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A team of researchers from Princeton and Oxford has uncovered a decades‑old handwritten note by Richard Feynman that formulates a mathematical solution to the classic “restaurant‑stopping” problem faced by travelers.Decoding Feynman's Hidden Stopping ProblemThe study, published in the Proceedings of the National Academy of Sciences, reconstructs Feynman's original equation, which advises diners to keep trying new venues until a quality threshold is met. That threshold is not static; it declines more rapidly as the remaining nights in a city decrease, reflecting the diminishing value of future visits to a discovered gem.Feynman's notes were handwritten in the 1970s after a lunch with friend Ralph Leighton.The model assumes a fixed range of restaurant quality and equal probability of encountering any quality level.When the distribution of restaurant quality is uneven, the optimal threshold shifts—higher when few gems exist, lower when most venues are above average.Experimental Findings from 2,520 ParticipantsTo test human behaviour, the authors recruited 2,520 volunteers for an online simulation where participants imagined staying in a city for varying lengths of time and chose restaurants from a grid.Participants’ thresholds fell linearly with the proportion of nights remaining, rather than the rapid decline predicted by Feynman's formula.Despite its simplicity, the linear rule performed comparably to the original solution in the simulated environment.Implications for Decision‑Making and Tourism BehaviourThe findings bridge theoretical optimal‑stopping theory with everyday intuition, suggesting that people naturally adopt a decreasing‑threshold strategy when faced with limited opportunities. This insight could inform:Tourism recommendation engines that adapt suggestions as a trip progresses.Behavioral economics models of consumer search in other domains (e.g., housing, job hunting).Design of AI assistants that balance exploration and exploitation in real‑time.Future Directions for Adaptive Choice ModelsThe authors propose extending the model to dynamic environments where restaurant quality distributions change over time, and to incorporate personal preference heterogeneity. Real‑world field trials in travel apps could validate whether a linear decreasing threshold improves user satisfaction and discovery rates.

The Energetic Cost of Pollen Collection Bees use as much energy collecting pollen through “floral buzzing” as they do taking off in flight, a study shows. Scientists have found the vibrations bumblebees use to shake pollen loose from flowers are among the most exhausting behaviours they perform, forcing bees to “carefully choose” which flowers are worth visiting. The Study's Findings The study, released by the Royal Society, is the first to directly measure the energy cost of floral sonication, or “buzz pollination” – where bees vibrate flowers to extract pollen. Natacha Rossi, a University of Sussex research fellow who led the study, said: “As nectar availability shifts due to climate change or habitat loss, the energetic demands of pollination could influence bee behaviour and, ultimately, where bees forage and which plants they pollinate. The Data Analysis Using lasers and respirometry equipment to monitor three colonies of buff-tailed bumblebees, researchers discovered that a single “buzzing event” required about the same amount of energy as a flight take-off. Because buzzing can last longer, the total drain on energy can be even greater. The metabolic rate of a floral buzzing bee is more than 30 times higher than its resting metabolism, according to the study, making the process among its most energetically demanding behaviours. The Impact Analysis The researchers warned that declining nectar supplies caused by climate crisis and habitat destruction could intensify the strain on pollinators. Prof Mario Vallejo-Marin, at Uppsala University, said: “We long suspected that buzz pollination was an energetically expensive affair. We can now put a number to it and begin making quantitative predictions of how it could affect the ecology and evolution of bees and buzzpollinated flowers.” The Prediction The study points out that the energetic drain on the bee does not stop when the pollination stops. According to the paper, after the bee vibrates the pollen loose, it must engage in a “grooming and pollen-packing phase”. This grooming takes even more energy. The bee then has to force a high-power take-off to carry its new, heavier load away, making the whole process a demanding two-phase sequence.

