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The LeadOpenAI says its new general‑purpose reasoning model has produced an original proof that disproves the famous geometry conjecture posed by Paul Erdős in 1946, ending an 80‑year open problem.OpenAI Announces Disproof of Erdős’s 1946 Geometry ConjectureThe company released a pre‑print and companion remarks signed by mathematicians Noga Alon, Melanie Wood and Thomas Bloom. The proof introduces a completely new family of constructions that outperform the long‑standing “square‑grid” belief.Timeline of Claims and CorrectionsJuly 2025: Former VP Kevil Weil tweeted that “GPT‑5 found solutions to 10 unsolved Erdős problems”.Later 2025: Critics including Yann LeCun and Demis Hassabis called the claim a misrepresentation; Weil removed the post.May 20, 2026: OpenAI publishes the new disproof, backed by external experts.Why This Disproof Could Redefine AI‑Driven ResearchThe breakthrough demonstrates that an AI system can autonomously manage long, intricate chains of reasoning and synthesize ideas across mathematical sub‑fields, a capability that researchers argue could translate to breakthroughs in biology, physics, engineering and medicine.What Comes Next for AI in Fundamental ScienceExperts anticipate a surge in AI‑assisted exploration of other long‑standing conjectures. If the model’s reasoning can be generalized, we may see a new era where AI acts as a co‑discoverer rather than a tool.

Keir Starmer announced a £3.7bn trade agreement with the six Gulf Cooperation Council (GCC) states, calling it a “huge win” for British business after four years of negotiations spanning four prime ministers.Starmer Secures £3.7bn GCC Trade Deal After Four Years of NegotiationsThe agreement, signed on 20 May 2026, removes tariffs on 93% of British goods sold to Saudi Arabia, Kuwait, Oman, Qatar, the United Arab Emirates and Bahrain. It follows earlier pacts with India and South Korea and is presented as the most significant agricultural deal since Brexit.Financial Upside: £3.7bn in Export Opportunities and Tariff EliminationsThe government estimates the deal will generate £3.7bn of export opportunities – double the original forecast – across food, luxury cars, defence, aerospace, hospitality and other services.Zero tariffs on: food, medical equipment, defence, aerospace, advanced manufacturing.Current tariffs removed: 5% blanket duty on most GCC imports; specific rates previously applied to cheddar cheese (6%), chocolate (15%), biscuits (10%) and cars (5%).Data‑storage: GCC states will allow UK firms to store data outside the region for the first time.Political and Human‑Rights Controversies Surrounding the DealCritics, including the Trade Justice Movement’s Tom Wills, argue the omission of a human‑rights chapter is “especially alarming” given documented abuses in the Gulf. Paul Nowak of the Trade Unions Congress called the agreement “disappointing” in light of the region’s record on workers’ rights. The government says political channels, not trade texts, are the preferred venue for addressing such concerns.Implications for UK Industries and Future Trade StrategyThe National Farmers Union hails the deal as the best agricultural arrangement since the EU exit, while the British Chambers of Commerce expects new business for firms in financial services, energy, construction, professional services, education, hospitality and technology. William Bain, head of trade policy at the BCC, stresses the pact’s potential to benefit “tens of thousands of UK firms.” Investor‑protection clauses have raised worries about future litigation over policy shifts, such as Heathrow expansion.Outlook: How the GCC Pact May Shape Britain’s Trade LandscapeBeyond immediate revenue, the agreement signals the UK’s intent to be the first G7 nation with a “modern and ambitious” GCC deal, potentially encouraging further Gulf investment in UK assets like Heathrow and Newcastle Football Club. The political window created for Starmer may influence upcoming domestic debates, while the lack of human‑rights provisions could shape future negotiations with other non‑EU partners.

