Breaking AI & Tech News Analyzed

Tanya Khovanova has long been a leading voice in the world of recreational mathematics, authoring a popular blog and running the Number Gossip site where enthusiasts can inquire about any number.She now debuts her first book, Mathematical Puzzles and Curiosities, co‑written with fellow puzzle‑enthusiasts Ivo David and Yogev Shpilman. Published by World Scientific, the volume offers fresh challenges and inventive twists on classic problems.To give readers a taste, Khovanova selected three puzzles for the Guardian column:1. Battleships – As a naval admiral you must choose between sending a single vessel with a success probability of P % or two vessels each with a P/2 % chance, where the mission succeeds if at least one ship does. Which strategy maximises the odds?2. The Two Oracles – You face two respondents, Randie, who answers randomly, and Rando, who randomly decides to tell the truth or lie before each answer. Is there a method to distinguish them?3. Bad Maths – A student computes 5548 − 5489 as 59, claiming the “548” cancels out. He then experiments with a subtraction of the form XXYZ − XYZW (distinct digits) and observes the result is XW. How many digits in the new expression match those in the original calculation?Solutions to the trio were later posted online (update), but readers were urged to avoid spoilers until the scheduled reveal.Khovanova also reminds fans that she has been curating puzzles for the Guardian every other Monday since 2015 and welcomes new submissions via email.

The ongoing US-Israel war on Iran has taken a critical turn with Donald Trump's announcement that the US Navy would start blockading the Strait of Hormuz. This strategic waterway is crucial for global oil shipments, and any disruption could have significant economic impacts. In response, Iran's Revolutionary Guard warned that approaching military vessels to the strait would be considered a violation of the ceasefire. This development has led to a surge in oil prices, with US crude oil rising 8% to $104.24 a barrel and Brent crude oil increasing 7% to $102.29. The blockade, set to begin on Monday morning, will be implemented by US Central Command (Centcom) and will affect all maritime traffic entering and exiting Iranian ports. This move is part of a broader strategy that may include resuming limited military strikes in Iran, according to reports. The situation has drawn international attention, with Australian Prime Minister Anthony Albanese stating that his government has not been asked to participate in the blockade and is keen on continuing negotiations between the US and Iran. Meanwhile, Iranian parliamentary speaker Mohammad Bagher Ghalibaf dismissed Trump's threats, asserting that they would have no effect on the Iranian nation.

The US has announced plans to blockade the Strait of Hormuz, a vital waterway through which about 20% of global oil passes. This move comes after ceasefire talks with Iran ended without an agreement over the weekend. The blockade, threatened by President Donald Trump, aims to pressure Iran into reopening the strait, which has been effectively closed since February 28. Trump's announcement on social media stated that the US Navy will begin the process of blockading any and all ships trying to enter or leave the Strait of Hormuz. He accused Iran of 'WORLD EXTORTION' and threatened that any person who attacked US vessels would be 'BLOWN TO HELL!' However, the blockade's scope appears to have been scaled down, with US Central Command (Centcom) stating it would be confined to vessels transiting through Iranian ports, permitting passage of ships headed to ports belonging to America's Gulf allies. The blockade is set to come into effect at 10am ET (2pm GMT). The UK will not be involved in any blockade of the strait, and Australian Prime Minister Anthony Albanese has stated that his country was not asked to participate. Oil prices have surged following Trump's announcement, with US crude increasing 8% to $104.24 a barrel and Brent crude oil rising 7% to $102.29. Experts warn that the blockade could lead to higher oil prices, but much depends on its 'scope and implementation.' The managing director of research at ClearView Energy Partners, Kevin Book, noted that leaner volumes generally mean tighter markets and higher prices. Iranian and/or Houthi reprisals against Gulf producers' alternative routes could drive prices still higher. The blockade could cut off one of the Iranian regime's major sources of funding but might also have a short-term negative effect on global prices. About 100 tankers have transited the strait since the US and Israel started bombing Iran, most carrying Iranian oil products bound for China and India. Iran's Revolutionary Guards have stated that any warships approaching the strait to enforce a blockade would be considered in breach of the current ceasefire and would be dealt with strongly. Trump floated the possibility of a resumption of US strikes inside Iran, citing missile factories as one possible target.