Breakthrough Cancer Drug Reveals Hidden TumorsA smart drug that stops cancer cells "hiding" from treatment can shrink tumours by at least 30% in six of the world's most common forms of the disease, according to early trial results. While immunotherapy treatments have improved survival rates for many patients, their effectiveness can stall or fail when tumour cells hide and then spread.How the Smart Drug WorksResearchers in Oxford have developed a drug designed to stop cancer cells concealing themselves from the immune system, allowing immunotherapy treatments to identify and destroy them. In a trial spanning the UK, France, Spain and Australia, 83 patients with cervical, bladder, liver, bowel, lung or head and neck cancers were given the experimental drug, GRWD5769, alongside the immunotherapy treatment cemiplimab.The smart drug was able to remove "invisibility cloaks" from tumour cells, exposing them to the parts of the immune system that attack infections and diseases. This allowed the cemiplimab immunotherapy to pinpoint and destroy the cancer.Trial Results Across Cancer TypesResearchers, led by the Christie NHS foundation trust in Manchester, England, found that tumours shrank in 26 patients. Of those, 15 experienced tumour reductions of at least 30%. All participants had previously failed to respond to treatment, and most had no options left when they joined the study.GRWD5769 was shown to shrink tumours in all six cancer types included in the trial. The drug halted progression of the disease for at least six months in 18% of cervical cancer patients, 32% of liver cancer patients, 36% of bladder cancer patients, 38% of those with neck and head cancer, and more than half of bowel (51%) and lung (55%) cancer patients.Significance for Cancer TreatmentImmunotherapy enlists T-cells – immune system cells that attack infections and diseases – to hunt and destroy cancer. Although it has revolutionised cancer care, it fails in about two-thirds of patients. This is because immunotherapy struggles when tumours hide from the immune system.Tumours can evade the immune system by manipulating an enzyme called ERAP1 (endoplasmic reticulum aminopeptidase 1). By altering this enzyme, cancer cells can hide from a patient's T-cells. GRWD5769 solves this problem by inhibiting ERAP1, which removes cancer's invisibility cloak and makes tumour cells visible to T-cells that could not previously find them.Future Outlook for Cancer TreatmentThe findings were presented at the American Society of Clinical Oncology's annual meeting in Chicago, the world's largest cancer conference. Prof Fiona Thistlethwaite, the principal investigator, noted: "For a drug that is given as a tablet, this is very impressive. It's early days, and we need further studies, but this is a new drug with a new mechanism that clearly helps immunotherapy perform more effectively."The tablets, which were developed by Oxford-based Greywolf Therapeutics and were tolerated well by patients. The trial remains ongoing, with a larger study planned. Cancer Research UK's research information lead, Dr Samuel Godfrey, noted: "Immunotherapy has transformed treatment for some cancers but it doesn't yet work for everyone. This trial seems to show how this new drug could make immunotherapy more effective, including in some cases where immunotherapy had previously failed."

The Guardian’s Curated Stream Picks for June 2026The Guardian’s weekly guide identifies the most compelling theatre productions you can stream this month, offering a mix of classic revivals, contemporary works, and rare ballet recordings. Each selection is paired with a platform and release date, making it easy for audiences to enjoy premium stage content from home.Why Fallen Angels Leads the Stream LineupThe 100th‑birthday revival of Noël Coward’s Fallen Angels tops the list. Starring Rose Byrne and Kelli O’Hara, the comedy blends sharp wit with a cocktail‑laden backstage intrigue. The production has earned five Tony nominations, signalling both critical acclaim and commercial buzz. It becomes available on BroadwayHD on 5 June 2026.Streaming Platforms and Access PointsBroadwayHD – Fallen Angels (available 5 June)BBC iPlayer – Romeo and Juliet featuring Rudolf Nureyev and Margot Fonteyn (classic 1965 ballet)Prime Video – Rent: Filmed Live on Broadway (2008 staging, superior to 2005 film)NT at Home – Oklahoma! (National Theatre’s 1998 production with Hugh Jackman)BBC Sounds – Flip! (radio adaptation of Racheal Ofori’s satirical play)BroadwayHD – Cyrano de Bergerac (RSC London run, featuring Kevin Kline)Arte.TV – François Chaignaud: Petites Joueuses (four‑hour performance filmed at the Louvre)Broadening Access to Live Theatre: Industry ImplicationsThese releases illustrate a shift toward high‑quality digital theatre archives. By partnering with established streaming services, theatres can reach global audiences, generate ancillary revenue, and preserve performances beyond their live runs. The inclusion of both classic ballet and contemporary drama signals that platforms are diversifying content to attract varied viewer demographics.What’s Next for Digital Theatre Distribution?Looking ahead, the trend suggests more theatres will negotiate exclusive streaming windows, potentially shortening the gap between live performance and online availability. As subscription fatigue grows, curated “best‑of” guides like this one will become essential tools for audiences navigating an expanding catalogue of digital stage offerings.

