The problem Greene and Lobb worked on predicts, basically, that every such path contains sets of four points that form the vertices of rectangles of any desired proportion.But again, the problem Greene and Lobb solved involves curves that are smooth, and therefore continuous.
Yet in the middle of the 20th century, mathematicians started uncovering deep relationships between them, and by the early 1970s, Robert Langlands of the Institute for Advanced Study had conjectured that Diophantine equations and automorphic forms match up in a very specific manner.
Earlier this year one of the top mathematicians in the world dared to confront the problem—and came away with one of the most significant results on the Collatz conjecture in decades.On September 8, Terence Tao posted a proof showing that—at the very least—the Collatz conjecture is “almost” true for “almost” all numbers.
For example, zero-knowledge proofs can be used to validate cryptocurrency transactions managed on a blockchain and combat fraud without revealing data about which wallet a payment came from, where it was sent, or how much currency changed hands.
The Keb is a technical shell, with features like a helmet-compatible hood, plasticized water-resistant zippers, and pockets on the chest so that you can access them while wearing a climbing harness or a hip belt.