OpenAI says a new artificial intelligence system has produced a proposed solution to the 90-year-old Navier–Stokes problem, one of the seven Millennium Prize Problems in mathematics, after deploying about 10,000 AI agents over 88 hours.

The company said in a release published Tuesday that its researchers used a system of coordinating AI agents powered by an internal model to work on the problem, which concerns the mathematical equations used to describe the motion of fluids such as water and air.

OpenAI said the agents began working on the problem on September 1 and arrived at what the company described as a resolution on Saturday, September 5, roughly 88 hours after the first agents were launched.

The claim has not yet been independently validated by the mathematical community. The Clay Mathematics Institute, which established the Millennium Prize Problems and offers a $1 million prize for a correct solution to each, had not commented on OpenAI’s proposed solution at the time of the announcement.

OpenAI’s announcement therefore marks a significant AI research claim rather than a formally recognized solution. For the problem to be considered solved, mathematicians would need to scrutinize the proposed proof and establish that it satisfies the requirements of the problem.

10,000 AI Agents Worked In Parallel

OpenAI said the system differed from a conventional chatbot interaction because it deployed large numbers of agents that could work on different aspects of the problem and communicate within groups.

“The agents had access to tools such as the ability to read from a cached version of the internet and the ability to run code,” OpenAI said.

The company said the agents were divided into groups of different sizes, with individual groups able to communicate internally. The group responsible for the Navier–Stokes work involved “on the order of 10,000 concurrent agents,” according to OpenAI.

The approach points to a broader shift in AI research from models that generate individual answers toward systems capable of coordinating large numbers of specialized computational tasks. Rather than asking one model to produce a mathematical proof from beginning to end, the architecture allows agents to explore possible approaches, test calculations, run code, and exchange information.

In principle, that can give an AI system substantially more opportunities to identify and correct errors in a difficult proof.

The speed claimed by OpenAI is notable because Navier–Stokes has resisted attempts by mathematicians for decades.

Why Navier–Stokes Matters

The Navier–Stokes equations are fundamental to fluid dynamics. They are used to describe how fluids move and have applications across physics and engineering, including the study of airflow, water, weather, and other fluid systems.

The Millennium Prize version of the problem asks mathematicians to establish whether sufficiently smooth solutions to the three-dimensional Navier–Stokes equations always exist and remain smooth, or whether solutions can develop singularities in finite time.

The difficulty is not simply solving the equations for a particular physical system. The challenge is proving a general mathematical result about the behavior of three-dimensional fluid flows.

That distinction is important when assessing OpenAI’s claim. Producing numerical evidence or solving particular cases would not be enough. A valid solution must provide a rigorous mathematical proof that addresses the full problem.

Mathematician Raises Questions About OpenAI’s Route

OpenAI’s announcement quickly attracted scrutiny from Tristan Buckmaster, a mathematics professor at New York University who has been working on Navier–Stokes with Levent Alpöge, a mathematician who works at OpenAI rival Anthropic.

Buckmaster said in a statement on his website that he and Alpöge had been collaborating personally on mathematical problems, including Navier–Stokes, and that Alpöge received information suggesting that details of their progress had reached OpenAI.

According to Buckmaster, the approach described by OpenAI appeared similar to work the two mathematicians had been pursuing. He questioned whether information from their work could have been accessible to OpenAI’s models, including through sessions conducted using the company’s Codex products.

Buckmaster was careful to distinguish those questions from an allegation that OpenAI had improperly accessed the mathematicians’ work.

“I would like to be clear about what I am not claiming. I have not seen OpenAI’s proof. I do not know what their model did, or how. I do not know whether our data was used,” he said.

His comments introduce a separate issue from whether the mathematics itself is correct: the provenance of the information used by an AI system in reaching a claimed breakthrough.

OpenAI said its work on Navier–Stokes began on September 1 after the company heard a rumor about progress on the problem. It later determined that the rumor concerned the work by Buckmaster and Alpöge.

The company said its researchers and AI agents did not see the mathematicians’ work before it was publicly released.

