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The Shifting Tides of Trump's Iran Policy In a week that began with Donald Trump revealing he was just an hour away from 'making the decision' to resume attacks on Iran, the United States president has oscillated between expressing hope for a lasting ceasefire and threatening military escalation. Diplomacy and Threats Trump's mixed messaging has also coincided with a renewed flurry of diplomacy, with Iran as of Thursday saying it had received and was reviewing Washington's response to Tehran's latest ceasefire proposal. The Hawkish Advisers Trump, meanwhile, appeared to indicate an appetite for a third option: a prolonged, grinding conflict. On Thursday, he reposted a New York Post op-ed by Richard Goldberg, a senior adviser at the Foundation for Defense of Democracies, a pro-Israel think tank that has long supported military action against Tehran. Trump's Statements This Week The Trump administration has continually sent broad and at times contradictory messages on Iran, even preceding the war. On Sunday, Trump threatened that the 'clock is ticking' for Iran, the latest instance of the US signalling an end to the current halt to fighting, which has run parallel to an ongoing naval blockade of Iran's ports. The Strategic Dilemma While Trump's supporters have characterised his everything-on-the-table approach as part of a wider 'mad man' foreign policy approach, others have said it reflects the president's entrenched dilemma as he tries to claim a convincing victory in the conflict.

The Shock Exclusion: Maguire’s Instagram RevealHarry Maguire used his Instagram story on Thursday, 21 May 2026 to announce that he is not part of Thomas Tuchel’s England roster for the upcoming World Cup in the United States, Canada and Mexico. The 33‑year‑old centre‑back called the decision “shocked and gutted” and wished his teammates the best. Statistical Snapshot of Maguire’s International Career66 caps for England since his debut in 20177 international goalsParticipated in the 2018 World Cup (semi‑finals) and Euro 2020 (final)Last appearance: 1‑0 loss to Japan in March 2026Missed Euro 2024 due to injury Implications for England’s Defensive Options Ahead of the 2026 World CupThe omission opens a pathway for younger defenders such as Marc Guehi and Ezri Konsa, who have been edging Maguire out of the pecking order. Tuchel’s final squad, due on Friday, 22 May 2026, is expected to feature a blend of experience and emerging talent, potentially shifting England’s tactical setup from a traditional back‑four to a more versatile defensive line. What This Means for Maguire’s Club Future and England’s CampaignHaving helped revive Manchester United’s season after the departure of former coach Ruben Amorim, Maguire’s international snub could affect his confidence and market value. At United, he remains a key figure, but a prolonged absence from the national team may prompt discussions about his role under new management. For England, the decision signals a clear move away from the Southgate‑era core, emphasizing form and fitness over legacy.

OpenAI has reported a major advance in AI reasoning after its model successfully challenged an 80‑year‑old conjecture in discrete geometry, the planar unit distance problem first posed by Paul Erdős in 1946.OpenAI’s Model Cracks the 80‑Year‑Old Planar Unit Distance ConjectureThe conjecture suggested that the number of equal‑distance dot pairs on a plane grows only slightly faster than the number of dots.OpenAI's reasoning system generated a family of point arrangements that exceed Erdős’s proposed limit.The result was announced on X and confirmed in a companion paper co‑authored by mathematician Thomas Bloom.Quantifying the Breakthrough: No Monetary Figures, but Scientific SignificanceWhile the article provides no financial data, the achievement is described as a “milestone in AI mathematics” by Tim Gowers.The validation by experts underscores the credibility of AI‑generated proofs, contrasting with a prior, unverified claim from last year.Implications for AI‑Driven Mathematical ResearchThe model’s ability to explore unconventional solution paths highlights AI’s potential to augment human intuition.Researchers, including Andrew Rogoyski, note that AI is becoming a fundamental tool for future scientific inquiry.The breakthrough may accelerate AI involvement in other open problems across mathematics.What the Next Steps Could Mean for AI and MathematicsFurther collaboration between AI systems and mathematicians is expected to refine the new constructions and explore their consequences.OpenAI’s upcoming IPO could bring additional resources to expand its reasoning capabilities.The community anticipates more AI‑driven insights that could eventually resolve the broader Erdős problems.