President Donald Trump declared that the U.S. Navy will commence a blockade of the Strait of Hormuz immediately after peace talks between Washington and Tehran in Pakistan ended without an agreement. In a social‑media post, Trump labeled Iran’s actions as “extortion” and warned that American warships would hunt down and interdict any ship that has paid Iran a toll to traverse the waterway, while also beginning mine‑clearing operations. Iran’s Revolutionary Guard responded that civilian vessels may still cross the strait under “specific regulations,” but any military craft attempting entry would be deemed a breach of the cease‑fire and would be “dealt with severely.” Since the February 28 war launched by the United States and Israel, Iran has effectively taken control of the strategic chokepoint, a route that carries about 20% of the world’s oil and liquefied natural gas shipments. Traffic has now dwindled to a trickle, sending shockwaves through the global economy and raising alarm among Gulf Cooperation Council (GCC) states. Al Jazeera correspondents noted that the rhetoric from the White House has amplified “alarm bells” across the GCC, where leaders had hoped the two‑week ceasefire would evolve into a longer‑term peace framework. Oman’s foreign minister, Badr Albusaidi, urged on social media that the ceasefire be extended and that all parties make “painful concessions” to avoid a return to war. Trump’s statements also included a stark threat: any Iranian forces that fire on U.S. or “peaceful” vessels would be “blown to hell.” He claimed the blockade would involve “other countries” and that the United Kingdom, along with “a couple of other nations,” were dispatching minesweeper vessels to assist – a claim the British government has not confirmed. Domestic criticism emerged quickly. Democratic Senator Mark Warner told CNN he “doesn’t see how blockading the strait will compel Iran to open it,” questioning the strategic logic behind the move. Iran denied U.S. allegations that two of its warships had recently passed through the strait for mine‑clearing, warning that any military vessel attempting such a passage would meet a “strong response.” Tehran officials have floated the idea of instituting a post‑conflict toll system for vessels using the waterway, a prospect that could further entrench Iran’s leverage over global energy flows. Analysts warn that heightened tensions in the Hormuz corridor could push oil prices higher, amplifying inflationary pressures worldwide. As the situation unfolds, mediators continue to press both sides to resume diplomatic talks and avoid a broader escalation.

President Donald Trump declared that the United States will commence a naval blockade of the strategic Strait of Hormuz in response to the breakdown of peace talks between Washington and Tehran held in Islamabad.In addition to the blockade, Trump warned that American forces could target Iran’s water‑treatment plants, power stations and bridges unless Tehran abandons its pursuit of a nuclear weapons capability.The announcement came after a 21‑hour round of direct negotiations between the two sides collapsed on Sunday morning, ending a brief cease‑fire that had been brokered by the United States, Israel and Iran.U.S. Vice‑President JD Vance, who led the American delegation, said Iran refused to renounce the possibility of developing nuclear weapons, while Iranian officials accused Washington of failing to earn their trust.Trump instructed the U.S. Navy to begin “blockading any and all ships trying to enter or leave the Strait of Hormuz” starting Monday at 10 a.m. ET (14:00 GMT). He also accused Iran of “extortion” for charging tolls to tankers and announced a de‑mining operation in the waterway’s central sector, although the exact number of mines remains unclear.The Iranian Revolutionary Guard warned that any warships enforcing the blockade would be deemed a breach of the cease‑fire and would be met with a strong response, insisting the strait remains under Iranian control.Two U.S. destroyers transited the strait on Saturday without incident, a move the Pentagon described as the start of a mine‑clearance mission, even as Iranian media claimed the vessels were threatened as they departed.Financial markets reacted sharply: U.S. crude oil jumped 8% to $104.24 per barrel and Brent crude rose 7% to $102.29, reflecting concerns that the blockade could disrupt the flow of roughly 100 tankers that have been paying up to $2 million each for passage.Vance reiterated that the United States seeks a clear, affirmative commitment from Iran not to pursue a nuclear weapon, describing it as the “core goal of the president.”Iranian parliament speaker Mohammad Bagher Ghalibaf argued that Tehran offered “constructive initiatives,” but U.S. demands were “excessive” and hindered an agreement, according to the semi‑official Tasnim news agency.Pakistani mediators urged both parties to avoid renewed hostilities and pledged to arrange fresh talks, emphasizing the importance of upholding the existing cease‑fire.In a televised interview, Trump warned that if a deal cannot be reached, the United States may resume bombing Iran, specifically targeting its water‑supply infrastructure, desalination plants and power generation facilities.Regional fallout continued: at least 11 people were killed in southern Lebanon amid a series of Israeli strikes, while Pope Francis called for an immediate cease‑fire, expressing solidarity with the Lebanese people.The broader conflict, now six weeks old, has claimed more than 3,000 lives in Iran, over 2,000 in Lebanon, dozens in Israel and several Gulf states, and has inflicted extensive damage on critical infrastructure across the Middle East.