“We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem,” OpenAI said.

The company added that, while it considered it unlikely, it could not rule out the possibility that de-identified data derived from users’ interactions with its products had contributed to improving its models.

That could become important as AI companies increasingly position their models as tools for scientific and mathematical research. Questions over training data, model access, confidentiality, and the boundaries between publicly available knowledge and private user work are becoming more consequential as AI systems are used to generate original research.

A Test for AI’s Role in Advanced Mathematics

If OpenAI’s proof survives independent mathematical scrutiny, the significance would extend beyond Navier–Stokes.

AI systems have already demonstrated an ability to assist with theorem proving, mathematical discovery, coding, and scientific research. A rigorously verified solution to a Millennium Prize Problem would represent a much more consequential milestone because it would demonstrate that AI can contribute to solving a problem that has resisted generations of human mathematicians.

It would also strengthen the case for multi-agent AI systems, in which large numbers of models cooperate rather than relying on a single model to reason through a problem.

But the most important test remains mathematical verification.

A computer-generated argument, no matter how sophisticated the underlying AI system or how many agents participated, does not become a proof simply because an AI company describes it as a solution. Independent mathematicians will need to examine the argument line by line, identify any hidden assumptions or logical gaps, and determine whether it actually resolves the question posed by the Clay Institute.

Seven Problems, Seven $1 Million Prizes

The Clay Mathematics Institute established the Millennium Prize Problems in 2000, selecting seven of the most important unresolved problems in mathematics and offering $1 million for a correct solution to each.

The institute said the prizes were intended to draw public attention to the fact that fundamental mathematical questions remain unresolved and to recognize achievements of “historical magnitude.”

Navier–Stokes is one of the seven problems. The others include the Riemann Hypothesis, which concerns the distribution of prime numbers, and the Birch and Swinnerton-Dyer Conjecture, which concerns elliptic curves.

Only one of the seven, the Poincaré Conjecture, has been officially solved.

OpenAI’s Navier–Stokes claim now enters that same long-running mathematical test: whether an AI-generated result can withstand the standards of proof that have governed mathematics for centuries.

Until independent experts validate the proposed solution, the most precise description of OpenAI’s achievement is that its AI system has produced a proposed resolution to one of mathematics’ most difficult open problems.

Crude reaches its highest level since July as disruptions through the Strait of Hormuz and Red Sea deepen, raising the risk of another global inflation shock

Brent crude briefly climbed above $100 a barrel on Wednesday for the first time since July as intensifying fighting across the Middle East heightened fears that disruptions to critical oil shipping routes could further tighten global supplies.

The international benchmark rose above the $100 threshold during early European trading and was trading at about $100.60 a barrel around 5:45 a.m. ET. U.S. West Texas Intermediate crude was trading just above $95 a barrel.

Brent has risen roughly 25% since the beginning of August as hopes for a lasting end to the six-month U.S.-Iran conflict have faded. The latest escalation came after U.S. forces attacked Iranian tankers, following what the U.S. military said was an attempted Iranian ballistic-missile strike on a U.S. Navy warship.

Iran-backed Houthi militants have also intensified attacks in the region, including strikes that set Saudi energy facilities on fire. The attacks have increased concerns over the security of oil shipments through both the Red Sea and the Strait of Hormuz.

Brent had previously surged as high as $126 a barrel in April before retreating as expectations of a ceasefire reduced the immediate supply-risk premium.

The Strait of Hormuz remains the most important pressure point for the global oil market.

Oil flows through the waterway have recently fallen below 2 million barrels per day, according to Rystad Energy estimates, compared with approximately 8 million to 9 million barrels per day in the week before fighting resumed on August 30.

The decline has sent shockwaves through the markets because Hormuz is one of the world’s most important energy chokepoints. Before the war began on February 28, the waterway typically handled about 125 large commercial vessels a day, including oil tankers and liquefied natural gas carriers, accounting for roughly 20% of global daily crude oil and LNG supply.

Preliminary shipping data showed only six commodity vessels passed through the Strait of Hormuz on Tuesday, down from nine the previous day and below the 10-day average of about 12.

