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Mathematicians learn little from AI completing unsolved problem : NPR

OpenAI’s tone of celebration was evident when it announced that its AI solved the toughest math problem in history earlier this month:
The company stated that “a major goal of the work we do is to empower researchers to advance technology and research for all humanity.”
Mathematicians, however, say humanity has not learned much from the AI solution that the company claims to have found. The dense, 166 page manuscript written by AI, although they consider it to be technically accurate, is difficult to read.
James Maynard is a mathematician from the University of Oxford. He said that it was difficult for humans to understand this AI proof.
Javier Gomez-Serrano is a mathematician from Brown University, who has used AI to advance his research. After “some serious editing,” he said, he believed the proof would help the field advance. “As it stands today, however, the paper does not teach us very much.”
AI is rapidly developing mathematical insight, and the solution was found at this time. NPR spoke to academic mathematicians who said that AI had exploded on the mathematics scene in the last six months. The first large language model appears to be capable of producing results which could lead new mathematical discoveries.
Few people see OpenAI’s announcement as a good example of mathematicians and AI working together. The announcement came just as mathematicians had been able to narrow down a possible solution.
Maynard said, “This entire episode could have served as a great proof-of concept of the power that collaboration can bring between humans and AI.” He signed the statement of 25 Fields Medal winners. This statement was released on September 11 and criticized “misaligned objectives” between AI companies, the math community, and other AI firms.
He said, “Unfortunately due to the human decisions involved it turned into this messy, scrappy battle.”
Rush to discover
OpenAI’s solution to the problem is regarded as one of the most significant unanswered mathematical questions.
The “Navier Stokes Problem” is a collection of equations that describe fluid flow. Tristan Buckmaster is a mathematician from New York University. He said that the equations are applied in physics and engineering every day.
Researchers don’t really understand how they work. Buckmaster believes that a deeper understanding of Navier-Stokes will likely lead to “a new set of tools to help understand fluids in their complex solutions.” This could then lead to improved models for things such as turbulence and lift, both of which are important in aviation.
Researchers were looking at scenarios in which the equations had “broken down” or stopped working. The Clay Mathematics Institute established the Millenium Prize Problems in 2000, and one of them was to describe such scenarios.
The community had known for some time that mathematicians were close to solving the Navier-Stokes Problem. Martin Hairer is a mathematician from EPFL in Lausanne. He also signed the declaration.
Buckmaster, Levent Aloge, and other mathematicians at Anthropic were working to find a solution. Both Buckmaster and Levent Alpoge were working with AI tools including OpenAI’s chatbot in order to find a solution.
OpenAI then caught wind of the fact that this problem could be resolved soon.
The company stated that “on Tuesday, September 1 we heard rumors of two Millennium Prize issues being resolved.” We were inspired by these rumors, and the dramatic improvement in our model’s performance. So we began evaluating it for all Millennium Prize and other problems of high impact.
It gathered 10,000 AI agents and put them to work solving the Navier Stokes problem. They worked for around 88 hours and used 130 billion tokens or text-based characters that were generated by the model. OpenAI estimates that the Navier Stokes problem solution cost around $6 to $10 million. The company claims to have spent more than $15-20million on its search for solutions.
Buckmaster’s public statements about how OpenAI approached him sparked controversy. Buckmaster said that they told him they’d put his name on the paper if he would drop Alpoge, a collaborator of rival company Anthropic.
Buckmaster said to NPR that he believed OpenAI had been tipped to his and Alpoge’s approach to Navier-Stokes.
He said, “There are so many circumstantial signs that they knew more than they admitted.” The word “they”, he said, does not necessarily refer to a specific person. He said that “it could be the agents”.
OpenAI denies that it used Buckmaster or Alpoge’s proofs and prompts to find a solution.
The results are muddled. OpenAI’s research paper was described as virtually unreadable by several mathematicians.
Buckmaster said, “It is a terrible written paper.”
The paper does not explain which parts are important. What are the routine parts? What are the other parts of this idea? Gomez Serrano added.
Buckmaster stated that OpenAI’s decision to release a quick answer forced him into publishing his own AI-influenced preliminaries. He said that those results are also not well-written. He said that “everything was rushed.” It’s not to the standard I am happy with but the introduction contains all of the main ideas.
Computers check computers
Few mathematicians think that OpenAI’s proof of 166 pages is wrong, even though it takes weeks to unravel. The company, in addition to publishing a proof of its own, also created a computer program called a Lean Formalization. Lean, a mathematical programming language, is used to verify that proofs are accurate. The proof will be considered complete if the code is compiled.
Gomez Serrano stated that the Lean code generated by OpenAI tools compiles as expected. According to this, the community appears to agree that “it is correct.”
Gomez Serrano, Buckmaster, and the other mathematicians NPR contacted all said that they saw a future in AI for mathematics. It’s open for new tools in part because it has ceded to computers for many decades the computations needed to make advances.
Maynard said that this incident is a good reminder of the fact mathematics involves more than finding a simple solution. He said, “It was not just about solving this problem. It was also about understanding the reasoning behind it.”