The U.S. Central Command (CENTCOM) reported that the destroyers USS Frank E. Peterson and USS Michael Murphy "transited the Strait of Hormuz and operated in the Arabian Gulf" as part of a mission to clear sea mines allegedly laid by Iran’s Islamic Revolutionary Guard Corps (IRGC).Admiral Brad Cooper hailed the operation as a turning point in the U.S.–Israeli campaign against Iran, saying the navy was establishing a "new passage" to restore safe commercial flow. Iran’s Khatam al‑Anbiya Central Headquarters immediately rejected the claim, stating that any vessel movement in the strait remains under the "Armed Forces of the Islamic Republic of Iran" and that the U.S. report is "strongly denied." The strait, a narrow chokepoint through which roughly 20% of the world’s oil and natural gas transits, has been a flashpoint since the February 28 U.S.–Israel attacks that prompted Iran to restrict passage to pre‑approved ships. The closure spiked global fuel prices and disrupted both commercial and military traffic. Analysts, such as Maria Sultan of the South Asian Strategic Stability Institute, argue that any U.S. navigation would require Tehran’s explicit permission, underscoring the strategic leverage Iran holds over the waterway. Simultaneously, senior delegations from the United States and Iran met in Islamabad for historic face‑to‑face talks—the highest‑level engagement since the 1979 Islamic Revolution. The negotiations, sparked by a preliminary ceasefire announced earlier in the week, focus on contentious issues including Iran’s nuclear program, frozen assets, and the future of Israeli operations in Lebanon. Both parties acknowledge that control of the Strait of Hormuz remains a major point of disagreement. Iran has signaled willingness to temporarily reopen the channel for commercial shipping but insists on maintaining leverage, proposing tolls to compensate for war damages. The United States, however, deems continued Iranian control a "non‑starter." U.S. President Donald Trump used his Truth Social platform to assert that Iran is "losing big" and to downplay the strait’s importance to the United States relative to its allies, claiming the mine‑clearing effort benefits nations such as China, Japan, South Korea, France, and Germany. Al Jazeera’s on‑the‑ground correspondents noted that despite a "deficit of trust," negotiators are working late into the night to bridge gaps, though fundamental disagreements over the strait’s governance persist.

A British warship together with a Royal Air Force P‑8 maritime patrol aircraft monitored three Russian submarines that were trying to survey key undersea infrastructure in the North Atlantic, the defence secretary John Healey said at a Downing Street briefing.Healey explained that the operation, which lasted **over a month**, took place not within UK territorial waters but in the country's exclusive economic zone – the area extending up to 200 nautical miles from the coastline and bordering neighbouring zones.The Russian vessels comprised an Akula‑class nuclear‑powered submarine and two deep‑sea research submarines from the GUGI directorate, a unit that normally conducts peacetime surveys of underwater infrastructure but possesses the capability to damage it in conflict.According to the minister, the British forces tracked and deterred any malign activity around the submarines 24/7, deploying regular sonar buoys to demonstrate continuous monitoring. The presence of the Royal Navy ship and the P‑8 aircraft, supported by NATO allies, left the Russian crews with “no doubt that they were being watched”.As a result, the Akula submarine “retreated home” and the two GUGI subs subsequently exited the UK’s maritime zone, heading northward. The operation involved **about 500 UK personnel**.Healey stressed that there was **no evidence of damage** to any pipelines or cables, but that UK forces and allies would verify the integrity of the infrastructure. He warned President Putin that any attempt to sabotage the network would “not be tolerated and will have serious consequences”.The defence secretary framed the incident as proof that Moscow is “the primary threat to the UK and to NATO”, underscoring the need for heightened vigilance over undersea assets amid the broader security fallout from the Ukraine war and recent tensions in the Middle East.He also linked the episode to broader defence policy, stating that the successful deterrence demonstrates the UK’s ability to detect, deter and, if necessary, respond to threats against its critical maritime infrastructure, while calling for continued investment in defence capabilities.

