Inside Ukraine's Wild Drone Strike on Russia Ft. Sandeep Unnithan
In this episode of In Our Defence, veteran defence journalist Sandeep Unnithan joins host Dev Goswami to break down Ukraine's daring drone strike deep inside Russian territory — an operation that has stunned the world.
Using covertly disguised container trucks and remotely launched drones, Ukraine struck key Russian airbases housing Tu-95 bombers and A-50 AWACS, marking a significant escalation in the four-year-old war.
Produced by Prateek Lidhoo
Sound mix by Aman Pal
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The Hindu
an hour ago
- The Hindu
One of the oldest unsolved problems
A young traveller, an able administrator The son of a pastor, Christian Goldbach was born on March 18, 1690 in Konigsberg – the historic German and Prussian name of the city we now know as Kaliningrad, Russia. Growing up in that city and attending university there, Goldbach studied some mathematics (don't raise your eyebrows), but mainly took to law and medicine. When he was out of his teens, he set out travelling. His journey around much of Europe began in 1710 and his lengthy travels enabled him to meet many of the leading scientists of the day. We'll get to that in a bit. After spending nearly 15 years thus, travelling, Goldbach settled down, so as to say. He had become an established mathematician by this point. Despite initial rejections, Goldbach became a professor of mathematics and historian at the newly set up Saint Petersburg Academy of Sciences. In 1728, when Peter II became the tsar of Russia, Goldbach was named as the new tutor of the young emperor. When Peter II moved the court from St. Petersburg to Moscow, Goldbach moved with him. From this time onwards, Goldbach grew in stature as an administrator too. Even though there were plenty of changes in the political scene, Goldbach remained unaffected. While there was a purge of officials along with the various political moves that accompanied the replacement of one Russian ruler by another, Goldbach was never one of them. He continued to rise in status, drew bigger salaries, and also received lands. He laid down the guidelines for the education of royal children, guidelines that remained in practice for nearly 100 years. By 1740, the administrative work occupied so much of his time that Goldbach asked his duties at the Academy to be reduced. When he further rose to a senior position in the Ministry of Foreign Affairs, he stopped working for the Academy. Goldbach died in Moscow on November 20, 1764, aged 74. Keeping in touch Travelling a continent and meeting prominent scientists was one thing. But keeping in touch with them years later was quite another. Goldbach was a letter writer par excellence and he was at it for nearly his whole lifetime. Having set off in 1710, Goldbach encountered German polymath Gottfried Leibniz in Leipzig in 1711. Goldbach moved on from Leipzig but the two continued to be in touch. Their correspondence between 1711-13 included 11 letters, with Leibniz writing five and Goldbach writing six, all in Latin. In 1712, Goldbach met French mathematician Abraham de Moivre and Swiss mathematician Nicolaus I Bernoulli, who himself was also on European travels, in London, England. Goldbach bumped into Bernoulli again in Oxford and the latter started discussing infinite series with Goldbach. It is worth mentioning that while Goldbach was fascinated by the mathematics that he was being exposed to this way, he had little in the form of formal knowledge in the subject. In fact, during the conversation about infinite series, Goldbach confessed his ignorance, prompting Bernoulli to loan him a book on the topic by his uncle Jacob Bernoulli. Goldbach, however, was intimidated by infinite series at that time, and gave up his attempts to understand the text after finding it too difficult. Things, however, changed in the years that followed. After reading an article about computing the area of a circle by Leibniz in 1717, Goldbach was drawn again to the theory of infinite series. He published a number of papers on mathematics in 1720 and 1724 and became a mathematician of repute by the time he decided to settle down following his travels. In 1721, Goldbach met Swiss mathematician Nicolaus II Bernoulli in Venice, Italy, while he was also on a tour of European countries. He suggested to Goldbach that he start a correspondence with his younger brother Daniel Bernoulli, a mathematician and physicist. Goldbach began his correspondence with Daniel in 1723 and it continued for seven years. Most famous correspondence For someone who made letter writing a part of himself, it is fitting that he is now best remembered for what he set out on one such letter. Swiss polymath Leonhard Euler met Goldbach in St. Petersburg in 1727 and even though Goldbach moved to Moscow the following year, they had a long lasting relationship. The correspondence between the two spanned 35 years and the nearly 200 letters