During the Russia‑China summit on 20 May 2026, Presidents Vladimir Putin and Xi Jinping announced a shared understanding on the main parameters of the Power of Siberia 2 (POS‑2) pipeline – its route through western Siberia, Mongolia and into China, and the construction approach. Detailed commercial terms remain unresolved.Summit Consensus on Route and Construction of POS‑2The leaders confirmed agreement on the pipeline’s alignment and the technical framework, but emphasized that pricing, financing and a detailed timetable still need to be finalised.Pipeline Capacity and Economic Scale Compared to Global BenchmarksThe proposed line will span roughly 2,600 km (1,616 mi) and transport up to 50 billion cubic metres (1.77 trillion cubic feet) of natural gas per year, equivalent to about 525 TWh – almost twice the United Kingdom’s annual electricity consumption. For perspective:Nord Stream 1 capacity: 55 bcm/yrPOS‑1 reached full capacity in 2024 after construction began in 2014Estimated project horizon: up to 10 years from construction start to full outputGeopolitical and Market Ramifications for Russia and ChinaFor Russia, POS‑2 offers a new outlet for gas previously destined for Europe, helping Gazprom recoup revenue lost after the 2022 sanctions. The pipeline also promises multiplier effects for Russian steel and construction firms.For China, the line reduces dependence on seaborne LNG that must navigate chokepoints such as the Strait of Hormuz and the Strait of Malacca, providing a more secure, lower‑cost supply and shielding the market from geopolitical volatility.Outlook: Timeline, Pricing Negotiations and Energy Market ShiftsNegotiations are stalled primarily over price – China seeks rates linked to its heavily subsidised domestic gas, while Russia aims for terms closer to those of POS‑1. No definitive timetable has been set. Analysts project that, if an agreement is reached, the pipeline could begin deliveries in the early 2030s, reshaping global gas flows by:Cutting China’s future LNG import demandSoftening Atlantic‑based LNG price pressuresAccelerating a regionalised gas market centred on long‑term bilateral contractsNevertheless, both sides face risks: Russia may become a price‑taker to a single customer, and China could over‑concentrate supply from a politically volatile partner.

The Funding Crisis The Board of Peace, which was founded by United States President Donald Trump in January to oversee the administration and reconstruction of the Gaza Strip, is facing a crippling cash crunch that threatens to derail its ambitious $70bn reconstruction plan for the devastated enclave. The US-led board recently reported a critical gap between its financial commitments and actual disbursements, warning of an urgent liquidity crisis, according to the Reuters news agency. The Structure of the Board However, experts tracking international aid to Palestinians said the funding shortfall is neither surprising nor purely administrative. Instead, they argued that the reluctance of Arab and European donors stems from the board’s controversial structure, a lack of a viable political horizon for a Palestinian state and Israel’s ongoing military expansion across the besieged enclave. Moath al-Amoudi, an expert in international aid to Palestinians, told Al Jazeera that the heavily publicised pledges are closer to a “talk show” than a genuine humanitarian effort. A History of Empty Promises “Out of the $17bn pledged, the actual liquidity that has reached the ground is zero,” al-Amoudi said. “Donors are terrified of engaging with a board that carries no political vision and treats Gaza merely as an American security protectorate.” The gap between pledges and actual disbursements is a historical constant in the Palestinian context, but the US has a particularly poor track record, al-Amoudi noted. Commercial Guardianship and the $1bn Seats Much of the international hesitation is rooted in the architecture of the Board of Peace itself. Previous Al Jazeera reporting revealed that the board operates as a complex three-tiered governing structure heavily stacked with American billionaires and pro-Israel figures, such as billionaire Marc Rowan, US envoy Steve Witkoff, Secretary of State Marco Rubio and Trump son-in-law Jared Kushner. Humanitarian Aid as Political Blackmail The board’s funding crisis is deeply intertwined with its strict political and security conditions. The three-phased US plan for Gaza explicitly demands the full disarmament of Hamas and all allied Palestinian factions as a prerequisite for reconstruction funds and the opening of border crossings while Israel has continued to violate the terms of an October “ceasefire”. The Yellow Line and Modern Ghettos Beyond the political and structural flaws of the board, the volatile reality on the ground makes meaningful reconstruction nearly impossible. Despite a nominal “ceasefire”, Israeli forces have continued their near-daily violations. According to local medical sources, 828 Palestinians have been killed since the “truce” went into effect.

