Vahab Mirrokni, a vice president at Google Research who leads its Algorithms and Optimization research teams, recently announced the Google team’s proof of the Courtade–Kumar conjecture, described as one of the most important open problems in information theory.

He also congratulated a Vietnamese research team comprising Dr. Vu Khac Ky of FPT University and Professor Tran Manh Tuan of the University of Science and Technology of China, who had also obtained a complete proof.

Remarkably, the two teams arrived at their solutions almost simultaneously, working entirely independently and taking very different approaches.

The Courtade–Kumar conjecture, also known as the “Most Informative Boolean Function Conjecture,” was proposed by Thomas Courtade and Gowtham Kumar in 2013.

anh man hinh 2026 09 24 luc 54414 ch 1790247630446.webp
Photo caption: Dr. Vu Khac Ky currently works at FPT University.

It stems from a natural question in information transmission and processing: when data is affected by noise during transmission, how should the original information be selected and processed to preserve as much information as possible?

Surprisingly, the conjecture proposes an extremely simple optimal strategy. Rather than combining multiple bits according to a complex rule, it is enough to retain a single bit. For more than a decade, however, mathematicians worldwide had managed to solve only special cases.

Ky said he first learned about the conjecture from Professor Chandra Nair around 10 years ago, while conducting postdoctoral research at the Chinese University of Hong Kong (CUHK) in Hong Kong, China.

He then spent about two years working intensively on it, without success. From January 2019 onward, he returned to the problem occasionally, but each attempt eventually stalled because he had not found a sufficiently powerful mechanism to overcome the known obstacles.

In 2025, Ky began working on the problem more seriously again. Around the same time, he started collaborating with Tuan, a specialist in discrete probability and combinatorics.

Their research backgrounds complemented each other, allowing them to continually test, discard and refine ideas. Step by step, they extended the range of cases they could handle, addressed the remaining cases and eventually arrived at a proof for the general case.

On September 21, their paper, “Dictators are most informative,” was posted on arXiv, an online repository for scientific preprints.

Before releasing the paper, Ky emailed Nair as a gesture of respect, informing him that he and his collaborator had found a solution.

“Professor Chandra Nair replied that his team, together with scientists from Google and several other universities, had also just completed a proof of the same problem,” Ky said.

The two teams then exchanged findings and realized they had independently reached the same result through two very different methods. Each approach has its own strengths, though both still need to be assessed by the mathematical community over time.

After learning of each other’s results, Ky and Tuan agreed to delay their release because Nair’s team needed more time to finalize a lengthy paper containing extensive calculations. The teams agreed to release their independent proofs at the same time.

“To me, this is also a beautiful story about scientific research,” Ky said.

Thuy Nga