US Defense Secretary Pete Hegseth announced on Wednesday that the United States had achieved a "decisive" military victory over Iran, claiming the Iranian missile programme has been "functionally destroyed." Speaking alongside General Dan Caine, chairman of the Joint Chiefs of Staff, Hegseth described the operation—codenamed Operation Epic Fury—as a "historic and overwhelming" triumph that met every objective, including the dismantling of Iran’s navy, air‑defence systems and missile‑production capability. The declaration came a day after President Donald Trump stepped back from a threatened full‑scale assault on Iran, just two hours before a self‑imposed deadline for Tehran to reopen the blockaded Strait of Hormuz. The resulting cease‑fire agreement stipulates that Iran will not possess a nuclear weapon and that the United States will monitor the country’s enriched uranium stockpiles. While Hegseth emphasized that "they can still shoot here and there, but that would be very unwise," he also warned that US forces will remain in the region to ensure compliance with the two‑week cease‑fire and to oversee the safe transit of vessels through the strategic waterway. Iran’s response was equally emphatic. The Supreme National Security Council, cited by IRNA, congratulated the Iranian people on a "victory" and urged perseverance until the details of that victory are finalized. The council highlighted Iran’s alliances with the so‑called "axis of resistance" in Lebanon, Iraq, Yemen and occupied Palestine, claiming the coalition has delivered blows to the enemy over the past 40 days. At the same briefing, General Caine confirmed that US military objectives in Iran have been met, but framed the cease‑fire as a "pause" rather than a permanent end to hostilities, noting that forces remain ready to resume combat if necessary. In parallel diplomatic developments, a senior Iranian official told Reuters that Tehran could reopen the Strait of Hormuz on Thursday or Friday, contingent on a cease‑fire framework being reached ahead of a scheduled US‑Iran meeting in Pakistan. The closure of the strait has previously disrupted global oil and gas markets, making its reopening a critical economic signal. Trita Parsi, vice‑president of the Quincy Institute for Responsible Statecraft, told Al Jazeera that President Trump needed an exit from a war he described as "an absolute disaster" and that the next two weeks are "crucial" for any genuine diplomatic opening, though he cautioned that the situation is not yet resolved. Analysts note that the cease‑fire’s success will hinge on Iran’s willingness to allow unfettered navigation through the Strait of Hormuz and on US verification of Iran’s uranium holdings. The coming fortnight will test whether the declared victory translates into lasting stability in a volatile region.

Israel’s armed forces posted a stark warning on X, urging Iranians to refrain from using trains or approaching railway lines until 21:00 Iran time (17:30 GMT). The message, issued on the military’s Persian‑language account, framed the advisory as a safety measure, hinting at imminent strikes on civilian rail infrastructure before U.S. President Donald Trump’s deadline to reopen the Strait of Hormuz lapses. Trump has publicly threatened to bomb Iran’s bridges and power plants if the strategic waterway remains closed, setting a deadline of Tuesday 8 p.m. EST (01:00 GMT Wednesday). In response, Tehran has pledged “devastating” retaliation against any attacks on its civilian targets. Recent Israeli air operations have intensified. New strikes hit Tehran’s residential districts and a nearby synagogue, and a petrochemical facility on Iran’s side of the South Pars gasfield—shared with Qatar—was also targeted. According to Iran’s Ministry of Health, the conflict, which began on 28 February, has claimed at least 2,076 Iranian lives over more than five weeks. Amid the escalating rhetoric, the King Fahd Causeway linking Saudi Arabia and Bahrain was suspended as a precaution against potential Iranian attacks on Saudi Arabia’s Eastern Province. The 25 km (16 mi) bridge is the sole road link for Bahrain, which hosts the U.S. Navy’s 5th Fleet. Gulf states report heightened alert levels: alarms sounded in Bahrain and the UAE, and the Saudi Ministry of Defense said it intercepted seven ballistic missiles in its eastern sector. Al Jazeera’s correspondent noted that the Gulf region has borne the brunt of the conflict. On the diplomatic front, the UN Security Council is slated to vote on a watered‑down resolution aimed at unblocking the Strait of Hormuz. The draft, seen by AFP, omits any language authorising force, but Russia and China retain the power to veto. Iran’s blockade has already rattled global energy markets, driving oil and gas prices to record highs and forcing nations to adopt austerity measures. Analysts such as Trita Parsi, vice‑president of the Quincy Institute, argue that President Trump retains the flexibility to extend the deadline without losing credibility, given his historically limited diplomatic leverage. As the deadline looms, the convergence of military warnings, infrastructure closures, and diplomatic maneuvering highlights the fragile balance between coercive pressure and the risk of broader regional escalation.