In 1657, French mathematician Pierre de Fermat issued a mathematical challenge via letters to English mathematicians like Kenelm Digby & other finest minds of Europe. He dared them to find the smallest positive, non-trivial whole-number solutions for a deceptively simple-looking quadratic equation (known today as Pell's Equation): x^2 - dy^2 = 1, for non-square (d), specifically highlighting hard cases like d = 61 & d = 109.
It looks almost trivial, like a middle school algebra problem. But it is a trap.
Because the relationship b/w x & y scales exponentially, finding a solution by naive trial & error/standard brute force search grids is computationally impossible by hand. The numbers are so massive that European mathematicians like Bernard Frénicle de Bessy struggled for months (for d = 61).
It was not rigorously solved in Europe until Lord Brouncker used continued fractions & Lagrange gave a general proof in 1766. Fermat thought he had found the ultimate limits of numerical complexity. He had no idea that a 12th-century Indian mathematician in Karnataka had already crushed the exact same eqn using a flawless, purely integer-based recursive loop.
500 yrs before Fermat’s challenge, Bhaskara II tackles this exact problem in his treatise Bijaganita. He realized that instead of guessing wildly for a perfect solution, you should start with a near-miss/an easy guess that has a small mathematical error & then systematically annihilate the error through a feedback loop.
He called it the Chakravala Method (Chakra meaning wheel/cycle). The algo works like this (for d = 61):
Start with a guess:
For, x^2 - 61y^2 = 1, choose an easy near-miss.
Since 8^2=64 (which is close to 61), let y = 1 & x = 8.
Calculate the error ((k)): Plug them in: 8^2 − 61(1)^2 = 3. Our error is +3
Bhaskara used a mathematical composition rule inherited from Brahmagupta (called Bhāvanā) to inject a new multiplier (m). The algo strictly optimizes m at each step to minimize the absolute size of the next error, ensuring the numbers stay as small & computationally efficient as possible.
The output of the 1st loop becomes the input for the next. The equation literally "cycles" like a wheel, squeezing the error down until (k) lands exactly on (1).
While European mathematicians were blindly guessing/dealing with messy, infinite fractional expansions, Bhaskara's recursive wheel landed precisely on the target after a few lines of clean arithmetic.
The smallest integer solution to Fermat's "impossible" challenge, computed by Bhaskara II in 1150 CE, is:
x = 1766319049, y = 226153980
Try plugging that into x^2 - 61y^2 = 1 by trial & error w/o a supercomputer. You have zero chance of stumbling onto it.
Who is next after the Ramanujan?
In the mid-20th century, Western academic cartels claimed that advanced mathematics was a European construct, brought to a colonized India via British education. Tekkath Amayankottukurussi Kalathil Sarasvati Amma responded by spending decades deep in the forgotten archives of Kerala, translating archaic Sanskrit palm-leaf manuscripts with razor-sharp mathematical precision.
She proved that centuries before Sir Isaac Newton/Gottfried Leibniz were even born, unheralded Indian astronomers had already built the foundations of calculus & high-level geometry. This is the story of how an Unsung Scholar reclaimed the Intellectual Sovereignty of a Nation.
For generations under colonial rule, a deeply damaging psychological narrative was hammered into the Indian psyche: Your ancestors were mystics & poets, but they lacked the rigorous, logical discipline for advanced science & mathematics. The global academic consensus was that high-level geometry, infinite series, & calculus were the exclusive property of Europe.
India was viewed as a nation that needed to be civilized with Western numbers, completely oblivious to the fact that it had once been the mathematical capital of the world.
T.A. Sarasvati Amma was born in Kerala, a land with a deeply hidden, rich intellectual undercurrent. She was not an "uneducated" woman in the literal sense, she was a brilliant scholar of Sanskrit & Mathematics, but to the global elite who only validated degrees from Oxford/Cambridge/Harvard, she was an outsider working in the shadows.
In the 1950s & 60s, while working under the guidance of legendary scholars like Dr. V. Raghavan at the University of Madras, she realized that the history being taught in schools was a lie. She did not seek validation from Western journals. She went straight to the dirt, the dust & the decaying private libraries of old Kerala families.
She began unearthing 100s of brittle, centuries-old palm-leaf manuscripts written in a highly technical, coded astronomical Sanskrit.