The Early Days of Trump's Soccer Career Drive north from New York City and into the Hudson valley. Take Exit 17 and follow Route 7 as it heads south along the river, past the abandoned shipyard and the aptly named Cadet Motel. Hang a left after a few miles, wind up a long driveway and you’ll arrive at New York Military Academy. The Culture of Hazing and Discipline at NYMA The NYMA of the 1960s was entirely unlike the sleepy, near-abandoned campus that exists today, with a well-documented culture of hazing and abuse akin to Full Metal Jacket. Most instructors were hardened veterans, many of whom had served overseas during the second world war. Individual discipline aside, they also pitted students against one another, as Dobias did during twice-weekly “cage matches”, where one student would beat another into submission. Trump's Time on the Soccer Team Trump became part of the Dutchess County Scholastic League, a collection of small schools scattered throughout tiny hamlets in the Hudson Valley and just beyond. Trump joined NYMA’s soccer team after suffering an injury playing gridiron football. A photo of the New York Military Academy soccer team, featuring Donald Trump, has surfaced, providing a glimpse into his early days as a soccer player. The Truth About Trump's Playing Career Yearbooks exist, as do newspapers. Combing through them in search of clues about Trump’s playing career paints an interesting picture of Trump’s brief moment as a soccer player at NYMA, and helps add even more depth to arguably the most polarizing leader in US history. Some accounts describe Trump as an incredible athlete, while others are starkly different. Many describe him as a bully, a character trait that was only hardened amid NYMA’s culture of hazing and rigid discipline. The Legacy of Trump's Soccer Career It’s debatable whether Trump truly cares about the sport itself or simply likes the attention it brings him. But it’s a fact that in 2018, he welcomed international and domestic club teams to the White House and presented the Club World Cup trophy to Chelsea. Cristiano Ronaldo, Wayne Rooney and Lionel Messi have all visited with Trump; the latter was made into wallpaper while Trump went on a rant about the war in Iran. Fifa’s president Gianni Infantino at times seems glued to the US president.

The World Cup SnubHarry Maguire has announced he has been overlooked by Thomas Tuchel for the England World Cup squad. The Manchester United centre-half had hoped to be included in the 26-man party for the tournament this summer, which Tuchel will name at Wembley on Friday morning."I was confident I could have played a major part this summer for my country after the season I've had," Maguire posted on social media. "I've been left shocked and gutted by the decision. I've loved nothing more than putting that shirt on and representing my country over the years. I wish the players all the best this summer."Resurgence at Manchester UnitedMaguire has excelled for United since Michael Carrick took over as the head coach in mid-January and was called up by Tuchel for the March international programme. The 33-year-old started against Uruguay and came on as a late substitute against Japan, when he brought a threat on set pieces.His performances had raised hopes that he would feature in the World Cup squad, especially after struggling for form under previous manager Ole Gunnar Solskjaer.Defensive Priorities for EnglandDespite Maguire's improved club form, Tuchel has decided to prioritise other players in the position. The decision suggests that the England manager may be looking for different attributes in his center-back options for the tournament.Maguire's omission comes as a surprise given his recent performances and his experience at international level, having been a regular starter for England in previous tournaments.Implications for Maguire's International FutureThis decision raises questions about Maguire's future with the national team. At 33 years old, this could potentially be his last chance to feature in a World Cup, making the exclusion particularly disappointing.However, his continued good form at Manchester United could give him opportunities to force his way back into contention for future England squads, particularly if Tuchel's preferred options underperform at the World Cup.

The Diplomatic Implication President Donald Trump has twice suggested, since his summit with China’s President Xi Jinping in Beijing last week, that he may speak with Taiwan’s President William Lai Ching-te. That would mark the first direct contact between leaders of the governments since the US switched diplomatic recognition from Taipei to Beijing in 1979. It remains committed, however, under the 1979 Taiwan Relations Act to supporting the defence of the self-governing democracy. Taiwan's Response In a foreign affairs ministry statement on Wednesday, Taiwan’s President responded to Trump’s comments, saying he would be “happy” to talk to him. Taiwan was committed to maintaining a stable status quo in the Taiwan Strait, he added, but “China is the disruptor of peace and stability”. Beijing regards Taiwan as part of Chinese territory. The Data Analysis The statement comes as the White House considers a $14bn arms deal with Taiwan. China’s foreign ministry responded saying it “firmly opposes official exchanges” between the US and Taiwan, as well as US arms sales to the island. The Impact Analysis Trump’s comments suggest he may be willing to break with decades of diplomatic protocol, which will likely jar with Beijing, say analysts. Based on past events, Beijing will not be happy if Trump does meet with or talk to Taiwan’s president. When the former US House Speaker Nancy Pelosi visited Taiwan in 2022, her two-day visit sparked heightened tensions between the two countries. The Prediction Analysts say that included in its response is an awareness in Beijing that Trump is unreliable and unpredictable. If Trump calls Lai and announces that the US will “continue to support Taiwan and provide a large arms package; all hell will break loose”. However, he said, the very fact that Trump even entertained the idea of speaking with Xi about whether the United States would sell weapons to certain countries was a win for Beijing.