On Monday morning, a jury in Oakland, California, delivered a decisive victory to Sam Altman and OpenAI, dismissing Elon Musk's $150 billion lawsuit against the AI giant and its top executives. The Verdict in Oakland: A Procedural Victory for Altman The nine-member jury found that Musk had waited too long to bring his claims, ruling that the statute of limitations had expired before he filed the lawsuit in 2024. US District Judge Yvonne Gonzalez Rogers accepted the finding and dismissed the case, preventing the trial from addressing the core question of whether OpenAI betrayed its nonprofit mission. Verdict: Musk lost on procedural grounds (statute of limitations). Deliberation: Jury deliberated for less than two hours. Outcome: Case dismissed; no ruling on mission betrayal. The $150 Billion Dispute and OpenAI’s Valuation The trial centered on a financial and structural clash between two of Silicon Valley’s most powerful figures. While Musk sought to recover $150 billion, the case highlighted the immense scale of OpenAI's commercial success, which is reportedly valued at over $800 billion. Legal Claim: Musk sought $150 billion for alleged enrichment. Company Valuation: OpenAI valued at more than $800 billion. Timeline: Founding (2015) vs. Resignation (2018) vs. Lawsuit (2024). Why the Ruling Reshapes the AI Landscape This ruling removes a major legal threat for OpenAI at a pivotal moment. The company is deepening commercial partnerships and moving toward a potential public offering, a process that was previously clouded by Musk's legal challenges. However, the dismissal leaves the broader debate on AI governance unresolved. The trial never addressed critical issues such as transparency, data extraction, or how to govern superintelligent AI systems. The Road Ahead: Appeals and Unresolved Questions Musk has announced his intention to appeal, ensuring the feud will continue. The ruling clears the path for OpenAI's commercial expansion but does not settle the philosophical conflict over whether AI should prioritize profit or public benefit.

The Lead US Secretary of State Marco Rubio broke from standard diplomatic protocol during a congressional hearing by acknowledging that "most of the world assesses" Israel possesses nuclear weapons, though he stopped short of confirming the official US position on this sensitive issue. Breaking the Nuclear Taboo The exchange occurred when Democratic Congressman Joaquin Castro pressed Rubio for clarity on whether Israel has nuclear weapons. Rubio initially declined to share Washington's official position but acknowledged global assessments that Israel does possess such capabilities. "Most of the world assesses that they do," Rubio told Castro at the hearing on Wednesday, suggesting instead that the issue should be discussed in private settings. The dialogue underscored a decades-long taboo in US politics against publicly discussing Israel's nuclear program, which Rubio himself acknowledged is a "feature" of US foreign policy. Geopolitical Implications The questioning took on particular significance as the United States is currently engaged in a joint war with Israel against Iran. Castro emphasized that understanding Israel's nuclear capabilities is crucial for oversight bodies making decisions about the conflict. "If they, in fact, possess nuclear weapons — and you're right, in open-source reporting, that has come across — we don't know what their red lines are for using those nuclear weapons," Castro stated. "I'm shocked that our government wouldn't make an effort to know, to understand and then to give our oversight body the information that we need." Rubio conceded the question was "fair" and offered to provide a more complete answer in a classified format, noting the need for "delicate balancing acts between different equities." Israel's Nuclear Status Israel, whose Prime Minister Benjamin Netanyahu is wanted by the International Criminal Court for war crime charges in Gaza, is widely believed to possess a nuclear arsenal despite never officially confirming this. The country is not a signatory to the Treaty on the Non-Proliferation of Nuclear Weapons (NPT). In November 2023, Israel's Heritage Minister Amichai Eliyahu suggested that dropping a nuclear bomb on Gaza was "an option." Several pro-Israel politicians in the US, including Congressman