Sarasvati Amma undertook a brutal, lonely intellectual pilgrimage. For yrs, w/o the aid of computers/digital databases/massive research grants, she painstakingly translated & mathematically mapped out texts like the Yuktibhasa, the Karanapaddhati & the Tantrasangraha.
Her pitch to the skeptical academic community was uncompromising: "I will not give you theories. I will give you the exact geometric proofs, calculated centuries before your European heroes walked the earth."
She discovered that in the 14th century, a mathematician named Madhava of Sangamagrama & his disciples in the Kerala School of Mathematics had already solved problems that Europe would not touch until the late 17th century.
Against all odds, in 1979, Sarasvati Amma published her magnum opus: "Geometry in Ancient and Medieval India." It was a masterclass in mathematical archaeology that fundamentally shook the foundations of global history.
She systematically proved that:
The Madhava-Gregory Series: The infinite series for pi*(4 X (1 - 1/3 + 1/5 - 1/7.......), attributed to the Scottish mathematician James Gregory in 1671, was recorded in India 300 yrs earlier.
For the 1st time in modern history, the West could not look down its nose. The proofs were right there, written on palm leaves, preserved by a quiet woman who refused to let her nation’s history be erased.
Sarasvati Amma’s work didn't build corporate empires/software companies, but it did something far more powerful: it restored the intellectual self-respect of an entire civilization. Her book became the absolute gold standard reference for the history of mathematics worldwide, forcing global historians to slowly & reluctantly rewrite their textbooks.
She lived a fiercely quiet, simple life, retiring as a prof & spending her final yrs in her hometown in Kerala, completely disconnected from the blinding lights of fame. She passed away in 2000, largely unknown to the millions of Indian students who daily study the very calculus her work reclaimed.
T.A. Sarasvati Amma proved that the ultimate form of patriotism is the preservation of truth. She showed that a nation’s backbone is nott just built by industrial concrete/military might, but by its memory.
T.A. Sarasvati Amma proved that a lone Indian woman, armed with nothing but dusty palm leaves & an iron will, could rewrite the mathematical history of the world.
This is 1 of the best 100% fictional & full of comedy piece, I have read in recent times. De casually throws in the phrase "Underage Siya at 20," which is factually, legally & logically absurd in India, where the legal age of majority & criminal liability is 18.
In Nyaya Sutras, Akshapada Gautama lists several types of logical fallacies used by sophisticated sophists to win debates using deception. 2 of them apply perfectly to Shobhaa De here:
A. Chhala (Quibbling/Trivialization) - De spends multiple paragraphs hyper-focusing on the victim's hair patch, calling it the "main motive" & writing flippant remarks like, "Come on, Siya… look at Anupam Kher!" De is trivializing a brutal crime into a shallow page-3 gossip column, trying to lower the moral weight of the act to match the superficiality of her narrative.
B. Viruddha/Savyabhicara Hetvabhasa (Contradictory/Irregular Reason) - De attributes the murder to deeper “fascinating subtexts” of class, coercion, privilege versus attraction, agency & “denied choice,” nodding to Gen Z sympathy for Siya as a trapped young woman. This reasoning is contradictory (viruddha)/erratic (savyabhicara): it directly undermines itself because a 20 yr old adult who can orchestrate multiple premeditated murder plots, divert ₹1 crore & bypass every legal/non-violent option demonstrates full criminal agency & convenience, not helplessness.
Shobhaa De’s column is a classic piece of Sophistry using flowery language, political deflections (bringing up the Ram Mandir & Modi out of nowhere) & superficial gossip to mask a terrifying moral reality.
When people try to find a "faultline" in the system to justify a 20 yr old adult's choices, they are engaging in moral cowardice. You do not look at a pilot who intentionally crashes a plane into a mountain 4x & write a column complaining about the airline's catering service. The pilot was an adult who owned the controls.
It seems this "2nd Chetan" woke up & decided that the best way to stay relevant was to write a controversial, contrarian take on this subjudiced matter.
Bhagat’s article operates on a flawed assumption of Linear Determinism, the idea that if we apply a massive external force (parental pressure), it directly & predictably dictates the resulting kinetic action (Pushing some1 off the cliff int his case).
