to uncover the answers, and we in the mathematics field are still developing these tools. The ultimate truth underlying number theory is still far off.”
The enduring beauty of mathematics
“In mathematics, the basic rule is: ‘what is beautiful survives forever’. This is true, for example, of the discovery of the Persian mathematician-poet Omar Khayyám,” said Ngô. “One thousand years ago, he conceived a way to solve cubic equations—equations of the third degree—using conic sections such as the ellipse. This idea continues to resurface in mathematics.”
Ngô told the story of Évariste Galois, a 19th century Parisian who died in a duel at the tender age of 20, but not before articulating that there is no such thing as a quantic formula (to solve equations of the fifth degree), and introducing a radical new mathematical concept called the Galois group.
“Galois is inspirational in how he completely changed the course of mathematics,” said Ngô. “Indeed, the Galois group remains the main object of investigation in modern number theory.”
Much like his mathematical forebears, there is romance to be found in Ngô’s own story. A native of Hanoi, Vietnam, and the only son of two academics, Ngô showed an immense aptitude for mathematics from a young age. As a teenager, he won gold medals at two consecutive International Mathematical Olympiads, a feat that had never been achieved before in Vietnam.
Upon graduating from high school, he moved to France to continue his studies, where he was later appointed professor at the University of Paris-Sud at the remarkably young age of 33. The same year, he received the title of professor in Vietnam as well, the youngest Vietnamese to receive such an honourable distinction.
The 20th century and beyond
Prior to his successes in number theory, Professor Ngô was inspired by yet another formative finding that would occur while he toiled away in college.
“Sir Andrew Wiles proof of Fermat’s Last Theorem, as completed in the early 1990s, was another major milestone in number theory,” he shared. “Most mathematicians had considered Fermat’s Last Theorem to be unsolvable, so for it to happen when I was doing my PhD in mathematical college—in my lifetime, basically—was incredible,” he added.
The inspiration would be crucial as Ngô applied himself to studying the Langlands Program. When Ngô’s proof of the fundamental lemma was confirmed by other experts, it not only validated decades of mathematical work, it also opened the path for more scholars to dive into the field.
What, then, will be the next major milestone in number theory? Only time will tell, but Ngô’s successes have certainly inspired would-be math prodigies to make their own mark on number theory, in the same way that he himself was inspired by the mathematical forefathers of old.
Asian Scientist Magazine is a media partner of the Global Young Scientists Summit (GYSS@one-north 2015), taking place from 18-23 January, 2015 at Nanyang Technological University, Singapore. GYSS@one-north 2015 is organized by the National Research Foundation of Singapore in collaboration with its partners.
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Copyright: Asian Scientist Magazine.
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