One of the greatest unsolved mysteries in math is also very easy to write. But we’ll need to solve the Collatz Conjecture for the subject to flourish. The study of dynamical systems could become more robust than anyone today could imagine. Why is such a basic question so hard to answer? It serves as a benchmark for our understanding once we solve it, then we can proceed onto much more complicated matters. It looks like a simple, innocuous question, but that’s what makes it special. The Conjecture lives in the math discipline known as Dynamical Systems, or the study of situations that change over time in semi-predictable ways. So, we might be working on it for decades longer. But he most likely can’t adapt his methods to yield a complete solution to the problem, as Tao subsequently explained. Tao’s recent work is a near-solution to the Collatz Conjecture in some subtle ways. The Conjecture is that this is true for all natural numbers (positive integers from 1 through infinity). You eventually land on 1, for every number we’ve ever checked. Take any natural number, apply f, then apply f again and again. And while the story of Tao’s breakthrough is promising, the problem isn’t fully solved yet.Ī refresher on the Collatz Conjecture: It’s all about that function f(n), shown above, which takes even numbers and cuts them in half, while odd numbers get tripled and then added to 1.
In September 2019, news broke regarding progress on this 82-year-old question, thanks to prolific mathematician Terence Tao.
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