Millions of young adults in India experience the exact same vector of external force. Personally, when I was growing up, I was a little better at Maths (used to solve problems mentally). So, after my matric exams, I went to my father & said, "Pappa Ji, I want to take Commerce because I feel I am good with calculations."
My father, w/o even looking at me, said, "Chappal dekhe ho... Engineering krna hai, woh bhi IIT jaana hai."
I completely absorbed it (elastic deformation) & wisely decided not to push some1 into the nearby Ganga river in my village.
For the system to collapse into a vector of cold-blooded decisions, F (internal) must be completely devoid of resistive moral mass. Bhagat is blaming the acceleration entirely on the push, ignoring the fact that the object’s own internal mechanics chose the direction of the cliff. In pure physics, we cannot blame the gravity of the slope for a car that was intentionally steered off the edge.
According to ancient Indian jurisprudence (Dharma Shastra), environment can never be used as an excuse for a Tamasik collapse. A person with a functional moral core (Sattva)/even a basic survival drive (Rajas) will exhaust every logical & kinetic option: crying/fighting/running away/public exposure before they ever cross the threshold into pure malice.
No journalist asks Rahul Gandhi, before Narendra Modi became Prime Minister of India, your grandmother, your two aunts, their husbands, and their children—in other words, your entire Italian family—lived right here in Delhi.
In what capacity were they given three government bungalows, and in what capacity did they attend all government functions?
And why did this entire "Maino" family flee to Italy like thieves just 15 days after Narendra Modi became Prime Minister?
Today, Rahul Gandhi often visits Italy under the pretext of visiting his grandmother; but during the 10 years of Congress rule—and even before that, when Rajiv Gandhi was Prime Minister—this cunning man never visited Italy.
This was because Sonia Gandhi's entire maternal family lived in Delhi and were given 5 bungalows in Lutyens' Zone.
Even Sonia Gandhi's childhood friend, Quattrocchi, lived in those Delhi bungalows.
Sonia Gandhi's mother, Paola Maino, participated in government work and attended many events at the Rashtrapati Bhavan, where the entire government machinery was at her service.
Sonia Gandhi has 3 sisters, two of them lived in India, while one ran a large antique shop in Rome and Milan.
Several archaeologists have reported that rare Indian artifacts were taken abroad under the guise of exhibitions and later declared stolen so they could be sold at Sonia Gandhi's sister's shop.
In this way, many precious and rare Indian statues were stolen. Artifacts were taken abroad for exhibitions and then returned to Sonia Gandhi's sister's shop under the guise of theft.
Now, do you understand why Congress is so angry with Modiji? Why do they want to remove him? It's so that the 'thieving family' can continue their thievery.
I have lived in Germany for 30 years. I also have travelled in almost 40 countries in Europe, South, Middle and North America, North Africa and Asia before coming to India. Yet, of all the countries I visited, I clearly love India the most. I once even dreamt that in front of me there was a thick, 3-dimensional map of India. Looking at it my heart expanded and I felt great love. Still dreaming I was surprised that one can love a country so much.
It was, however, not love at first sight. After my first visit during my studies, I supposedly even said, “Never again India”, my mother claimed. I had come back to Germany weak from a stomach upset. Only on my second visit – intended as a short stopover that lasts meanwhile 45 years – India showed me what amazing treasure she hides under her noisy and often challenging surface.
I realized that in India an intensive, dedicated and essential inner search for what is truly true has been made since time immemorial. The findings of this search are startling and comforting to all of humanity and corroborated by modern nuclear physics:
‘Beneath’ EVERY appearance in this universe, including our own person, there is the same ‘Real Presence’ (or whatever one wants to call That which is formless and nameless) – living, loving, indestructible, mighty, infinite. To uncover it is the purpose of life and its fulfillment.
Every country has good and bad people. But India has also wise and enlightened people, more than any other place, and they make India special – a country of light (Bharat) in spite of occasional, apparent darkness.
May the Light illumine the intellect of all….
This is how cunningly the Leftist-Islamists are still attempting to mass brainwash Hindus through movies and ads, a phenomenon that started from the late 60s !
In this series ‘Raakh’ by Prime Amazon note the changes made :
Real life Inspector VP Gupta of the Delhi Police, becomes Jayprakash Jatav in the series, purposely portrayed as a Dalit officer, to mask the truth using the excuse of social-justice narrative.