The LeadSpotify has introduced a new AI-powered audiobook creation tool in partnership with ElevenLabs, allowing authors to self-publish audiobooks without exclusivity. The platform is expanding to support 10 more languages and aims to generate $100 million in annualized recurring revenue from its Audiobook+ subscriptions.AI Audiobook Creation Platform LaunchAlongside tools for AI-generated podcasts, Spotify on Thursday introduced a new, ElevenLabs-powered AI tool for self-publishing audiobooks within the Spotify for Authors platform. The company said at its Investor Day event that the feature will launch in beta this June on an invite-only basis, initially with support for the English language only.The AI-powered audiobook generation won't bind authors to an exclusive contract, meaning they are free to publish their generated audiobooks anywhere. This approach contrasts with some other platforms that require exclusivity for audiobook distribution.The news builds on Spotify's previous partnership with ElevenLabs, which allowed writers to submit audiobooks created on the voice AI startup's platform to Spotify. The audio streaming platform also already had a partnership with Google Play Books to allow for digitally narrated content. However, it may have wanted authors to access newer voice models that sound more expressive and human-like, like those offered by ElevenLabs. Notably, ElevenLabs had released its own self-publishing platform for authors in 2025.Financial Performance and Growth MetricsSpotify has increased its focus on audiobooks heavily in the last few years and has managed to build its catalog to 700,000 titles. Through these initiatives, the company has managed to bump up listening hours by 60% year-on-year, the company claims. Spotify also said that more than half of its audiobook listeners started in the last year.To date, Spotify has clocked in over a million Audiobook+ subscriptions, and it is on track to generate $100 million in annualized recurring revenue for the platform. The company will expand its Audiobook+ plans this year to allow for higher listening limits and will add new options for students and families in the future.Industry Transformation and Market ExpansionSpotify is also expanding its "Spotify for Authors" platform to support 10 more languages, including French, Canadian French, German, Dutch, Latin American Spanish, Swedish, Finnish, Icelandic, Danish, and Norwegian. This expansion will significantly broaden the platform's reach and accessibility to authors and listeners worldwide.The company brought the program to international markets, made an investment in non-English titles, enabled in-app purchases, and released audiobook charts. This year, it also started a program for authors to sell physical books in the U.S. and the U.K., creating a comprehensive ecosystem for content creators.Future Outlook and User Experience EnhancementsAt the event, the company introduced a new way for users to ask questions using natural language for audiobook discovery. This summer, Spotify will also expand a feature that allows users to create prompt-based playlists for podcasts and music to include audiobooks, it said.These enhancements reflect Spotify's strategy to leverage AI not just for content creation but also for improving user discovery and engagement. The integration of natural language processing for audiobook discovery could potentially revolutionize how users find and consume audiobooks, making the platform more intuitive and user-friendly.

