A Chinese mathematician spent 7 years making sandwiches at Subway after his PhD, and at 58 solved a 150-year-old math problem nobody thought was solvable.
His name is Yitang Zhang. The problem is called the Twin Prime Conjecture.
He was born in Shanghai in 1955 and knew he wanted to spend his life on mathematics by the time he was nine years old. That year he found his own proof of the Pythagorean theorem. Nobody taught it to him. He just worked it out.
Then the Cultural Revolution arrived and took everything.
The Chinese government closed the schools. Zhang's father had political troubles with the Communist Party, so Zhang was sent to the countryside with his mother to work in the fields. He spent 10 years as a farm laborer. No high school. No classroom. No teacher.
He read math books in the fields when he could find them.
When the revolution ended, Zhang was 23. He sat the university entrance exam and got into Peking University, one of the most competitive mathematics programs in China. He finished his bachelor's degree, then a master's. The president of Peking University personally recommended him for a full scholarship at Purdue University in the United States.
He arrived at Purdue in 1985. He earned his PhD in 1991.
Then the second wall hit.
His relationship with his doctoral advisor collapsed. The advisor did not write him letters of recommendation. Without those letters, the academic job market was closed. Zhang applied. Nothing came back. He spent the years after his PhD working as an accountant, doing delivery work, sleeping in his car during the stretches when nothing else was available.
A friend eventually opened a Subway sandwich restaurant in Kentucky and offered him a job. Zhang took it. He kept the books and made sandwiches. A man with a PhD in mathematics from Purdue, working a Subway counter because the academic world had no place for him.
He did this for seven years.
He was finally hired as a lecturer at the University of New Hampshire in 1999. Not a professor. A lecturer. The lowest rung of the academic ladder, with no research funding, no graduate students, and no institutional support. He taught calculus to undergraduates and worked on mathematics alone in whatever time was left.
Most people would have stopped believing by then.
Zhang did not stop.
The Twin Prime Conjecture is one of the oldest unsolved problems in number theory. Twin primes are pairs of prime numbers separated by exactly two: 5 and 7, 17 and 19, 41 and 43. The conjecture predicts that these pairs never stop appearing no matter how far you go along the number line. Mathematicians had believed this for over 150 years. Nobody had been able to prove it.
The deeper version of the problem asks something slightly different. Not whether twin primes are infinite, but whether there is any finite gap between prime numbers that appears infinitely often. This is called the bounded gap problem. The best mathematicians in analytic number theory had been attacking it for decades. A landmark 2005 paper by three researchers came agonizingly close and still could not close it.
Zhang worked on it alone. No collaborators. No funding. No department seminars where he could road-test his ideas. He once said he would go to a friend's house and think in the garden for hours.
In 2012, during a visit to a friend's home in Colorado, something unlocked.
He submitted his paper to the Annals of Mathematics in April 2013. The Annals is the most prestigious mathematics journal in the world. Papers sit in review for months, sometimes years. The editors read Zhang's submission and immediately knew something was different. They sent it to the leading experts in analytic number theory for review.
It was accepted in three weeks.
The paper proved that there are infinitely many pairs of prime numbers separated by a gap of less than 70 million. Not two. Not the twin prime gap specifically. But a finite gap. For the first time in history, someone had proved that prime numbers keep coming back together, that the universe of numbers never lets them drift apart forever.
Peter Sarnak, one of the most respected mathematicians at the Institute for Advanced Study, said: "He is not a fellow who had done much before. Nobody knew him. His result was spectacular."
Zhang was 58 years old.
Within a year he had the MacArthur Fellowship, the Cole Prize, the Rolf Schock Prize, and a full professorship at UC Santa Barbara. The man who spent seven years at Subway was now one of the most celebrated mathematicians alive.
He said in an interview: "I was not lucky. Maybe it is more important for a person to make himself known to the public. But that was not so easy for me."
He was not complaining. He was just being precise.
The mathematics establishment has a quiet belief that great work happens young. The Fields Medal cuts off at 40. Most mathematicians who change the field do it in their thirties. Zhang proved his most important theorem at 58, after a decade of farm labor, seven years of sandwiches, and a decade of teaching calculus to freshmen with no one watching.
He did not beat the deadline.
He proved there was no deadline to beat.
Before the world knew the power of Big Pharma, a journalist in a tiny lab in Bombay created a substance so potent it triggered a trade war with London. It was a yellow grease that did not just soothe headaches but funded a movement, bypassed British blockades, & became 1 of the few Indian products to make the Empire's own medicine look like scented water.
Unlike other brands started by chemists, Amrutanjan was founded by Kasinadhuni/Kasinathuni Nageswara Rao, a man who was primarily a journalist & a freedom fighter. In the late 1800s, the pain balm market in India was a British monopoly. If your head throbbed, you bought imported ointments. Rao saw this as a tax on pain. He retreated into a lab & perfected a formula that was significantly more potent than anything coming out of London.
