Mamata Banerjee, Suvendu Adhikari

Kolkata: Bengal’s decisive match is being played in Bhawanipur, South Kolkata, where the CM Mamata Banerjee He will have to take on Suvendu Adhikari, a one-time BJP ally, which is an election contest with much bigger consequences than losing to him by a narrow margin in Nandigram in 2021. For the Trinamool Congress, retaining Bhawanipur is not just about securing Mamata’s fort and preserving the aura of invincibility around it. In many ways, this constituency represents the party’s conflict with the BJP over larger issues of identity, ideology and governance. BJP breaching Mamata’s stronghold will deal a psychological blow to Trinamool, even if the saffron party fails to win Bengal. The social mix of the constituency makes it an unusually sensitive voting area. This includes the so-called Bengali Bhadralok families, Marwari and Gujarati business families, Sikh and Jain residents, immigrants from Bihar and Odisha and a large Muslim electorate. “This diversity has turned this seat into a laboratory of competitive political tactics,” said Trinamool Ward 70 councilor Ashim Bose, whose challenge is to turn last year’s Lok Sabha loss into Mamata’s gain in his ward. The numbers show why both sides are brimming with confidence in Bhawanipur. CM Mamata won the 2021 by-election there by a record margin of 59,000 votes. But in the 2024 Lok Sabha elections, Trinamool’s lead in the assembly constituency has dropped to a little over 8,000. The BJP led in five of the eight wards, showing that while the Trinamool retained emotional capital, the saffron party gained regional depth.

One seat, many challenges

Mamata aims to prevent Bhawanipur from turning into a fragmented social competition. His party’s strategy rests on familiarity and emotional ownership. Its “Ghorar Meye” (daughter of the house) pitch attempts to reduce the election from a verdict on governance to a display of neighborhood loyalty. “If there was any other candidate on the seat, it would have been extremely challenging for us,” said Trinamool worker Subhankar Roychowdhury. This approach is appropriate for a constituency where coexistence often matters as much as ideological mobilization. In mixed wards where Bengali Hindus, non-Bengali businessmen and Muslims live in close proximity, Trinamool’s emphasis on continuity and emotional connect is meant to reassure rather than provoke. Mamata’s appeal in such areas has long rested on welfare delivery, symbolic reach and the perception that she protects the pluralistic urban social order. BJP’s strategy is the opposite. Official election managers have tried to divide the constituency into its component communities and turn each into a manageable electoral block. During the campaign, this was noticeable in wards 63, 70, 71, 72 and 74, where the BJP’s recent gains indicate growing receptivity among non-Bengali businessmen and sections of the Hindu middle class. Muslim voters also remain at the center of arithmetic. They constitute a quarter of the electorate, and a united minority vote in a close urban seat could balance fragmentation among Hindu groups. That is why notice of deletion and investigation has been given in the case of voter list. BJP worker Jayant Ghosh said that Trinamool’s hold could be loosened due to the deletion of names of about 11,000 Muslim voters in Ward 77 during the SIR. Rajan Majumdar, an octogenarian supporter of the Left Front, said, “Bhabanipur adds the

Imagine trying to stack oranges as tightly as possible so that no space is wasted. Pretty simple at the grocery store. Now imagine doing this in a world of eight dimensions, a place that exists not in physical reality but in the abstract architecture of mathematics, and proving without a doubt that you have found the most perfect arrangement possible. For more than 400 years, the greatest mathematical minds on Earth couldn’t do it. In 2016, a quietly determined Ukrainian mathematician named Maryna Viazovska did just that. She was 31 years old and working alone in Berlin. What he created wasn’t just a solution, it was a masterpiece.

Marina solved a 400 year old problem! viazovska

The problem of packing spheres seems deceptively simple: What is the most efficient way to arrange identical spheres so that they fill space with as few wasted gaps as possible? In three dimensions, the answer is intuitive, a pyramid shape, the way fruit is stacked in a market. Johannes Kepler proposed this arrangement as optimal in 1611, but it took until 1998 for a formal mathematical proof to be completed, and even that proof required long, controversial computer calculations running hundreds of pages.However, move beyond three dimensions, and the problem becomes an entirely different animal. In dimensions four, five, six, seven, mathematicians had almost nothing. As MIT’s Henry Cohn described it after Viazowska’s success: “It is this catastrophic gap in our knowledge that is almost shameful to humanity.”Of all the higher dimensions, eight were special. Mathematicians long suspected that the answer lay in a structure called the E8 lattice, an arrangement of extraordinary symmetries that exists only in eight-dimensional space. More than a decade before Viazovska’s proof, Kohn and mathematician Noam Elkies had calculated that the E8 lattice was accurate to within one billionth of one percent of the theoretical optimum. They could almost touch the north. But they could not prove it. No one could do it.

