OpenAI says it has solved one of the "Millennium Problems". Mathematicians are asking for proof
Technology
Искусственный интеллект
Инвестиции
Setúbal

OpenAI says it has solved one of the "Millennium Problems". Mathematicians are asking for proof

ZAP Notícias9 September 2026 at 08:00

OpenAI announced this Tuesday that one of its artificial intelligence systems found a solution to the problem of existence and smoothness of the Navier-Stokes equations, one of the Seven Millennium Problems defined by the Clay Mathematics Institute in 2000. The resolution of each of these problems is worth a one million dollar prize and, until now, only one had been previously solved.

The company states that the AI system demonstrated, in about 88 hours, that the Navier-Stokes equations can "blow up". The proof was made public, but still needs to be validated by the mathematical community, a process that can take months or years.

The announcement has already opened a dispute over credits, private data, and alleged pressures. The controversy arises in the context of a technological race between AI companies in solving complex mathematical problems.

OpenAI hopes that the publication of the proof will allow the scientific community to analyze and verify the work, in a process that is traditionally time-consuming and requires peer review.

Related articles

Technology

Advances in Digital Literacy: Challenges and Disparities Between Generations

According to a 2025 report from the National Statistics Institute, nearly three in every five people between the ages of 16 and 74 have basic or above basic digital skills, showing a significant advance in the digital literacy of the Portuguese population. However, the study reveals marked disparities: young people between 16 and 24 years old show greater digital proficiency, while elderly people have considerably lower digital literacy rates. Education level also directly influences digital skills, with people holding higher education demonstrating greater mastery compared to those with only basic education. Authorities are already considering measures to promote training and technological inclusion, aiming to prepare society for the challenges of digitalization.

Notícias Portugal09/09/26, 11:03
Technology

Investigation reveals that LG televisions record audio with the screen off

An investigation discovered that LG smart TVs have functionalities that allow mapping nearby devices, capturing audio even with the screen off, and potentially functioning as covert listening devices, raising serious questions about user privacy.

TV RECORD EUROPA09/09/26, 10:49
OpenAI resolve equação centenária em 88 horas, mas enfrenta suspeitas de plágio
Technology

OpenAI solves century-old equation in 88 hours, but faces plagiarism allegations

OpenAI managed to solve the Navier-Stokes equation, formulated by mathematicians in the 19th century and widely used in meteorology and aeronautics, in just 88 hours using its artificial intelligence model. However, mathematicians Tristan Buckmaster and Levent Alpöge, who worked on related research, suspect that their previous work may have influenced or been improperly used in the solution developed by the company, raising questions about plagiarism and intellectual property in the use of academic research by AI systems.

Expresso09/09/26, 10:45
Technology

Polytechnic University of Guarda Registers Three Patents

The Polytechnic University of Guarda (UPG) has registered three patents in the areas of health and digital technology, representing a milestone in the institution's affirmation as a reference polytechnic university, according to the rector. The patent applications were officially filed by the university, marking a significant step in its research and innovation activity.

Observador09/09/26, 10:42