Some of the hardest problems in mathematics are the easiest to explain. Take the twin prime conjecture: are there infinitely many pairs of prime numbers that are just two numbers apart: like 3 and 5, or 11 and 13? It’s a question that’s been around since the time of the ancient Greeks, and anyone with a basic understanding of numbers can grasp it, but none had seemed to prove it for thousands of years.
Enter Yitang Zhang, a name that, until 2013, meant nothing in elite math circles. After earning his Ph.D., Zhang couldn’t land a research job. He spent years working at a Subway and later lecturing quietly at the University of New Hampshire, far from the limelight. But he never stopped thinking about numbers. In near-isolation, he obsessively chipped away at the twin prime problem. Then, seemingly out of nowhere, he submitted a paper to the Annals of Mathematics, one of the most prestigious journals in the field.
In it, he proved that there are infinitely many pairs of primes less than 70 million apart. It wasn’t quite twin primes—but it was the first major breakthrough in centuries. Zhang’s result lit a fire. Inspired by his lone achievement, mathematicians around the world launched a massive online collaboration called the Polymath Project. Building on Zhang’s techniques, they began narrowing the gap—70 million dropped to 246. It was a breathtaking example of collective momentum.
There’s something deeply poetic about it: a man working alone, driven by pure curiosity, cracked a problem that had resisted proof for millennia. In an age of academic prestige and institutional polish, Zhang reminded us that breakthroughs can come from anywhere - especially from those who live in the trenches with their questions, not for recognition, but for the love of the chase.
Craving more? Check out the source behind this Brain Snack!