The figures may understate actual traffic because vessels can switch off their Automatic Identification System transponders to reduce their visibility. Of the six vessels recorded, five were entering the strait, and one was exiting, according to preliminary data from ship-tracking firm Kpler. The vessels included a Panamax and an intermediate tanker.

The decline in traffic suggests that the conflict is affecting not only physical oil production but also the willingness and ability of shipowners to move cargo through the region.

A U.S. blockade of Iran-related shipping has also halted Iranian crude exports since it was reimposed in mid-July, further tightening the market.

U.S.-Iran Conflict Intensifies

The energy-market shock has been compounded by a broader escalation in military activity. The conflict intensified Tuesday after Tehran-backed Houthis launched strikes on several Saudi Arabian cities. U.S. forces also attacked multiple Iranian oil tankers, while Iran struck a U.S. base in Jordan.

Marine intelligence firm Marisks reported that U.S. forces had rendered five Iran-linked crude tankers inoperable: the M/T Kaviz, Charminar, Horizon 1, Riesco and Derya.

Four of the vessels were reportedly struck in the Gulf of Oman, outside the Strait of Hormuz, while another was hit near Kharg Island, Iran’s most important oil export terminal.

The attacks introduce another layer of risk for the oil market because damage to tankers and export infrastructure could restrict both the movement of existing supplies and Iran’s ability to bring crude to market.

The Red Sea is facing a separate disruption.

Houthi militants have announced a blockade of Saudi-related shipping, while 25 commodity vessels crossed the Bab el-Mandeb strait on Tuesday. Eleven entered, and 14 exited, compared with an average of about 27 vessels over the previous 10 days.

The traffic included two Suezmax tankers, eight Aframax tankers and one very large crude carrier.

Together, the disruptions at Hormuz and Bab el-Mandeb raise the possibility that shipping companies will increasingly avoid major Middle Eastern routes, forcing vessels to take longer and more expensive journeys and increasing freight, insurance and delivery costs.

Oil Shock Threatens Inflation Outlook

The oil rally is becoming an increasingly important economic issue as well as a geopolitical one. Higher crude prices feed into gasoline, transportation, shipping and manufacturing costs, potentially pushing consumer inflation higher. A sustained Brent price at or above $100 could therefore complicate the outlook for central banks that are attempting to balance economic growth against persistent inflation.

The risk is becoming a cause for alarm because the shock is occurring alongside disruptions to shipping routes. Even if global crude production remains sufficient, higher freight and insurance costs can amplify the price impact throughout the supply chain.

The International Energy Agency said last month that global oil supply was expected to fall by about 4.3 million barrels per day this year, or roughly 4%, despite increased production from countries including the United States, Canada and Guyana.

Major investment banks have responded by raising their oil-price forecasts, with Goldman Sachs, Bank of America and HSBC among those taking a more bullish view of crude prices in recent days.

The oil market has some protection from higher production outside the Middle East, but the scale and speed of the disruption remain difficult to assess.

Additional output from the U.S., Canada and Guyana can cushion some losses, but those barrels cannot immediately replace supplies stranded by a shipping blockade or a prolonged closure of a critical maritime chokepoint.

That makes the duration of the disruption more important than the initial price spike.

If traffic through Hormuz remains severely depressed for an extended period, traders could begin pricing a more persistent physical shortage rather than a temporary geopolitical premium. That would increase pressure on refiners, fuel distributors and consumers while raising the risk of broader inflationary effects.

Conversely, a restoration of shipping flows or a credible ceasefire could quickly remove some of the risk premium that has pushed Brent toward $100.

For now, the direction of the oil market is increasingly tied to events on the battlefield and the safety of commercial shipping.

Brent’s brief move above $100 is therefore more than a psychological milestone. Analysts see it as a signal that traders are beginning to price a conflict in which disruptions are spreading across multiple energy corridors at the same time. But the longer those disruptions persist, the greater the risk that an initially regional oil shock becomes a broader global inflation and growth problem.