between the two were written in a number of languages – Latin, German, and French – and covered a whole gamut of topics, including, of course, mathematical subjects. In fact, Euler's interest in number theory was kindled by Goldbach. Their intimacy also meant that Goldbach was the godfather of one of Euler's children. Most of Goldbach's important work in number theory was contained in his correspondence with Euler. While Goldbach's conjecture is the most famous remnant of their correspondence now, they also discussed Fermat numbers, Mersenne numbers, perfect numbers, the representation of natural numbers as a sum of four squares, Waring's problem, and Fermat's Last Theorem, among others. Goldbach's conjecture In a letter to Euler dated June 7, 1742, Goldbach expressed what we now know as Goldbach's conjecture. In his own words, he asserted that 'at least it seems that every number that is greater than 2 is the sum of three primes.' Bear in mind that in Goldbach's time, the number 1 was considered prime, a convention that is no longer followed. An equivalent form of this conjecture stated in modern terms therefore asserts that all positive even integers >=4 can be expressed as the sum of two primes. It's been over 275 years since Goldbach stated his conjecture, but it hasn't been proven yet. Computers have shown that it holds true for trillions of numbers, but that's not quite enough. It is one thing to show through brute force that it is valid up to a certain number, quite another to prove it for all numbers. The hunt, naturally, has been on to find a solution and Goldbach's conjecture now holds place of prominence as one of mathematics' – number theory in particular – oldest unsolved problems. There have been numerous attempts to crack that armour, but it hasn't been achieved just yet. There have been breakthroughs, of course. Soviet mathematician Ivan Vinogradov in 1937 proved that every sufficiently large odd number is the sum of three primes. Chinese mathematician Chen Jingrun, meanwhile, showed that all sufficiently large even numbers are the sum of a prime and the product of at most two primes in 1973. There have also been competitions and awards encouraging and challenging mathematicians to solve the problem. The British and American publishers of Apostolos Doxiadis' novel, Uncle Petros and Goldbach's Conjecture, for instance, offered a $1 million bounty to anyone who could prove Goldbach's conjecture within two years in March 2000. The prize, naturally, went unclaimed. The conjecture, however, continues to remain open – alluringly simple and tantalising in its wording, but beyond the best mathematical brains for centuries.
Time of India
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- Time of India
‘Badman' Gulshan Grover Reveals His YouTube Dream, And It's Wickedly On-Brand
'Russian In Our Language, Do Whatever You Want': NATO Nation Leader's Bold Step Irks Kyiv Backers A Latvian lawmaker, Aleksey Roslikov, was expelled from parliament after a bold pro-Russia statement. The incident occurred during a session focused on combating Russification in Latvia. Roslikov spoke mostly in Latvian but ended his speech with a phrase in Russian, declaring, 'There are more of us and Russian is our language.' His remarks sparked outrage among lawmakers. The Saeima swiftly voted to expel him from the session. Moscow praised Roslikov for defending the Russian language, sharing the video and condemning Latvia's alleged Russophobic policies. 2.6K views | 7 hours ago
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Business Standard
2 hours ago
- Business Standard
Russian strikes on Kharkiv kills four, injure dozens in latest escalation
Russian attacks targetting the eastern Ukrainian city of Kharkiv killed at least four people and wounded more than two dozen others on Saturday, officials said, as hopes for peace dimmed further. The first wave on Ukraine's second-largest city was a large Russian drone-and-missile attack in the early hours. It killed at least three people and wounded 21 others, according to local officials. In the afternoon, Russia dropped aerial bombs on the city centre, killing at least one person and wounding five more, Kharkiv's mayor said. The warring sides also accused each other of trying to sabotage a planned prisoner exchange, nearly a week after Kyiv embarrassed the Kremlin with a surprising drone attack on military airfields deep inside Russia. Saturday's barrage the latest in near daily widescale attacks on Ukraine included aerial glide bombs that have become part of a fierce Russian onslaught in the all-out war, which began on February 24, 2022. Kharkiv residents describe fiery trap As firefighters and emergency workers bustled around attack sites in Kharkiv, residents described the strikes that damaged their homes and nearly took their lives on Saturday morning. Alina Belous said that she had tried to extinguish flames with buckets of water to rescue a young girl -- trapped inside a burning building -- who had called out for help. We were trying to put it out ourselves with our buckets, together with our neighbours. Then the rescuers arrived and started helping us put out the fire, but there was smoke and they worried that we couldn't stay there. When the ceiling started falling off, they took us out, she said. Local resident Vadym Ihnachenko said that he thought at first that it was a neighbouring building going up in flames. But when we saw sparks coming from the top, we realised it was our building, he said. 