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Frontier AI labs say their models refuted the Exponential Time Hypothesis. What does that mean?

Published

1 day ago

October 27, 2026

OpenAI released solutions to three blockbuster math problems that have long vexed researchers yesterday. One was a surprise rejection of the Exponential Time Hypothesis (ETH), a durable assumption in computer science that plays a large role in how we understand what is difficult to compute.

As with previous proof-drops from the frontier lab, scientific communities responded with a mixture of thrill and dismay. Anthropic mathematician Levent Alpöge suggested that OpenAI was basing its solutions from pre-existing work, and hours later, Anthropic subsequently released its own refutation of ETH.

However, OpenAI’s process is evolving. This time, the lab structured its releases differently for each of the three disciplines involved: Mathematicians got the work dropped on GitHub; the computer scientists formed a working group, asked for the proofs to be shared publicly and OpenAI to fund a conference to discuss them; the physicists formed a working group that will determine how their result will be released.

MIT Professor Ryan Williams is the computer scientist who is organizing his field’s response to the new finding. Williams, whose work focuses on these questions of computational complexity, has criticized OpenAI’s approach in the past, calling its proof dump earlier this October a “DDOS attack on mathematicians.”

However, he agreed to collaborate with the frontier labs in order to help shepherd ideas that are vital to the field, he told TechCrunch. The lab asked him to help interpret the solution, along with UC San Diego computer scientists Russell Impagliazzo and Ramamohan Paturi, who first published the ETH in 1999.

Their first step was to release an open letter calling for feedback from scientists interested in these problems and a discussion of the norms around AI contributions to their work.

“Some parts [of OpenAI’s proof] are, maybe you could say routine, but then yes, there are two or three alien-looking parts, and it’s exactly these parts that that I saw that made me think, wow, this is something that the whole community needs to work on together,” Williams told TechCrunch.

Are you down with P vs NP?

The ETH is part of a broader class of problems known as P vs NP, which has animated computer science and many other fields for decades. Reductively, researchers are trying to understand if any problem whose solution can be easily verified (NP) can also be easily solved (P).

A simple example is the game Sodoku: Once a solution to a puzzle is in place, it can be quickly verified, but finding the solution is time-consuming. That dynamic is true across a range of important problems, and the insight underpins cryptographic systems: When you have the key to an encoded message, you can reveal it, but actually cracking an effective code takes too long to be useful.

However, scientists have yet to prove whether that is always true. “P = NP is saying that, not only can you verify Sudoku solutions when they exist, you can just generate them,” Williams said. “P = NP is asserting that this is true for every single problem you can verify quickly — if you can verify it quickly, you can solve it quickly. So this just seems too good to be true.”

That’s why most scientists assume that P ≠ NP. ETH provided evidence for that. It basically says that even the fastest computer algorithm needs exponentially more time to find a solution as the number of variables grow in a specific class of tricky logic puzzle.

The claims from OpenAI and Anthropic is that their models have come up with algorithms that solve those puzzles in “sub-exponential” time, meaning faster than the speeds previously thought possible. If true, they may have proven the EFT to be false — refuted it, in scientific terms — and maybe opened up a path for algorithms that generally perform P = NP.

“Every computer scientist should probably put a little more weight on the plausibility of P = NP, but one’s weight may vary,” Williams said. “I do think that it kind of calls into question a lot of the intuitions that we thought we had about … how tractable [hard NP problems] are. I also think that this is probably not the final answer either. I don’t think that OpenAI’s algorithm could possibly be the best algorithm you can get.”

The work ahead for computer scientists

The durability of ETH has lead to it being included in many scientific papers over the past decade that will need to be revisited if the AI labs claims that they’ve proven it wrong holds up, Williams said.

“This is partly why I was asking or pushing OpenAI to support a conference on this — it’s going to affect many researchers’ works, and we need to figure out, okay, what happens next besides understanding the algorithms. We need to understand, how should the foundations change compared to what we had before?” he said.

Before scientific concerns, there are cybersecurity questions. Williams said that an improved algorithm could imply that cryptographic systems relying on certain key sizes could be considered broken. So one of the first questions he asked OpenAI science lead Dan Roberts “was if they had checked that this affects any crypto systems … is anything insecure now? And apparently, they checked, and they were reasonably confident that this didn’t … imply any breaks.”

This new AI paradigm of scientific discovery is still a work in progress, but Williams says he is optimistic despite real concerns, particularly about training the next generation of scientists. Being a computer scientist who does high level math has perhaps made the adjustment easier for him than for pure mathematicians.

Still, he says AI is “forcing people to be a little more ambitious about the kind of work that they do, and to think more deeply about, okay, if all the things I used to work on are now low hanging fruit for AI, how can I raise the bar for the kind of scientific questions I want to ask?”

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Related Topics:Exponential Frontier Hypothesis Labs models refuted time

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From Producing Nigerian Internationals to Building Their Own Stadium: Buruj Sports Academy Takes Bold Step as Ikorodu Football Dream Attracts Investors

Published

1 hour ago

October 28, 2026

PlateauReports

Buruj Sports Academy is turning years of grassroots football success into an ambitious infrastructure project, unveiling a proposed stadium development in Ikorodu, Lagos State, aimed at transforming opportunities for young Nigerian footballers.