The British tried to push their own balms like Vicks/early menthol rubs as sophisticated & odorless. They attempted to smear Amrutanjan as primitive because of its overpowering scent. Rao leaned into the scent. He realized that in a country where literacy was low, a brand could not just be a name, it had to be an experience.
He distributed free samples at music concerts (Sabhas) & religious festivals. By the time the British tried to patent the market for pain relief, the entire Indian public had already associated the smell of camphor & menthol with trust. The British balms felt alien & weak compared to the sensory explosion of the yellow tin.
The smell of Amrutanjan... that piercing, camphor-heavy aroma became the literal scent of the freedom struggle. If you walked into a room & it smelled of Amrutanjan, it was a silent signal: A patriot is present. It was a scent the British police could not arrest, yet it was everywhere.
The British had a Patent Medicine Tax that made imported drugs expensive. However, by classifying Amrutanjan as an Ayurvedic Proprietary Medicine, Rao managed to navigate a complex legal gray area. He essentially used the British legal system against itself. By proving his ingredients were ancient yet his manufacturing was modern, he avoided the crippling taxes that applied to purely Western drugs, while maintaining a price point (initially 10 annas) that made British imports look like daylight robbery Rao fought back not just in the market, but in the press. He used the profits from the balm to fund Andhra Patrika, 1 of the most influential anti-British newspapers.
The British were literally paying for their own downfall. Every time a British officer’s wife bought a jar of Amrutanjan for a migraine (because it worked better than the London balms), she was inadvertently funding the printing of revolutionary literature that called for the end of the Raj.
By the 1930s, this Indian yellow grease was being exported to Indian diaspora & locals in South Africa & Ceylon. It became a global symbol of Eastern Wisdom defeating Western Chemistry. It was 1 of those few occasions, an Indian OTC (Over the Counter) product achieved cult status internationally w/o a single pound of British investment.
In fact, the yellow tin became so iconic that it did not need a label in the villages. The color & the smell were the brand. It was a biological Swadeshi. While others were fighting with words, Rao was fighting with molecular relief.
Happy to have played all the string layers in this song, “Phir Se”, for
#dhurandhar2therevenge. Thank you @shashwatology Sachdev bhaiya for the epic sounds and music, and hearty congratulations to you. Thank you @AdityaDharFilms sir 🙏🏾🤍. @arijitsingh bhaiya, you sound like a dream, as always. Such honest, pretension-less, gut wrenching singing ♥️🙏🏾.
#ramanabalachandhran #arijitsingh #dhurandhar2therevenge #shashwatsachdev
#adityadhar
https://t.co/qnfhIqrVps
This is WILD.
Peter Thiel just bet $2 billion on a collar that wraps around a cow’s neck.
The company is called Halter and it has a proprietary algorithm that runs the entire operation.
They actually trademarked the name for it and called it the Cowgorithm and here's how it works.
A farmer opens an app, taps a button, and 600,000 cows across three countries start walking toward the milking station on their own.
No farm dogs, fences or physical labor, it's just a solar-powered GPS collar sending sound and vibration cues to each animal.
The collar does more than move cows around.
It monitors digestion, fertility cycles, and health patterns in real time, 24 hours a day, using machine learning trained on the behavior of hundreds of thousands of animals.
Halter was founded by a rocket engineer who built spacecraft at Rocket Lab before deciding that farming was the bigger unsolved problem.
US ranchers alone have already used the technology to build over 11,000 miles of virtual fencing, roughly the full perimeter of the continental United States, saving an estimated $220 million in physical fencing costs.
Halter's previous funding round valued the company at $1 billion.
This new round, led by Thiel's Founders Fund, doubles that valuation to $2 billion before the new money even hits the account.
And they charge farmers between $5 and $8 per animal per month on a subscription model, meaning the more cows they collar, the more locked-in the revenue becomes.
The most powerful venture capitalist on earth just decided that the future of food and farming runs through an algorithm named after a cow.
He might be right.
what i did with OpenClaw this weekend
1. setup in a VM (not to give control to my Mac)
2. Telegram - Yes, No email control (yet), simple use-case of tracking weather- news -TODO lists
3. Used Openrouter to get a feel of it
4. Switched to Google Gemini API for budget use
what i think will be the future of AI agents
each one of us would create personalized agent ( which can take persona of co-worker, friend, family person- various mask you wear) and interact, that is the only way you can be available 24/7 and immortal
it may sound strange but..
smart move
Playing with OpenClaw over this weekend, in a VM - as i am not fully convinced to give lot of powers to autonomous agents, with OpenAI they would monetize it
Anthropic or Google should have acted fast!
Peter Steinberger is joining OpenAI to drive the next generation of personal agents. He is a genius with a lot of amazing ideas about the future of very smart agents interacting with each other to do very useful things for people. We expect this will quickly become core to our product offerings.
OpenClaw will live in a foundation as an open source project that OpenAI will continue to support. The future is going to be extremely multi-agent and it's important to us to support open source as part of that.