Africa’s richest person, Aliko Dangote, is pushing a plan to develop another oil refinery – this time, a 700,000-barrel-per-day refinery in Kenya, in East Africa. The move comes less than three years after bringing Africa’s largest oil refinery into operation in Nigeria.

The proposed Lamu refinery, expected to cost between $15 billion and $16 billion, represents one of Dangote Group’s most ambitious projects outside Nigeria. The company plans to hold a groundbreaking ceremony later this month and aims to complete the facility by 2030.

But the project faces a fundamentally different set of challenges from those encountered at Dangote’s Lagos refinery, particularly over crude supply, financing and supporting infrastructure, according to a Reuters report.

Nigeria has abundant oil reserves and an established crude-producing industry. Kenya, by contrast, currently has no commercial-scale oil production, meaning Dangote will need to secure reliable feedstock from neighboring producers or the international seaborne market.

The project’s location has also evolved rapidly.

Until April, discussions centered on Tanzania. In May, Dangote told the Financial Times that he was leaning toward Mombasa, before a company executive said in July that the refinery would instead be built in Lamu, a deep-water port whose maritime access is central to the project’s proposed logistics model.

The refinery is expected to be located within the Lamu Port-South Sudan-Ethiopia Transport, or LAPSSET, special economic zone, linking the facility to one of East Africa’s largest planned transport and energy corridors.

Dangote Industries Vice President Devakumar Edwin said the company did not see regulatory, financing or feedstock challenges as obstacles that could not be overcome. The company has said the refinery would strengthen regional fuel supply and energy security.

Yet the scale of the undertaking has prompted warnings about execution risk.

“If not successfully implemented, it runs the risk of becoming a very expensive white elephant,” said Brendon Verster, senior economist at Oxford Economics.

The central question is whether Dangote can create a reliable supply chain around a refinery whose capacity would be larger than Kenya’s domestic fuel market requires.

Financing A Second Mega-Project

Dangote Group plans to finance the Kenyan refinery through a combination of internal cash flow, bonds and an initial public offering, according to a company executive. The financing strategy could also include equity from Dangote, commercial bank loans and development finance institutions such as Afreximbank, following elements of the financing structure used for the Lagos refinery.

But Dangote is simultaneously committing more capital to its existing Nigerian operations.

The group said Monday that it would spend $14.3 billion to double the processing capacity of its Lagos refinery. The additional investment comes alongside other oil and energy projects being developed by the conglomerate.

That competition for capital could become one of the biggest constraints on the Lamu project.

“Given that the group is seeking some $40 billion (including Lamu) between 2025 and 2030 for announced energy projects, raising the capital for Lamu could become a formidable challenge,” said Kaase Gbakon, a petroleum economist and former employee of Nigeria’s state-owned oil company, NNPC.

Dangote has also suggested that Rwanda, South Sudan, Tanzania and Uganda could collectively take as much as a 30% equity stake in the refinery. Such participation could provide another source of funding while giving governments across the region a direct financial interest in the project.

No details of potential agreements have been disclosed, however.

The planned initial public offering of Dangote’s Lagos refinery is considered crucial to the broader financing strategy. If the listing raises substantial capital, it could provide Dangote with additional funding for expansion while bringing institutional investors into the refinery business.

The Crude Supply Problem

Financing may be difficult, but securing enough crude could prove even more fundamental.

A senior economic adviser to Kenyan President William Ruto has said the refinery could obtain up to 600,000 barrels of crude a day from East African sources, including Kenya, South Sudan and Uganda, according to Kenyan media reports.

The problem is that none of those supply routes is currently straightforward. Kenya has proven oil reserves but has struggled for years to establish commercial production. Small-scale output is expected later this year, but domestic production is nowhere near the volumes required to supply a 700,000-barrel-per-day refinery.

A proposed pipeline connecting oil fields in Kenya’s Lokichar Basin and South Sudan to Lamu could eventually provide a regional supply network, but that infrastructure remains a long-term prospect.

