![]() Perelman was offered the million-dollar Millennium Prize, as well as the Fields Medal, often called the Nobel Prize of Math. It was groundbreaking, yet modest.Īfter the math world spent a few years verifying the details of Perelman’s work, the awards began. Perelman’s proof had some small gaps, and drew directly from research by American mathematician Richard Hamilton. After some revisions and developments, the conjecture took the form of “Every simply-connected, closed 3-manifold is homeomorphic to S^3,” which essentially says “the simplest 4D shape is the 4D equivalent of a sphere.”Ī century later, in 2003, a Russian mathematician named Grigori Perelman posted a proof of Poincaré’s conjecture on the modern open math forum arXiv. ![]() Poincaré then went up to 4-dimensional stuff, and asked an equivalent question. In some significant sense, a ball is the simplest of these shapes. For shapes in 3D space, like a ball or a donut, it wasn’t very hard to classify them all. Here’s the idea: Topologists want mathematical tools for distinguishing abstract shapes. Henri Poincaré was a French mathematician who, around the turn of the 20th century, did foundational work in what we now call topology. Today, they’re all still unsolved, except for the Poincaré conjecture. In 2000, the Clay Mathematics Institute, a non-profit dedicated to “increasing and disseminating mathematical knowledge,” asked the world to solve seven math problems and offered $1,000,000 to anybody who could crack even one.
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