The Lead: A New Global OrderRussian President Vladimir Putin and his Chinese counterpart, Xi Jinping, have signed a joint declaration following their meeting in Beijing, focusing on building a "multipolar world and a new type of international relations". The two countries also announced that they had signed a large package of deals solidifying bilateral cooperation in the future.The meeting came just days after United States President Donald Trump completed his own visit to China for a two-day summit with Xi.Establishing a Multipolar World OrderOn Wednesday, the Chinese Foreign Ministry said: "The two countries will also issue a joint statement on advocating for a multipolar world and a new type of international relations." Russian presidential aide Yuri Ushakov described this declaration as a 47-page policy document.A "multipolar world" is understood as one in which economic, military and diplomatic power and influence are placed in the hands of three or more countries, rather than just one or two."Xi is calling for a more multipolar world, where the US has less power and influence," Al Jazeera's Katrina Yu reported from Beijing as the meeting was under way.Both Putin and Xi have spoken out against the "unipolar" hegemony that they say the US has over the world.In 2022, shortly after the beginning of Russia's war with Ukraine, Putin accused the US of stoking hostilities in Ukraine to maintain its global influence."They need conflicts to retain their hegemony," Putin said during a speech. "The era of the unipolar world order is nearing its end."Chinese state media reported that during the latest meeting, Xi said to Putin: "The tide of unilateral hegemony is running rampant."Russia-China Relations Reach Unprecedented LevelA press statement posted on the Kremlin website said relations between Russia and China had reached "a truly unprecedented level and continue to develop".The Chinese Foreign Ministry statement said: "Both sides should follow the trend of peace, development, cooperation, and win-win results to promote higher-quality development of China-Russia relations."The statements added that bilateral cooperation extends to the worlds of economics, sport, education and the media.The Kremlin statement adds that this year marks the 70th anniversary of partnership between the Russian TASS news agency and the Chinese Xinhua news agency.Deepening Economic Cooperation and Moving Away from the US DollarThe Kremlin statement said Beijing and Moscow had signed around 40 intergovernmental, interagency and corporate documents. "Many of these focus on the further deepening of our economic cooperation," it noted.The statement added that, last year, trade between the two countries reached almost $240bn, while the Chinese statement said bilateral trade grew by 20 percent in the first four months of this year.Since the war in Ukraine broke out in February 2022, Russia has become increasingly reliant on Chinese technology and manufacturing. Last month, Bloomberg reported that Russia now imports more than 90 percent of the technology targeted by US and European Union sanctions via China, using Chinese suppliers and intermediaries to obtain components with military and dual‑use applications vital to drone production and other defence industries."Both sides should build on this momentum, deepen the alignment of China's 15th Five-Year Plan with Russia's development strategy until 2030, promote the upgrading of mutually beneficial cooperation in various fields, and serve the development and revitalization of both countries," the Chinese ministry statement said.The Kremlin statement said that nearly all import and export transactions between Russia and China are in roubles and yuan. "In other words, we have actually created a stable system of mutual trade that is protected from external influence and negative trends in the global markets," it said.Securing Energy Supplies Through Siberia 2 PipelineThe Kremlin said on Wednesday that an understanding had been reached for the route and construction of the long-delayed joint Siberia 2 pipeline, but details are still being negotiated. Once completed, the pipeline will transport 50 billion cubic metres of Russian gas annually to China via Mongolia, significantly expanding energy flows between the two countries.The Kremlin's statement said that Russia and China are actively cooperating in the sphere of energy."Our country is one of the largest exporters of oil, natural gas (including LNG) and coal to China. We are definitely ready to continue to ensure reliable and uninterrupted supplies of these types of fuel to the rapidly growing Chinese market," the statement said.As European markets have largely closed to Russia as a result of the war in Ukraine, China has emerged as a crucial buyer of Russian oil and other energy products, benefitting from steep discounts on Russian products.In December 2022, the Group of Seven (G7), the EU and Australia placed a cap on the price of Russian oil at $60 per barrel, ostensibly to reduce Russia's ability to fund its war in Ukraine. The cap was later reduced to around $48 by the EU and the United Kingdom.Expanding Educational and Scientific TiesBoth statements said Xi and Putin had agreed to expand student exchange programmes and cooperation between universities and research platforms to boost joint scientific research.

The LeadRachel Reeves is preparing to announce a planning shake-up that would fast-track clean energy and infrastructure projects by curbing judicial reviews, the Treasury said.The Planning Reform DetailsThe chancellor will propose that parliament should be able to designate and approve the most important clean energy projects as of "critical national importance", as part of a wider package seeking to blunt the impact of the Iran crisis."That would reduce the exposure from judicial review on all but human rights grounds," the Treasury said.It comes as pressure grows on the government to accelerate its energy infrastructure development to meet its goal to build a virtually zero-carbon power system by 2030.The Renewable Energy LandscapeRenewable energy developers have long bemoaned the difficulty in gaining planning permission for projects, from offshore windfarms to onshore solar and battery storage developments, and waiting times to connect to Great Britain's electricity grid.A spokesperson for the Treasury said that vital infrastructure delivery had been "delayed by judicial reviews of projects the country needs."They added: "The chancellor won't stand for it any longer and is bringing forward bold changes to support delivery. She is clear that parliament must take back control – to get Britain building the power plants, windfarms and grid connections that will bring bills down, strengthen our energy security, and deliver growth in every part of our country."The Current State of Renewable Energy ApprovalsLast year a record number of renewable energy projects were given the go-ahead in Great Britain, according to analysis by the consultancy Cornwall Insight. It found that the energy capacity of new battery, wind, and solar projects that received approval climbed to 45GW, 96% higher than in 2024.However, it also found the pace of projects starting up lagged behind, largely as a result of long construction timelines and grid connection delays.The Broader Infrastructure ApproachFor other infrastructure, such as transport and water projects, the government will introduce a fixed legal challenge window. When this ends, planning consent could be updated to address "any legitimate issues", the Treasury said.The Political ContextThe proposal comes amid a series of policy moves by Reeves despite uncertainty around the future of Keir Starmer as prime minister.On Tuesday it emerged that the government asked UK supermarkets to consider freezing the prices of some essential foodstuffs to protect the public from inflation fuelled by the Middle East conflict.Reeves is expected to announce measures to help households with the cost of living on Thursday, on which she is also planning to cancel a planned rise in fuel duty.