Real life SI Ram Chander becomes a Muslim SI Javed Murtaza in the series.
Babulal, a bystander, who had tried to save the children, and later helped the police in identifying the killers by providing their descriptions, becomes a Muslim named Salem in the series.
The journalist who covered the case was Prabha Dutt, who is turned into another Muslim, with the name Nisar.
Meanwhile to demean Hindus, a worthless hawaldar character is added, with the name Mishra.
These bustards have taken a real life horrific incident of murder, r@pe, and kidnapping, and turned it into a propaganda campaign!
There should be multiple FIRs filed against producers, directors, actors, and Amazon prime. It should be such, that a lesson is made out of these people and media companies, so that in future they don’t dare to misrepresent the truth!
@MinOfCultureGoI@MIB_India@DelhiPolice@AshwiniVaishnaw
The Tragic Story of How India Was Deindustrialized
Between 1813 and 1853, 3 Acts of British Parliament killed 3 world-leading Indian industries.
Bengal cotton, South Indian wootz steel, and Indian Ocean shipbuilding - all demolished within forty years. Manchester, Sheffield, and Lloyd's of London grew on the corpses.
The Most Evil Marketing Trick of the 21st Century: How BP Made us Guilty for Climate Change!
In 2004, oil giant British Petroleum (BP) hired the global public relations firm Ogilvy & Mather to launch an international marketing campaign. Together, they popularized the concept of the personal "carbon footprint" & launched the world's 1st online personal footprint calculator.
The strategy was brilliant corporate psychology: it successfully pivoted the entire global climate conversation away from institutional energy production & industrial manufacturing, instead placing the moral burden squarely on the shoulders of ordinary consumers. People stopped protesting outside oil refineries & started arguing with each other over using plastic straws, taking shorter showers & calculating their personal driving emissions.
Although, BP did not invent the word footprint from scratch. They stole it from 2 Canadian academics. In 1992, Prof William Rees & his student Mathis Wackernagel at the UBC created a concept called the "Ecological Footprint." Ogilvy & Mather realized that if they took this concept, stripped away the parts tracking systemic industrial depletion, focused exclusively on carbon & narrowed the lens from a global system down to a single human being, they could weaponize it.
The carbon footprint calculator was actually Phase 2 of a massive $200M rebranding stunt launched in July 2000 by BP's then-CEO, John Browne. They officially ditched their century-old name, British Petroleum, changed it simply to BP & adopted the green & yellow sunburst logo we see today. They rolled out the slogan "Beyond Petroleum," masquerading as a forward-thinking energy company that was heavily investing in solar & wind.
The advertising was so effective that it won a prestigious Gold Effie award in 2007 for marketing excellence. Meanwhile, behind the scenes, BP quietly began divesting from its alternative energy projects. By 2013, they had completely dumped all of their solar & wind assets to double down on fossil fuels.
This post needs actual promotion!
A French moto vlogger "Frenchy" was traveling through India on his bike, He had a lump on his neck. Curious about the cost and process to remove it, he inquired locally and was quoted just $500 for the treatment.
Stunned by both the price and the short waiting time, he went ahead with the procedure. Within a week, the lump was removed. He documented the whole journey on camera.
He later shared that the same type of surgery in Australia after an accident had cost him $12,000.
If manufactured online hate and negative perceptions in the West didn’t exist, India could easily be earning hundreds of billions of dollars every year from medical tourism alone.
And this is why India needs to fight bad image/perception, that is being promoted by India's adversaries.
A cartoon being circulated on X says Indians should thank the British because James Prinsep deciphered the Brahmi script & helped recover our history. :))
Do you know before he became a so-called expert on our ancient scripts, Prinsep’s primary day job was serving as the Assay Master (chief metallurgist & currency controller) at the Banaras & Calcutta Mints. He was not an academic; he was an economic agent sent to fundamentally alter India's wealth distribution system.
Until the 1830s, India had a beautifully diverse, highly resilient decentralized currency system. Local kingdoms, merchant guilds & regional mints issued their own silver and gold coins. Local money-changers (Shroffs) evaluated coins based on pure metal weight. James Prinsep was the literal architect who destroyed this system.
