Prof. Ngo Bao Chau and Langlands lemma

In recent days, the whole nation was happy about Prof. Ngo Bao Chau - Vietnamese mathematician receiving the most prestigious mathematical prize in the world, the Fields Medal . Many people want to know the content of your work, but this is not easy. We can only provide readers with some of the most basic and understandable expressions about this issue.

>>> Professor Ngo Bao Chau won the Fields math prize
>>> Over 3000 people attended the ceremony to welcome Professor Ngo Bao Chau
>>> Ngo Bao Chau's childhood

In mathematics, lemma is a hypothesis that has been proved or will be proven to be the foundation from which mathematicians continue to study and achieve a higher result.

Professor Ngo Bao Chau

Can be briefly understood when omitting all the concepts of mathematical expertise: In 1967, mathematician Robert Langlands, Canadians introduced a series of bold hypotheses that most so far have not been proven. , and will be a research topic for future generations of mathematicians. If proven, it will link many areas of modern mathematics into a unified whole, such as between algebraic geometry and arithmetic.

One of the tools developed from the Langlands program is ' Arthur-Selberg trace formula ', an equation that shows that it is possible to use geometric information to calculate arithmetic information.

But Langlands has a big problem when using this formula, because it appears that there are complex numbers. According to Langlands these totals are equal but he cannot prove it. He sees this as a simple problem and calls it 'lemma' - a secondary result used to prove more important results. But no one can prove it, people call it by the more important name: ' Basic Lemma' (PCB).

Many leading mathematicians have put effort to prove the PCB but only succeeded in some special cases. And Professor Ngo Bao Chau has demonstrated this lemma in the general case, clarifying long-standing questions, creating new beliefs in mathematical research and many other sciences.

Please borrow from GS Chau in an interview with the former Thanh Nien newspaper about the PCU and the Langlands Program:

' The Langlands hypothesis is the driving force for the development of theoretical mathematics in the past forty years. Many problems seem to be individual bricks, now arranged by Langlands' hypotheses into a great architecture. I personally rank Langlands' hypotheses with Euclid's flat geometry or invent Galois group in solving algebraic equations .

PCBB is a 'lemma' because it itself is a technical problem. But it is not necessarily lemma because Mr. Langlands only proved it in a special case and the general case is stated as a hypothesis. And the 'basic' is because a large corner of the above building structure will collapse if the PCB is not correct. In addition, proving that the CCB is a lot of people interested because its idea is not encapsulated in the Langlands program, but it has a tendency to dream about some issues of theoretical physics . '

We have the right to expect that Prof. Ngo Bao Chau will contribute more to the world mathematics and the country of Vietnam.