'More pressure on Moscow is required' Ukraine's air force said that Russia struck with 215 missiles and drones overnight, and Ukrainian air defences shot down 87 drones and seven missiles. Several other areas in Ukraine were also hit, including the regions of Donetsk, Dnipropetrovsk, Odesa, and the city of Ternopil, Ukrainian Foreign Minister Andrii Sybiha said in an X post. To put an end to Russia's killing and destruction, more pressure on Moscow is required, as are more steps to strengthen Ukraine, he said. The Russian Defence Ministry on Saturday said that its forces carried out a night time strike on Ukrainian military targets, including ammunition depots, drone assembly workshops, and weaponry repair stations. There was no comment from Moscow on the reports of casualties in Kharkiv. Kharkiv's mayor, Ihor Terekhov, said that the strikes also damaged 18 apartment buildings and 13 private homes. Terekhov said that it was the most powerful attack on the city since the start of Russia's full-scale invasion. Children among the wounded Kharkiv's regional governor, Oleh Syniehubov, said the morning's attacks saw two districts in the city struck with three missiles, five aerial glide bombs and 48 drones. Among the wounded were two children, a baby boy and a 14-year-old girl, he added. Six people are believed to be trapped under the rubble of an industrial facility in Kharkiv's Kyiv district, the Kharkiv prosecutor's office said in a statement on Telegram. Contact with those trapped was lost and rescue attempts have been ongoing since early afternoon, it said, without naming the facility. On Saturday afternoon, Russian aerial bombs struck Kharkiv again, killing at least one person and wounding five others, the mayor said. The morning strikes also wounded two people in the Dnipropetrovsk province further south, according to local Gov Serhii Lysak. Meanwhile, Russia's defence ministry said that its forces shot down 36 Ukrainian drones overnight, over the country's south and west, including near the capital. Drone debris wounded two civilians in the suburbs of Moscow, local Gov Andrei Vorobyov reported. No breakthrough on a peace deal On Friday, Russia struck six Ukrainian territories, killing at least six people and wounding about 80. Among the dead were three emergency responders in Kyiv, one person in Lutsk and two people in Chernihiv. A US-led diplomatic push for a settlement has brought two rounds of direct peace talks between delegations from Russia and Ukraine, though the negotiations delivered no significant breakthroughs. But both sides remain far apart on their terms for an end to the fighting. Prisoner swap called into question Later on Saturday, Russia and Ukraine each accused the other of endangering plans to swap 6,000 bodies of soldiers killed in action, agreed upon during direct talks in Istanbul on Monday that otherwise made no progress towards ending the war. Vladimir Medinsky, a Putin aide who led the Russian delegation, said that Kyiv called a last-minute halt to an imminent swap. In a Telegram post, Medinsky said that refrigerated trucks carrying more than 1,200 bodies of Ukrainian troops from Russia had already reached the agreed exchange site at the border when the news came. In response, Ukraine said Russia was playing dirty games and manipulating facts. According to the main Ukrainian authority dealing with such swaps, no date had been set for repatriating the bodies. In a statement Saturday, the agency also accused Russia of submitting lists of prisoners of war for repatriation that didn't correspond to agreements reached on Monday. It wasn't immediately possible to reconcile the conflicting claims. New video of airfield drone attack Ukraine's Security Service on Saturday released a video said to show its audacious attack on Russian air fields Sunday in which Kyiv said that 41 Russian military aircraft was destroyed. The video shows the flight path of one explosive-laden first person view, or FPV, drone from takeoff from the roof of a modular building to the Belaya air field where it appears to strike a Russian strategic bomber. Other aircraft are seen engulfed in flames, apparently from previous hits in Ukraine's Operation Spiderweb. A previous round of negotiations in Istanbul, the first time Russian and Ukrainian negotiators sat at the same table since the early weeks of the full-scale invasion, led to 1,000 prisoners on both sides being exchanged.