Using his position as Assay Master, Prinsep spent yrs systematically studying the purity of native Indian coins. He did not do this out of cultural curiosity, he did it to calculate how the East India Company could completely monopolize India's money supply.
His efforts directly culminated in the Coinage Act of 1835: The Elimination of Indian Heritage: Prinsep spearheaded the policy that completely banned all local Indian regional coins & traditional designs. He personally oversaw the design of the new, uniform colonial Silver Rupee. He forced the removal of traditional Indian symbols, replacing them with the cold, imperial face of British King William IV.
What makes this a financial "thug" operation is how the transition was enforced on ordinary Indians. By passing laws that declared traditional regional currencies invalid for tax payments, the British forced Indian merchants, farmers & citizens to bring their centuries-old ancestral coins to Prinsep's mints. Under Prinsep's direct technical supervision, the British mints engaged in massive institutional exploitation:
- They took the pure, high-quality silver coins of Indian states.
- They melted them down in giant cauldrons.
- They charged the native Indians a heavy seigniorage (a minting fee/tax) just to exchange their own ancestral silver for the new British currency.
This artificial bottleneck triggered a massive shortage of circulating cash in rural India, causing local economies to crash while systematically vacuuming pure silver out of Indian hands & placing it directly under East India Company control. It was 1 of the largest state-sanctioned currency manipulation schemes in world history.
But what is often sold to us is the idea that Prinsep was a polymath who single-handedly deciphered our ancient scripts. Ask the same people who Rathnapala was & you are likely to be met with complete silence. :(
🇺🇸 US: Diesel
🇨🇦 Canada: Diesel
🇦🇺 Australia: Diesel
Major economies run double-stack freight trains, but they still rely on diesel because standard electric lines can't clear two-story trains.
But instead of settling, India custom-built a 7.5-meter high-rise grid. Today, India is the FIRST and ONLY country on Earth running double-stack containers on pure electric power. This is the scale of transformation happening under the Modi govt.
The year is 1949.
The Nobel Prize in Medicine has just gone to the man who invented the lobotomy. Your doctor suggests one for your sister, who has not been herself since the baby came. It is the most celebrated advance in psychiatry of the age, and he is simply current. By the time the prize curdles into an embarrassment, close to twenty thousand Americans have had the operation, and proportionally more here in Britain.
The year is 1956.
Lay the baby down on his front, the doctor says. So does the most trusted childcare book ever written, the one on every new mother's shelf. On his back he might choke, the reasoning goes. Millions obey. The advice holds for nearly thirty years, long after the evidence has quietly turned, and a generation of cot deaths is counted before anyone thinks to roll the babies over.
The year is 1966.
A bestselling book informs your wife that menopause is a disease, that she is, in the author's word, a castrate, and that a small daily pill will keep her youthful and tolerable to live with. Her doctor agrees. The drug becomes one of the most prescribed in the country. Nobody mentions that the author sat on the payroll of the company that made it. That detail surfaces decades later, in the same year the landmark trial is halted early for raising rates of breast cancer, stroke and clots.
The year is 1979.
Your ulcer is caused by stress and sharp food, the doctor explains. Calm down, drink milk, take the antacid that happens to be the best-selling medicine on earth. Two Australians are about to prove that most ulcers are caused by a bacterium and cured by a fortnight of antibiotics. The profession laughs. One of them eventually drinks a beaker of the stuff to settle the matter. The establishment takes the better part of twenty years to stop laughing. The Nobel lands in 2005.
The year is 1985.
Butter is dangerous, the doctor says. Switch to margarine, it is modern, it is heart-healthy, the experts are united. The spread he nudges you toward is loaded with trans fats, which the next decade will identify as the genuinely dangerous one, and which will eventually be banned outright. The butter goes quietly back in the fridge. No correction is ever printed at the volume of the original warning.
The year is 1992.
There is a pyramid on the surgery wall, and the very same one in your grandchild's classroom. Bread, cereal, rice and pasta form the broad virtuous base, up to eleven servings a day. Fat is exiled to the tiny tip. The chart was reportedly held back a year while the relevant industries had their say. It is wrong at the bottom and wrong at the top.
Now it is today.