Randy Fine, have also made similar statements. Key Developments February 28: US President Trump joined Israel in attacking Iran with the stated objective of preventing Iran from obtaining nuclear weapons May 2026: Congressman Castro and 30 other lawmakers sent a letter to the US Department of State seeking clarification on Israel's nuclear program November 2023: Israeli Heritage Minister Amichai Eliyahu suggested nuclear weapons could be used against Gaza Policy of Silence The US policy of not commenting publicly on Israel's nuclear capabilities has come under increasing scrutiny from lawmakers. Castro's letter to the State Department argued that this official hinders the development of coherent nonproliferation policy for the Middle East. "We cannot develop coherent nonproliferation policy for the Middle East, including with respect to Iran's civil nuclear program and Saudi Arabia's civil nuclear ambitions, while maintaining a policy of official silence about the nuclear weapons capabilities of one party central to the ongoing conflict," the lawmakers wrote. Future Outlook As tensions in the Middle East continue to escalate, the question of Israel's nuclear capabilities may face increased public scrutiny. The current US administration's close alignment with Israel, combined with the ongoing conflict with Iran, suggests this long-standing diplomatic taboo may face further challenges in the coming months. Lawmakers like Castro appear determined to push for greater transparency, potentially forcing a reevaluation of the decades-old policy of silence regarding Israel's nuclear program.

The Evolution of World Cup UpsetsThis year, the biggest ever World Cup will feature 48 teams, an increase from 32, opening up the tournament to even more upsets, shocks and surprises. The vagaries of the World Cup draw have given rise to classic underdog victories over the years, from an amateur USA team's shock defeat of the then-favourites England in 1950 onwards. But what does the data tell us about upsets in football's modern era?Starting from the launch of the Fifa men's world ranking system in 1993, we have analysed each World Cup match in which an underdog beat a higher-ranked team, along with the ranking disparity between the teams: the bigger the gap, the higher the "upset score", and the larger the circle in the graphics below. Upsets are marked in red, while matches decided on penalties are represented with a white border.USA 1994: Regional Rivalries and Bulgarian BrillianceThis World Cup was characterised by a consistent stream of upsets, particularly in the group stages, with a couple of surprise regional rivalries including Belgium (Fifa ranking 27) triumphing over the Netherlands (2) and Saudi Arabia (34), in their World Cup debut, seeing off Morocco (28).The first World Cup after the dissolution of the USSR featured the first appearance by a unified German team and arguably the tournament's most iconic underdog moment, when a header by Yordan Letchkov secured Bulgaria's (29) victory over top-ranked Germany (1) in the quarter-finals. Bulgaria enjoyed a strong competition overall, including beating Argentina (8) in the group stages and a surprise round of 16 win against Mexico (16) in a penalty shootout.France 1998: Upsets All the Way

The Historic Quarter-Final VictoryFlavio Cobolli made tennis history by becoming the first Italian to reach a grand slam semi-final in the men's singles, defeating fourth seed Félix Auger-Aliassime 4-6, 6-4, 6-4, 6-4 in the French Open quarter-finals. The Italian 10th seed pulled off a stellar recovery from a set and a break down to secure his place in the last four, setting up an unprecedented all-Italian semi-final in the tournament.The victory means there will be an all-Italian men's grand slam semi-final for the first time in history in the very half that the top-ranked Italian Jannik Sinner had been heavily favored to advance through en route to the title. The last semi-final spot will be determined in Wednesday's night session between the unseeded Italians Matteo Berrettini and Matteo Arnaldi.The Comeback PerformanceAuger-Aliassime started the match strongly, serving brilliantly and dominating the baseline with his forehand as he established a 6-4, 3-1 lead. The match began with an open roof in the same brutally windy conditions that had felled Aryna