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Stock market today: Dow slips, Nasdaq drifts higher as oil falls, AI trade powers market

As the major indexes waver in early afternoon trading, here’s a look at some other stocks that Yahoo Finance users are looking up:
PayPal (PYPL) shares popped over 2% after the payments platform announced it’s partnering with Meta (META) to allow customers to use their Muse personal AI agents to shop online. Meta stock was up 1%.
Viking Therapeutics (VKTX) stock soared over 25% after the company’s experimental obesity drug showed 22% weight loss in patients in a clinical trial. The company also said its drug showed promising signs of helping patients maintain weight loss with less frequent injections.
AutoZone (AZO) stock jumped 5% after the auto parts retailer reported a rise in fourth quarter profits and said it expects sales to accelerate in 2027. Listen to the earnings call here.
Shares of SanDisk (SNDK) rose 5% after Rosenblatt Securities initiated coverage of the company with a Buy rating and a $2,400 price target (the stock currently trades at $1,860 per share). The firm expects AI demand to support SanDisk’s growth, with NAND memory chips becoming “a more system-critical component of AI infrastructure.”
The US stock market held steady at Tuesday’s open after investors received fresh signals that oil supply constraints in the Middle East could ease, sending oil prices lower.
The tech-heavy Nasdaq Composite (^IXIC) rose 0.4% flat after the index touched a record high on Monday, while the S&P 500 (^GSPC) and the Dow Jones Industrial Average (^DJI) rose slightly at the opening bell.
51,879.72 -169.11 (-0.32%)
As of 2:44:41 PM EDT. Market Open.
^DJI ^GSPC ^IXIC
Futures on both international benchmark Brent crude (BZ=F) and US benchmark WTI (CL=F) eased overnight after news that Iran is open to diplomatic talks with the US, and Saudi Arabia is in the early stages of restarting a key oil pipeline after a drone attack earlier this month.
US gasoline now averages over $4.47 per gallon nationally, according to AAA. Meanwhile, US diesel prices are holding a record high of $6.52 per gallon.
In the world of corporate earnings, shares of AutoZone (AZO) rose 3% after the auto parts retailer reported earnings earlier Tuesday morning, beating profit expectations while missing revenue forecasts.

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What has happened since Trump killed US EV tax credits?