South Sudan also faces major logistical problems. Its crude exports depend on pipelines through Sudan, where conflict has repeatedly disrupted oil flows.

Uganda has oil resources, but its planned exports are being routed toward Tanzania through the East African Crude Oil Pipeline, or EACOP.

“That leaves the coastal facility dependent on a volatile international seaborne market,” said Maximillian Ezeude, an oil and gas lawyer in Lagos.

That dependence could expose the refinery to global freight costs, geopolitical disruptions and crude-price volatility. The issue is particularly significant given that the nearest major sources of seaborne crude are in the Middle East, where the continuing Iran war has disrupted regional energy flows.

For a refinery designed to process hundreds of thousands of barrels each day, supply interruptions could quickly translate into lower utilization and weaker economics.

Lamu Infrastructure Is Still Developing

The refinery also depends on infrastructure that is not yet fully in place. Lamu Port is a critical component of the LAPSSET corridor, but it currently lacks operational oil storage terminals capable of supporting a refinery of the proposed scale.

The LAPSSET plan includes oil storage facilities with capacity of between 1 million and 1.5 million barrels, along with marine-loading infrastructure designed to handle vessels up to Suezmax size.

Much of that supporting infrastructure remains unbuilt. And that creates a sequencing challenge. Dangote needs reliable port access, storage, pipelines and marine facilities to secure crude and distribute refined products, while the wider economic case for developing that infrastructure depends partly on the refinery itself.

The project therefore extends beyond construction of a processing plant as it requires the simultaneous development of an integrated energy logistics network.

Kenya sees the refinery as a potential solution to a major structural weakness in its energy economy. The country’s only refinery was closed by India’s Essar Energy in 2013, leaving Kenya heavily dependent on imported petroleum products.

Kenya spent roughly $4 billion, equivalent to 511.5 billion Kenyan shillings, on petroleum products last year, according to official data. Petroleum was the country’s largest import.

Ruto has argued that a new refinery could reduce that import dependence while supporting industrial development and economic growth.

“We have to make those decisions that will change our country, that will transform our country,” Ruto said of the Lamu project.

A large refinery could also position Kenya as a regional fuel supplier to landlocked markets including Uganda, Rwanda and South Sudan, potentially creating demand beyond the domestic market. That regional opportunity is essential to the economics of the project. A 700,000-barrel-per-day refinery would require access to a much larger market than Kenya alone can provide.

The business case is expected to hinge largely on Dangote’s chances to secure long-term customers across East and Central Africa while competing with imported refined products and other regional refineries.

Environmental And Execution Risks

The Lamu development also faces environmental and community concerns. Lamu Old Town, a UNESCO World Heritage site on Lamu Island, is about 10 kilometers from Lamu Port. Environmental groups have raised concerns about potential habitat destruction and marine degradation associated with industrial development in the area.

Greenpeace Africa has called for the project to be halted over environmental concerns.

Those issues could affect permitting, project timelines and access to some sources of international financing, particularly lenders with stringent environmental, social and governance requirements.

Benjamin Oluwatobi Ajayi, an energy analyst based in Lagos, said the project faces several overlapping execution risks.

“The size of the debt requirement, ESG-related financing constraints, competition for capital across multiple projects, and the need to coordinate numerous lenders and stakeholders within a compressed timeframe all increase execution risk,” he said.

For Dangote, the Lamu refinery is therefore a much broader test than simply building another large processing plant. The Lagos refinery demonstrated that the group could finance and complete a huge energy project in an oil-producing country after years of cost overruns, infrastructure problems and construction challenges. Lamu will test whether that model can work in a country where the crude supply chain, storage infrastructure and regional distribution network still need to be developed.

The proposed facility could reduce East Africa’s dependence on imported refined fuels and establish Kenya as a regional energy hub. But its success will depend on three conditions arriving together: sufficient capital, dependable crude supplies and infrastructure capable of moving hundreds of thousands of barrels a day.

If Dangote can solve those problems, Lamu could become the anchor of a new East African petroleum network. If it cannot, the refinery’s enormous scale could become its biggest vulnerability.