The academy, founded by Dr. Waheed Salaudeen, has presented a new development layout featuring a standard 105m × 68m football pitch, spectator stand, changing rooms, administrative and first-aid facilities, toilets, parking spaces and perimeter security.

The project represents a significant step toward establishing a permanent home for the academy’s growing football development programme.

Buruj’s ambitions are backed by its record of nurturing promising talents, including former Nigeria Under-15 internationals Raheem Moyinoluwa Salaudeen and Fawas Ayomide Adeleke, who represented Nigeria in youth competitions in Morocco and Algeria.

The academy has also facilitated opportunities for players in Spain and Lithuania, while six Buruj youngsters recently earned selection for an international football exposure programme following the Italian Consulate General U-20 Tournament.

Unlike its earlier three-acre, 5,000-seat stadium concept, the latest architectural proposal adopts a more practical, phased approach, beginning with an approximately 80–100-seat stand and essential football facilities. Punch Newspapers +1

Dr. Salaudeen, who serves as founder and Chief Executive Officer, has consistently championed football development alongside education.

“This dream is bigger than Buruj Sports Academy alone. We are appealing to private individuals, corporate organizations, investors, and well-meaning Nigerians to support this vision.”

His appeal reflects a determination to build a sustainable sporting institution capable of serving generations of young Nigerians. Sports247 Nigeria +1

For potential investors, the project offers opportunities in stadium naming rights, facility sponsorship, youth development partnerships, football tournaments and community sports programmes.

With a survey document and proposed layout now presented, Buruj is inviting partners to help turn its vision into reality, subject to necessary technical assessments and development approvals.

From discovering football stars to building the infrastructure that produces them, Buruj Sports Academy is no longer simply dreaming of the future — it is preparing to build it.

News

ADC Postpones Presidential Campaign Flagoff, Fixes New Date

Published

1 hour ago

October 28, 2026

PlateauReports

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The African Democratic Congress (ADC) has postponed the flag-off of its presidential campaign in Sokoto State, earlier scheduled for Saturday, October 31, to Wednesday, November 4.

The party’s Presidential Campaign Council in Sokoto State announced the postponement in a press statement issued on Wednesday, and signed by its Director-General, Bello Aliyu Goronyo.

According to the statement, the decision was taken to address certain planning and coordination issues to ensure the successful conduct of the campaign event.

The council appealed to party leaders, stakeholders, supporters and members of the public to take note of the new date, while expressing regret over any inconvenience caused by the change in schedule.

“The African Democratic Congress (ADC) Presidential Campaign Council in Sokoto State wishes to announce the postponement of its Presidential Campaign Flag-off, earlier scheduled for Saturday, 31st October 2026, to Wednesday, 4th November 2026,” the statement read.

Explaining the reason for the change, the council said, “The decision follows the need to address certain planning and coordination considerations to ensure the successful conduct of the event.”

“The Campaign Council regrets any inconvenience the change may cause and sincerely appreciates the understanding, patience and continued support of party leaders, stakeholders, supporters and members of the public,” Goronyo added.

He urged all concerned to take note of the new date and expressed the council’s readiness to welcome party leaders, supporters and other stakeholders to the event.

The postponement comes amid reports of difficulties involving hotel accommodation in Sokoto ahead of the campaign flag-off originally scheduled for Saturday.

Reports had emerged that hotel rooms were being booked ahead of the planned ADC event, with allegations that some hotel owners were refusing to release rooms to prospective guests.

The development comes as the ADC continues preparations for the 2027 general election, with former Vice President Atiku Abubakar as the party’s presidential candidate.

The party is seeking to strengthen its support across the country as opposition parties prepare to challenge President Bola Tinubu and the ruling All Progressives Congress in the forthcoming presidential election.

Earlier on Wednesday, the ADC Presidential Campaign Council at the national level disowned an unsigned campaign timetable circulating on social media, urging party members, supporters and other stakeholders to disregard the document.

The council said the timetable, which contained proposed dates and locations for campaign rallies and other political activities across the country, had not been authorised by the campaign organisation.

In a statement signed by the Director of Media and Publicity of the ADC Presidential Campaign Council, Kola Ologbondiyan, the party clarified that the document did not originate from the council or its campaign office.

“The African Democratic Congress Presidential Campaign Council (ADC-PCC) has disowned an unsigned campaign timetable currently in circulation, clarifying that the document did not emanate from the Council or its campaign office,” the statement said.

Ologbondiyan urged party members and stakeholders to wait for official announcements regarding the campaign schedule.

“Accordingly, all members and stakeholders are urged to disregard the document and await official communications from the ADC-PCC on campaign activities and schedules,” he added.

The unsigned timetable listed Sokoto State as the proposed starting point for the presidential campaign on October 31, 2026, and outlined proposed activities in several other states before a closing rally scheduled for Adamawa State on January 11, 2027.

The document also contained proposed dates for rallies, town hall meetings and other political engagements in states including Kebbi, Zamfara, Ogun, Oyo, Rivers, Delta, Edo, Cross River, Anambra, Enugu, Ebonyi, Abia, Benue, Plateau, Kaduna, Kano and Borno.