Sabalenka hours earlier, but after the first set the roof was closed. Conditions that should have favored the Canadian indoor specialist shifted dramatically when one loose service game at 3-1 was enough to shift momentum in Cobolli's favor.From that early deficit, Cobolli neutralized the Canadian's weapons, pinning him in his backhand corner, making plenty of returns and narrowing the court with his supreme defensive skills. The Italian's well-rounded game, featuring a destructive forehand and exceptional athleticism, proved too much for Auger-Aliassime as he secured three consecutive sets to complete the remarkable comeback.Ranking Implications and Career MilestoneThis victory marks several significant milestones for Cobolli. It was his first win against a top 10 opponent at a grand slam tournament, and will catapult him into the top 10 in the world rankings unless Jakub Mensik wins the title. The 24-year-old's rise represents the culmination of years of development, as he has long been considered one of the best athletes on tour with the talent to compete at the highest level.More importantly, this is an immense opportunity for Cobolli to compete for a major title. While players around him have been embroiled in bruising five-set tussles, pushing their bodies to the limit, Cobolli has been efficient, conceding just two sets in his five matches and playing authoritative tennis in the decisive moments.Historic Moment for Italian TennisCobolli's victory represents a significant shift in Italian tennis fortunes. The emergence of multiple Italian players capable of competing at the highest level signals a new era for the sport in Italy. With Jannik Sinner previously considered the primary Italian hope, the country now has a deep pool of talent capable of making deep runs at grand slam tournaments.For Auger-Aliassime, this defeat will go down as one of the most difficult of his career. Despite still being just 25, the Canadian has been around for a long time but is still trying to take the next step and compete for majors. This was a huge chance for him in the absence of any of the top players who have stopped him during his previous grand slam runs.The Path to the FinalStanding just one win away from a grand slam final, Cobolli faces a significant opportunity to cement his place among tennis elite. His efficient play throughout the tournament has conserved energy while still maintaining high-level performance, positioning him favorably for the semi-final and potentially the final.Regardless of the outcome against Berrettini or Arnaldi, Cobolli has already secured his place in tennis history as the first Italian to reach a grand slam semi-final in the men's singles. His performance at the French Open has announced his arrival as a serious contender for major titles and has set the stage for what could be a historic run for Italian tennis.

The EU's Technological Sovereignty Proposals The EU executive wants to ensure no foreign government or company has access to a “kill switch” to turn off or disrupt vital tech services across the continent, as part of an effort to cut dependencies on the US and China. Reducing Dependency on Foreign Suppliers Publishing “technological sovereignty” proposals that risk further tensions with Donald Trump, the European Commission said on Wednesday the bloc needed to reduce dependency on foreign suppliers in cloud computing, artificial intelligence and semiconductor production. The Data Analysis The EU’s vulnerabilities were exposed last year when China stopped semiconductor exports, almost bringing the European car industry to a halt. Meanwhile, there is concern that Trump or a future US president could use a “kill switch” to terminate US cloud computing services overnight, or require providers to hand over sensitive data. The Impact Analysis Henna Virkkunen, the European Commission vice-president for tech sovereignty, said the 2018 US Cloud Act – enabling federal authorities to access data stored by US providers in other countries for national security reasons – “was not in line with our rules here”. The Prediction The proposals, which have to be agreed by member states and the European parliament, could open a new front in ongoing tensions with the Trump administration, which has criticised EU digital regulation and routinely threatened allies with tariffs.