Evidence that will shock the world in just 23 pages

Viazovska had been struggling with this problem for years. The key insight came from an unexpected direction: his doctoral work on modular forms, a type of highly symmetric mathematical function that normally resides in the world of number theory, which appears to be very far from geometry. He studied under the renowned mathematician Don Zagier at the Max Planck Institute for Mathematics in Bonn, where he completed his PhD in 2013.His success was in using the tools of Fourier analysis and modular forms to construct a special “magic function” that could serve as an exact upper bound, a mathematical ceiling for which dense regions could possibly be packed. When he compared that roof to the E8 mesh, they matched perfectly. This type of exact match is exceptionally rare. In mathematics, this is the equivalent of cutting a key in the dark and finding it to open a lock.

Visualization of the E8 lattice, a highly symmetric structure that solves spherical packing in eight dimensions.

The proof was uploaded to the academic preprint server in March 2016. It was 23 pages long. Earlier attempts at related problems spanned hundreds of pages. The mathematical community was stunned not only by the solution, but also by its beauty. Experts described it as “surprisingly simple” and praised its clarity and originality. Within a week of its publication, Viazowska had solved that version of the problem using a structure called a Leech lattice, joining with four colleagues to extend the same approach to 24-dimensional space. Two big problems, both solved within a few days.

Why are any of these matters beyond pure mathematics?

It would be easy to dismiss this as beautiful but impractical mathematics conducted in a rarefied universe that normal life never touches. That would be a mistake.Sphere packing in higher dimensions is deeply linked to error correction codes, the technique that allows information to be accurately transmitted across noisy channels. Every time you stream a video, make a phone call, or receive a file without any corruption, error correction codes are working quietly in the background. The mathematical structures that govern optimal field packing are the same structures that underlie how to efficiently encode and decode information. Viazowska’s work not only satisfied centuries of curiosity, but it expanded the theoretical foundations on which applied mathematicians and engineers work.Their results have also opened new doors in theoretical physics and cryptography, fields where the geometry of high-dimensional space has direct and practical consequences.

the woman behind the math

Viazovska was born in Kyiv in 1984, the eldest of three sisters, and showed an early passion for mathematics through school competitions and Olympiads. He received a bachelor’s degree from Taras Shevchenko National University of Kyiv, a master’s degree from the University of Kaiserslautern in Germany, and a doctorate from the University of Bonn. She is now full professor and chair of number theory at the École Polytechnique Fédérale de Lausanne in Switzerland.

Her teenage son Michael once recalled being the last child picked up from a Berlin kindergarten while his mother was busy working on an E8 proof. When he later learned of the Fields Medal, he reportedly said: “Now I understand why he worked so hard.”In July 2022, Viazovska was awarded the Fields Medal, widely considered the Nobel Prize of mathematics and restricted to mathematicians under the age of 40. She became only the second woman to receive it in the 86-year history of the prize, after Iranian mathematician Maryam Mirzakhani in 2014. The award was announced just weeks after Russia began its full-scale invasion of Ukraine. In interviews, Viazowska spoke quietly but strongly about her country: “Tyrants can’t stop us from doing mathematics. At least there’s something they can’t take away from us.”More than four centuries after Kepler first asked the question, the answer in eight dimensions came not through brute computational force, but through a woman’s creative intuition and a set of tools borrowed from an unrelated corner of mathematics. This is what makes Maryna Viazowska’s story so remarkable and worth remembering.

As Ishqbaaaz completes 10 years, Surabhi Chandna Opens up about the emotional milestone on the popular show that changed her life, and the love and memories that have yet to fade even after a decade of the iconic soap opera.Speaking about the same, Surbhi said, “Yesterday was a special day as Ishqbaaaz completed 10 magical years. I don’t even know how to express my feelings in words because it doesn’t feel like 10 years have passed since then. I am overwhelmed with emotions. For me, it was never just a show, it was a journey that changed my life. The love from the fans hasn’t stopped pouring in even today. It’s an overwhelming feeling and makes me happy. Is.“She adds, “It was a great experience and I met a lot of amazing people there. There are so many fun moments there that I will remember throughout my life. We used to have lunch together on the set. We used to eat rajma rice, bhindi and experimented a lot with Thai curry, and there were a lot of things we discussed. Nakuul Mehta, Nehalakshmi Iyer and the entire team. I was so lucky to share such beautiful times with my co-stars. I feel. Travel is still the best part of my life. My character is my family.”Reminiscing about the memories of shooting for ‘Ishqbaaaz’, she says, “When I look back at this journey, I feel very happy for my co-stars. We have great chemistry and we have become very close friends. They mean a lot to me. From funny banter to emotional scenes, I cherish all those moments – we have created a lot of beautiful memories together. More than that, I think That the love I got from the fans is still alive. They are still with me after 10 years, even as their posts and videos show how much they love flirting. I’m really grateful for that because their love is a major part of my life.”Emotionally she says, “It’s a moment of celebration, but also a little sad thinking about Grandma Navninder Bahl. She was such a sweet soul and I will never forget all the wonderful days we spent together.”Surbhi concluded, “I feel like I was living a dream. Ishqbaaaz will always be in my heart. Salute to the memories, the crazy moments we had together and salute to Ishqbaaaz that will always be timeless.”