But still so far.
Terence Tao is one of the greatest mathematicians of our time. At age 21, he got his Ph.D. at Princeton. At 24, he became the youngest math professor at UCLA—ever. And in 2006 he won the Fields Medal, known as the Nobel Prize of math, at the age of 31.is like a modern-day da Vinci’s notebook. Name a subject in advanced math, and he’s written about it.
Take any natural number. There is a rule, or function, which we apply to that number, to get the next number. We then apply that rule over and over, and see where it takes us. The rule is this: If the number is even, then divide it by 2, and if the number is odd, then multiply by 3 and add 1.For example, let’s use 10. It’s even, so the rule says to divide by 2, taking us to 5. Now that’s odd, so we multiply 5 by 3 and then add 1, landing us on 16. Now 16 is even, so we cut it in half to get 8.
It’s definitely true for all numbers with less than 19 digits, so that covers whatever you probably had in mind. But even if computers check up to 100 or 1,000 digits, that’s far from a proof for all natural numbers..” Let’s break that down slightly. Collatz Orbits are just the little sequences you get with the process we just did. So the Collatz Orbit of 10 is . Since half of 4 is 2, half of 2 is 1, and 3*1+1 is 4, Collatz Orbits cycle through 4, 2, and 1 forever.
In essence, Tao’s results says that any counterexamples to the Collatz Conjecture are going to be incredibly rare. There’s a deep meaning to how rare we’re talking here, but it’s still very different from nonexistent.
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