Gaza's Reconstruction Stalled Despite PromisesGaza remains in a grim limbo more than seven months after Donald Trump brokered a ceasefire deal, with no reconstruction underway, the Board of Peace struggling with funding, and Palestinian technocrats chosen to run the strip sidelined in Egypt. The ambitious vision for Gaza's future has been hampered by political obstacles and financial shortfalls, leaving millions of Palestinians in dire conditions.The Board of Peace Faces Implementation ChallengesThe Board of Peace, established to oversee Gaza's reconstruction, has identified Hamas's refusal to hand over weapons and cede control of the strip as the "principal obstacle" to Trump's plan. However, several people familiar with the body indicate that funding shortfalls could jeopardize the entire effort. Palestinian technocrats selected to administer Gaza have been effectively sidelined, with decisions being made in Egypt rather than locally.Severe Funding Shortfalls Undermine Reconstruction EffortsNine countries pledged $7 billion (£5 billion) to a "Gaza relief" package at the inaugural meeting of the Board of Peace, chaired by Trump. However, only the United Arab Emirates and Morocco have sent funds, with the group receiving just $23 million to fund its operations, plus an additional $100 million for a future Palestinian police force. This amounts to only $1.75 for every $100 pledged. The UN has estimated the total cost of rebuilding Gaza to be upward of $70 billion over decades, highlighting the massive gap between promises and reality.International Reluctance and Geopolitical ComplicationsSeveral countries that initially committed to funding the Board of Peace are now reluctant to fulfill their pledges after months of stalled diplomacy and no visible progress on the ground. The Iran conflict has provided convenient cover for payment delays, according to sources familiar with the organization. "Countries are hesitant to pay their portions," stated one diplomat involved in international Gaza negotiations. The geopolitical complexities have created a situation where "nobody with money and resources wants to work with the Board of Peace," as one anonymous source put it.Humanitarian Crisis Deepens as Promises Remain UnfulfilledThe stalled reconstruction efforts have exacerbated the humanitarian crisis in Gaza, with displaced Palestinians living in makeshift tents after their homes were destroyed in Israeli attacks. Images of destruction and temporary shelters underscore the urgent need for reconstruction that has not materialized. Nickolay Mladenov, the Bulgarian diplomat serving as "high representative" for Gaza, acknowledged last week that Palestinians in Gaza had been let down by the international community. "The door to the future of Gaza is still closed. It is not what the Palestinians were promised, and it is not what they deserve," Mladenov stated, adding that the impasse also jeopardizes Israel's long-term security.Uncertain Path Forward for Gaza's ReconstructionWith funding shortfalls, political obstacles, and competing international priorities, the path forward for Gaza's reconstruction remains uncertain. The Board of Peace continues to exist on paper but lacks the resources and political will to implement its ambitious plans. Unless significant changes occur in the international commitment to Gaza's reconstruction, the territory faces a prolonged period of instability and suffering, with millions of Palestinians continuing to live in conditions far below what was promised under the original ceasefire agreement.