Your doctor has new guidelines, new studies, a fresh consensus, delivered with precisely the steady confidence of every guideline above. He believes it, and he has good reason to. So did every doctor in this thread. None of them were villains. Each was sincere, most were kind, and all were certain, reading from a map that somebody else had drawn and handed them. That is the part worth sitting with.
So when the man in the white coat tells you what to eat, what to fear, and what to swallow every morning for the rest of your life, you are allowed to ask. Who paid for the study. What the evidence says beneath the headline. What he was just as certain about thirty years ago, and where that advice sits now.
Then make up your own mind. Call it scepticism, or call it whatever your grandmother called it when she ignored the advert, kept the butter where it was, and lived to ninety-one.
It has outlasted every consensus on this list. It will outlast this one too.
It's hard to beat Israeli technology!
TEL AVIV, Israel - The Israelis are developing an airport security device that eliminates the privacy concerns that come with full-body scanners.
It's an armoured booth you step into that will not X-ray you, but will detonate any explosive device you may have on your person.
Israel sees this as a win-win situation for everyone, with none of this crap about racial profiling.
It will also eliminate the costs of long and expensive trials.
You're in the airport terminal and you hear a muffled explosion. Shortly thereafter, an announcement:
"Attention to all standby passengers,
El Al is pleased to announce a seat available on flight 670 to London.
Shalom!
Meet Shehnaz Treasury !!
Failed actress, Millions of followers.
She says in video that @GovtOfIndia_ is breaking mountains to send it to Bangladesh
Lets expose her :
The mountains are not being cut to send rock or soil to Bangladesh.
Most hill-cutting is for road and highway projects to improve connectivity within Meghalaya and the Northeast.
Border roads near Bangladesh are being upgraded to improve trade, tourism, and movement in border areas such as Dawki.
These projects also have strategic and security value, allowing faster movement of people, goods, and security forces in a sensitive border region.
Well lots of influencers spreading fake propaganda but no action!!
Absolute Treason
@AshwiniVaishnaw@ShenazTreasury@Dev_Fadnavis
💥Our Man and his Army!
People are talking about breaking Nehru's record. It is very dim to even compare our PM with a British negotiator who took terms as a PM by deceitful means.
Let us celebrate 12 more years to come and wish the opposition, which is aiming for more partitions of our nation in the name of secularism, to form a single Unemployed party 😀
घर से भाग कर शादी करने का यही अंजाम होता है
मैंने दो-तीन मित्रों को देखा है उन्होंने भी घर से भाग कर शादी की थी और उनको भी ऐसे ही जिंदगी गुजारनी पड़ी
लेकिन सबसे कड़वी सच्चाई है यह नशा यह ऑक्सीटोसिन यह टेस्टोस्टरॉन मात्र कुछ समय के बाद एकदम डाउन हो जाता है उसके बाद जमीनी सच्चाई का पता चलता है जिसे ग्राउंड रियलिटी बोलते हैं
फिर जब आंखें खुलती है तब तक बहुत देर हो चुकी होती है और उसके बाद ऐसी लड़कियों का अंजाम बहुत दुखद होता है
क्योंकि आपको सामाजिकता भी निभानी पड़ेगी आपको लोगों के बराबर कम से कदम मिलाकर चलना पड़ेगा अपना एक स्टेटस भी मेंटेन करना पड़ेगा।
नमक दाल चावल आटा रोटी बच्चों की फीस फ्लैट यह सब प्रेम की बड़ी-बड़ी कसमो से नहीं आत
तो जाहिर सी बात है फिर कुछ समय के बाद इस तरह की शादियों में यानी प्रेम विवाह में टकराव बढ़ जाते हैं और मामला अंत में बिगड़ जाता है
EVEN AFTER BEING HIT BY 11 BULLETS,
SHE DIDN’T STEP BACK.
Kamlesh Kumari, India’s first woman to receive the Ashoka Chakra, displayed extraordinary courage and dedication in the line of duty.
On 13 December 2001, during the terrorist attack on the Indian Parliament, she alerted security forces and helped prevent the attackers from gaining unhindered access to the Parliament complex. Despite being shot multiple times, she continued her duty until her last breath.
For her exceptional bravery and supreme sacrifice, she was posthumously awarded the Ashoka Chakra, India’s highest peacetime gallantry award.
Salute to a true hero, Kamlesh Kumari.