The Record-Breaking Quarter Nvidia has announced record quarterly profit and revenue amid explosive demand for its advanced AI chips. The US tech behemoth said on Wednesday that profit soared to $58.3bn for the February-April period, up 37 percent from the previous quarter and more than 200 percent year-on-year. Revenue jumped to $81.6bn, up 20 percent from the prior quarter and 85 percent compared with the same period in 2025. Nvidia forecast revenue for the current quarter to hit $91bn, more than most analysts' estimates. The AI Chip Surge Nvidia's data-centre business was the main driver of growth, with quarterly revenue surging 92 percent year-on-year to $75.2bn. The Santa Clara, California-based chip giant's hardware unit racked up revenue of $6.4bn, up 29 percent from the previous year. In a sweetener for shareholders, the world's most valuable company said it would buy back an additional $80bn in shares and raise its quarterly cash dividend from $0.01 a share to $0.25 per share. Nvidia CEO Jensen Huang hailed the "extraordinary" results as proof of the growing utility of AI. "Demand has gone parabolic," Huang said in a conference call with investors and analysts. "The reason is simple. Agentic AI has arrived," Huang said, referring to the advent of semi-autonomous AI models. "AI can now do productive and valuable work." Market Expectations vs Reality Despite once again blasting past analysts' expectations, Nvidia's latest results received a muted market response. Shares in Nvidia fell nearly 1.3 percent in after-hours trading, an indication of the sky-high expectations attached to a company whose blistering growth since 2022 has lifted its market capitalisation to more than $5 trillion. "Expectations are very high, and when a company like Nvidia has been doing as well as it has for so long, it takes a lot for people to get excited," Jay Goldberg, a senior analyst for semiconductors and electronics at Seaport Research, told Al Jazeera. "That's just kind of the nature of Wall Street." "All these stocks have run a lot this year, but a lot of it is driven by press releases," Goldberg said, adding that tech firms have yet to demonstrate a "broad-based consumer case" for AI. The AI Valuation Debate Nvidia's spectacular rise and the sky-high valuations of other tech giants, such as Microsoft and Amazon, have stirred discussion about whether AI is overhyped and creating a massive market bubble. William Rhind, the CEO and founder of New York-based investment firm GraniteShares, said the muted reaction showed that expectations had "caught up to fundamentals." "Nvidia is no longer beating a high bar – it is the bar," Rhind told Al Jazeera. Rhind said the bullish case for Nvidia nonetheless remains strong, pointing to the dividend hike and share buyback scheme as signs of a company with "more cash than it can possibly redeploy into the business". "When the marginal use of capital starts shifting toward buybacks and dividends, you're watching a hypergrowth story begin to mature in real time," he said. "That's not bearish – it's a different kind of bullish." Future Outlook John Belton, a portfolio manager at Gabelli Funds, said Nvidia's latest results should not "dramatically shift the story one way or another". "Overall, another solid earnings," Belton told Al Jazeera, saying the results mirrored the "strong numbers" of previous quarters "albeit without any new earth-shattering developments." As Nvidia continues to dominate the AI chip market, the company faces the challenge of maintaining its extraordinary growth trajectory while navigating increasing scrutiny about whether current valuations reflect sustainable business fundamentals or speculative enthusiasm.

The Comeback of Manuel Neuer Bayern Munich's Manuel Neuer has come out of international retirement to compete in next month's World Cup after being named as the starting goalkeeper in Germany coach Julian Nagelsmann's squad for the tournament. Nagelsmann's Decision Nagelsmann made the decision after having long labelled Hoffenheim's Oliver Baumann as his first-choice keeper. "Yes, I plan with that [with Neuer as number one]," Nagelsmann told a press conference. "The main task was to nominate the best three keepers. So we decided that these three are part of that." Neuer's Career Revival The 40-year-old Neuer, who last competed for Germany at Euro 2024 before his international retirement, is now set to play in his fifth successive World Cup, joining an elite group of football players with five or more tournaments. Neuer, a 2014 World Cup winner, enjoyed a solid season with champions Bayern, who could win the domestic double with victory over VfB Stuttgart in the German Cup final on Saturday. Germany's World Cup Squad There were few other major surprises in Nagelsmann's 26-man squad for the tournament starting next month. But the coach also called up Bayern's teenage player Lennart Karl, who enjoyed a meteoric rise this season, as well as Nadiem Amiri and Leroy Sane, who both had outside chances of earning a spot. Germany's World Cup Goals Germany, who face Curacao, Ecuador and Ivory Coast in Group E at the World Cup, have set their sights on a fifth title after shock first-round exits in the past two editions in 2018 and 2022. "The statement stands," Nagelsmann said. "We want to become world champions. Every player who is nominated needs to show it now every day." Full Germany Squad Goalkeepers: Manuel Neuer, Oliver Baumann, Alexander Nubel Defenders: Nico Schlotterbeck, David Raum, Nathaniel Brown, Jonathan Tah, Waldemar Anton, Pascal Gross, Joshua Kimmich, Felix Nmecha, Malick Thiaw, Aleksandar Pavlovic, Antonio Rudiger, Angelo Stiller Midfielders/Forwards: Leon Goretzka, Maximilian Beier, Jamal Musiala, Nadiem Amiri, Jamie Leweling, Kai Havertz, Lennart Karl, Florian Wirtz, Deniz Undav, Nick Woltemade, Leroy Sane