The federal government’s $7,500 EV tax credit was eliminated on September 30, 2025.
U.S. EV sales were down nearly 24% in the first half of 2026 compared to the same period in 2025.
Several automakers have since scaled back EV production plans in favor of hybrid models.
At this time last year, electric vehicle buyers in the United States were rushing to take advantage of the final weeks of the federal government’s popular $7,500 tax credit for plug-in models that was set to expire at the end of September 2025.
That tax credit, which was first adopted during former President George W. Bush’s administration in 2008 to help spur EV adoption, was eliminated on Sept. 30, 2025, by a law that was passed by Republicans in Congress and signed by President Donald Trump.
EV sales have been closely watched since then, as both supporters and detractors sought to understand how much demand for plug-in cars there would be without any government support. In recent months, in a bid to replace some of the lost federal support, state leaders in California stepped in to offer $3,750 in instant EV rebates to first time buyers in their state, which accounts for about a quarter of the nation’s EV market.
According to Cox Automotive, U.S. EV sales were down nearly 24% in the first half of 2026, which is the most recent data available, compared to the first half of 2025, when the $7,500 federal tax credit was still available. But the group said EV sales in the second quarter of 2026 were up more than 14% over the first quarter of the year as rising gas prices pushed shoppers toward more fuel-efficient models.
With that in mind, the USA TODAY Cars Team took a look at where the U.S. EV market stands one year after Trump killed the federal tax credits and what shoppers can expect moving forward.
What happened after the federal EV tax credit went away?
Several of the most popular electric car models experienced steep sales drops in the fourth quarter of 2025, after setting records in the third quarter as car buyers rushed to take advantage of the $7,500 federal tax credit before it expired at the end of September 2025.
Here’s how some of the top selling U.S. EVs fared in the third quarter of 2025 compared to the fourth quarter of that year, which was the first since Trump pulled the plug on the federal tax credit:
Tesla Model 3 and Model Y | Q3 2025: 481,166 | Q4 2025: 406,585
Ford Mustang Mach-E | Q3 2025: 20,177 | Q4 2025: 9,658
Hyundai Ioniq 5 | Q3 2025: 8,408 | Q4 2025: 2,279
Honda Prologue | Q3 2025: 20,236 | Q4 2025: 2,641
Volkwagen ID.4 | Q3 2025: 4,518 | Q4 2025: 248
As the auto industry moved forward into 2026, several automakers responded to Trump’s decision to eliminate the U.S. EV tax credit by announcing plans to pull the plug on low-selling electric models.
Ford announced plans to transition its F-150 Lightning pickup from a fully electric vehicle to a hybrid car type known as an Extended Range Electric Vehicle, or EREV.
Meanwhile, Honda axed three of the three electric models that it planned to build and sell in the United States. The Japanese automaker announced in a March 12 statement that it ended its plans to produce the electric Honda 0 SUV, Honda 0 Saloon and Acura RS.
Lamborghini also abandoned plans to develop fully electric cars by the end of the decade in favor of building more hybrids. The Italian automaker, a subsidiary of Volkswagen, confirmed to USA TODAY that they are not following the plan to build battery electric cars by 2030 because of weakening demand in the United States.
Also, Tesla is planning to end production of its Model S luxury electric sedan and Model X luxury electric SUV in the spring in favor of building robots, company CEO Elon Musk told investors on Tesla’s January earnings call.
Where does the US EV industry stand now?
Early signs pointed to continued increases in EV interest as summer turns the fall. Cox said carmakers sold an estimated 78,895 electric cars in August, which the group said was up 2.5% from July but, as expected, was down 46.9% from August 2025. By contrast, hybrid sales were forecasted to increase by approximately 9% in the first half of 2026.
“August brought further evidence of a steadily maturing electric vehicle (EV) market,” Stephanie Valdez Streaty, Cox Automotive’s director of Industry Insights, said.
“New and used EV sales increased from July, inventory levels moved closer to ICE+ vehicles and growing off-lease returns continued to expand used EV availability,” she continued. “At the same time, lower-priced models gained share in the new market, helping narrow the price gap between EVs and ICE+ vehicles.”
California started its “MyFirstEV” rebate program in August, and 13 major automakers confirmed plans to participate in California’s new $3,500 instant rebate program for new EV buyers in the state. California accounted for nearly 20% of all U.S. EV sales in the first half of 2026, according to the Alliance for Automotive Innovation, which lobbies in Washington for most major carmakers.
New polling from the Zero Emission Transportation Association, which lobbies for EV-friendly policies in Washington, shows willingness to consider EVs may be more closely tied to age than partisan affiliation, which was the assumption in the early days of the second Trump administration.
ZETA’s poll showed 75% of Americans under 35 say they are likely to purchase or lease an EV within five years, compared to just 23% of adults over 65 who said they would consider buying a plug-in model soon. By comparison, ZETA said 57% of Democrats and 45% of Republicans. The group said the 52% spread on the age comparison dwarfs the 12% spread on the partisanship question, showing age is a better predictor of openness to EV adoption now than politics.
“What this data shows us is that EVs are the cars of today and of the future,” Corey Cantor, research director at ZETA said in a statement. “Even if they don’t own one now, many people see themselves driving EVs within the next five years. Consumers want industry and policy choices that will make that ownership easier to attain, not harder.”