The Radical Tax Overhaul to Solve London's Housing Crisis The Centre for London has proposed a radical overhaul of London's property taxation, suggesting the scrapping of Stamp Duty and Council Tax in favor of a Proportional Property Tax (PPT). This proposal aims to address widening inequality, release housing stock, and fund the construction of 106,000 new social homes over the next decade. A Radical Shift in London's Taxation Model The core of the proposal involves replacing the current Stamp Duty Land Tax (SDLT) and the outdated Council Tax system with a new annual property wealth tax. The new Proportional Property Tax (PPT) would be calculated as a percentage of a home's value, with rates increasing for higher-value properties. Base Rate: 0.39% on properties up to £800,000. Incremental Charges: Additional 0.01% for homes up to £999,999, and 0.02% for every £200,000 over £1m (capped at 0.82% for properties worth £5m). Under this model, a £500,000 home in Greenwich would pay £1,950 annually, saving the owner over £15,000 in the first 10 years compared to current taxes. Conversely, a £5m home in Westminster would pay £41,000 annually, saving £86,792 over a decade. Quantifying the Housing Inequality Gap The report highlights a stark disparity in space utilization and affordability. Despite London having more housing per person than 20 years ago, inequality has widened significantly. Floor Space Growth: Average floor space rose by 30% between 2004 and 2023. Income Disparity: Top 20% of homeowners saw a 27% rise in space, while the bottom 40% saw only a 6% rise. Price-to-Earnings: House prices are now 12 times earnings, up from 7 times in the early 2000s. The crisis is further evidenced by the fact that homelessness costs £5.5m daily and a third of children live in poverty after housing costs. Economic Implications for Renters and First-Time Buyers The proposed tax shift aims to alleviate the crushing financial burden on younger generations and renters. By removing Stamp Duty on primary residences, the thinktank estimates an extra 79,000 homes could be released annually as owners move. Renter Savings: Private renters would no longer pay Council Tax, saving more than £1,890 per year. First-Time Buyer Savings: Buyers would save £8,593 across five years of ownership. Deposit Support: The policy aims to help renters save for a deposit, which currently averages £150,000 without family assistance. The Future of London's Housing Market Rob Anderson, the director of research at the Centre for London, argues that the crisis cannot be solved by simply "building more homes." He emphasizes that the current system incentivizes holding onto property rather than downsizing or releasing stock. The proposal suggests that by removing the disincentives of Stamp Duty and Council Tax, the city can unlock existing housing stock and generate the necessary revenue to build 106,000 social and affordable homes, fundamentally altering the trajectory of London's housing affordability.

The Lead The National Audit Office (NAO) has issued a stark warning about the UK's £38 billion Sizewell C nuclear plant, highlighting that the costs may outweigh benefits for households until at least 2064. The spending watchdog describes the project's financial outlook as subject to 'significant uncertainty' with risks that are 'immediate, substantial and borne by the public.' Financial Uncertainty of the Nuclear Project The government claims the Sizewell C nuclear reactor, expected to generate enough low-carbon electricity to power 6 million homes when operations begin in the late 2030s, could save £2 billion annually from the electricity system compared with other low-carbon technologies. However, the NAO warns that for households, these savings could be outstripped by the cost of supporting construction until nearly halfway through the plant's 60-year operational life. The project could take even longer to 'break even' if there are cost overruns or delays, according to the spending watchdog. Sir Geoffrey Clifton-Brown, chair of the public accounts committee overseeing the NAO, emphasized that 'Sizewell C is a project of exceptional scale, complexity and significance for taxpayers,' noting that comparable nuclear projects in the UK and overseas have shown vulnerability to delays and cost overruns. Economic Impact and Investment Structure Sizewell C is being developed by French state nuclear company EDF as a successor to the Hinkley Point C reactor in Somerset. EDF has invested £1.1 billion to take a 12.5% stake in the project, while the UK government has invested £14.2 billion as the majority stakeholder. Other investors include British Gas's parent company Centrica (15%), the Canadian pension fund La Caisse (20%), and the investment fund Amber Infrastructure (7.6%). Nigel Cann, chief executive of Sizewell C, defended the project as an 'investment in lower long-term electricity costs' that will 'deliver value to consumers and to the country for the rest of this century.' He highlighted that the project has already created thousands of jobs and boosted businesses across the country, with 70% of its construction value sourced from UK suppliers and nearly £5 billion spent to date. Household Costs and Financial Framework Households began paying for the Sizewell C project via home energy bills at the start of 2026 to help fund construction. This financial framework, known as a regulated asset base model, represents a departure from the Hinkley Point deal, which will begin earning guaranteed revenues from energy bills only once generation commences in the early 2030s. Critics of the regulated asset base model, including the campaign group Stop Sizewell C, have warned that construction delays could mean bill payers support the project without receiving power for longer than expected. The group contends that the risks surrounding Sizewell C 'could easily turn into a financial disaster' while the funding model ensures its investors 'are the only ones who can't lose.' Government Response and Future Outlook A government spokesperson defended the investment, stating that large-scale nuclear power is 'the only way to get our country off the rollercoaster of volatile global gas markets.' The NAO has urged the government to mitigate risks through 'close monitoring, greater transparency to parliament, and by securing value for money from the significant public and private investment.' Despite the concerns, Sizewell C's leadership maintains that all major infrastructure projects involve uncertainty and that the report highlights steps being taken to reduce risk and control costs. The project's future will likely depend on how effectively these risks are managed and whether the long-term benefits can materialize as promised.