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Anthropic launches Claude Opus 5.5 with stricter safeguards for cybersecurity

Claude Opus 5.5 comes with improvements to certain behaviors, like attempting to escape testing environments.
Claude Opus 5.5 comes with improvements to certain behaviors, like attempting to escape testing environments.
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Live updates: Bitcoin trades near $86,000 as U.S. stocks post small gains

PayPal (PYPL) customers can now use Meta’s (META) AI consumer agent, Muse to check out after shopping, the company said a short while ago.
PYPL is higher by 1.2% on the news, but remains lower by 21% year-over-year.
Crypto and U.S. stock market prices are about flat in early afternoon trading, but former bitcoin miners who are now AI infrastructure providers are higher across the board.
Keel Infrastructure (KEEL) and Hut 8 (HUT) are leading with roughly 4% gains, while IREN (IREN), HIVE Digital (HIVE) and Cipher Mining (CIFR) are ahead closer to 2%.
Reiterating a social media post from last week, President Trump — addressing the United Nations — again said he’s approaching decision time on whether to completely annihilate Iran or make a deal to end the war he started.
The price of oil is rising as Trump speaks, with WTI crude now down just marginally for the day at $91.67 per barrel. Earlier, it had fallen as low as $89.18.
Bitcoin is slipping a hair, now trading at $85,700.
Kalshi Klear, the prediction market’s internal clearinghouse, has submitted a regulatory filing seeking permission to offer leverage on event contracts, a step aimed at drawing more institutional liquidity to the platform.
Leverage would let traders borrow funds to take larger positions than their cash deposits alone would allow, increasing their potential gains and losses.
The change could address a key hurdle for Wall Street firms considering prediction markets. Institutions eyeing the sector have widely viewed leverage as a critical feature needed for larger players to participate.
Kalshi would still need to clear the regulatory process before offering leveraged trading.
SoFi (SOFI) has started using its SoFiUSD stablecoin to settle transactions from its $25 billion debit and credit card program on Mastercard’s (MA) payments network.
The move puts blockchain-based settlement behind everyday card payments without requiring merchants to accept or hold stablecoins. SoFiUSD is issued by SoFi Bank, a nationally chartered U.S. bank, and is redeemable 1:1 for dollars.
SoFi said it is also in talks with large U.S. merchants and plans to explore cross-border payments and remittances with Mastercard.
The launch comes as SoFi shares are down 37% year to date despite growth in its business. Second-quarter adjusted net revenue rose 40% to $1.2 billion, while membership reached 15.8 million, but higher Treasury yields, valuation concerns and greater lending exposure have weighed on investor sentiment.
Things in markets are relatively quiet after Monday’s fireworks.
About 20 minutes into the U.S. trading day, the Nasdaq is higher by 0.4% and S&P 500 by 0.1%.
Crude oil remains under pressure as the UN General Assembly meeting gets going, with President Trump set to speak shortly.
Among tech names outperforming are SanDisk, up 6.7%, and Google, up 1.9%.
In the S&P, the financial sector continues to underperform as the new Fed rate hike cycle flattens the yield curve (and thus the profit margins of lenders). JPMorgan (JPM), Wells Fargo (WFC) and Citigroup (C) are all lower by about 1%.
Bitcoin (BTC) is trading right at $86,000, up more than 1% over the past 24 hours, but down about 1.5% from Monday evening’s highs above $87,000.
Iranian sources have denied reports from Kyodo and Reuters that the country is ready to reopen the Strait of Hormuz if the U.S. ends the blockade, LiveSquawk announced, quoting the Fars News Agency.
WTI futures prices have recovered to $90.20 from a low of $89.16 early today, according to data source TradingView.
Bitcoin is trading at just over $86,000, down 0.6% since midnight UTC.
Roughly $14 billion of bitcoin options expire on Deribit on Friday, the largest single expiration date this year. Mauricio Di Bartolomeo, co-founder of lender Ledn, which has originated more than $10 billion in bitcoin-backed loans since 2018, argues the consequential part has already happened.
“Quarterly expirations like September’s are a two-act event,” he said.
The first act came last week, when options tied to BlackRock’s IBIT fund expired in what he calls the largest such expiration on record for the ETF. The book leaned heavily toward calls, contracts that pay off when the price rises above a set level, with maximum pain, the point at which the most contracts expire worthless, near $40 a share. Bitcoin’s run through $80,000 carried a large block of those calls above their strike prices.
The dealers who sold them sit on the losing side as the price climbs, and they cover by buying the asset. For IBIT that means buying the fund’s shares, and issuing new shares of a spot bitcoin ETF requires buying bitcoin, so the hedging reaches the coin itself.
Friday’s Deribit book inherits that setup. Di Bartolomeo points to the heavy concentrations of calls at $85,000 and $100,000 as the levels where the mechanism repeats, and bitcoin is already trading above the first of them.
Iran could reopen the Strait of Hormuz within seven days if the U.S. eases military pressure and lifts its port blockade, according to multiple reports citing a senior Iranian official.
Oil prices subsequently fell with WTI crude more than 2.5% lower at $89 a barrel, roughly 15% below its September high. Brent crude dropped below $98 a barrel.
A sustained de-escalation in the Middle East could provide a tailwind for risk assets, with lower energy prices easing inflationary pressures and concerns over further interest rate hikes.
Bitcoin is consolidating around $86,000 following Monday’s sharp rally, which took it to an intraday high of $87,300. Gold is little changed over the past 24 hours at approximately $4,336 an ounce.

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Revealed: The Oracle cloud roles hit hard by layoffs

A leaked document has provided the clearest picture yet of how Oracle’s latest layoffs have reorganized its vitally important cloud business.
Oracle began a new round of layoffs last week as the tech giant continues to cut costs amid an expensive AI infrastructure push.
Business Insider obtained a previously unreported document showing the scale and scope of the cuts at Oracle’s cloud infrastructure division.
It shows the job titles and ages of 546 employees in Oracle’s America Cloud Infrastructure organization who were laid off, representing around 7.6% of the 7,185 employees listed. Of those, managers, engineers, software developers, and workers in the company’s data center maintenance and servicing division were most affected.
Oracle said in the document that the information was provided to comply with federal age discrimination laws.
It provides an insight into the type of roles the company is eliminating in its second major round of job cuts this year. Oracle has not said how many people it laid off in total last week.
The document states that it includes all employees in Oracle America’s Cloud Infrastructure organization eligible to receive severance benefits.
Business Insider could not determine if the document listed all the employees laid off from Oracle’s cloud infrastructure org. The company did not respond to a request for comment.
Oracle previously disclosed that its workforce declined by 21,000 employees, or 13%, in the 2026 fiscal year ended May 31, and the company said it had 141,000 employees before the most recent round of layoffs.
How Oracle’s cuts break down
Oracle’s cloud infrastructure organization is one of the most important parts of its business, with the company reporting in its most recent earnings that quarterly revenues from the division had soared 121% year over year.
Of the employees listed in the document, the cloud org roles hit hardest by the layoffs were software developer III, with 57 workers made redundant, followed by program manager IV and principal core infrastructure engineer.
Software developers were heavily affected, according to the doc, making up around 17% of the roles cut.
Developer roles have long been predicted to be especially vulnerable to AI, especially as AI tools have become increasingly proficient at coding, with some forecasting that Big Tech companies could eventually cut as many as 50% of their engineers.
So far, that scenario has not come to pass, despite a growing number of companies citing AI in their layoff announcements — and recent data from job site Indeed suggests there has been a modest increase in software engineering job postings.
Oracle’s layoffs also fell heavily on the company’s data center support services, which provide maintenance and tech support for the company’s data centers.
Forty-one employees from Oracle’s data center support services were selected for termination, around 7.5% of the total, including the vice president of the division and two senior directors.
The layoffs come as Oracle continues to double down on its investments in AI data centers.
The company has racked up tens of billions of dollars in debt and expects to spend $90-$95 billion this year on building new data centers as it bets demand for AI will continue to surge.
Managers hit hard
The recent layoffs also eliminated 128 roles containing the word “manager” across the cloud infrastructure division, according to Business Insider’s analysis of the document, around 23% of the total cuts.
Program manager was among the roles that saw the highest number of terminations, with 61 employees eliminated in total.
It comes as other Big Tech companies — including Meta, Snap, Coinbase, and Block — have increasingly cut management roles to pursue “flatter” organizations with fewer layers of bureaucracy.
Managers were by far the hardest-hit group when Meta cut 10% of its workforce earlier this year, although Business Insider recently reported that the company had begun asking some employees in its Applied AI division if they want to take on management roles again.
An analysis of the Oracle layoff document also showed how the company’s cuts in this group fell more heavily on older, experienced workers.
The majority of employees affected in Oracle’s cloud infrastructure division were over 40, Business Insider’s analysis found, and around 16% were 60 or over.

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