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Many unsolved problems still stump mathematicians today. Some are simple to state, but maddeningly difficult to solve. One such problem is the Collatz conjecture, or the 3n+1 problem.
Take any number, say the number 10. If it is even, halve it. If it is odd, multiply it by 3 and add 1. Repeat. Now 10 is even, so we halve it, yielding 5. 5 is odd, so multiply 5 by 3 and add 1: 3x5+1=16, which is also even. Halving it yields 8. Halve it again to yield 4, then 2, then 1. 1 is odd, so 3x1+1=4 again, and we are in an infinite loop 4, 2, 1, 4, 2, 1, … .
The Collatz conjecture says that this always happens. No matter what number we start with, we will eventually reach the repeating sequence 4, 2, 1, 4, 2, 1, … .
Using computers, this has been verified for all starting numbers up to at least 5x10^18 (i.e. 5 followed by 18 zeroes!). But nobody knows how to prove this. Mathematician Terence Tao has come the closest so far, spurred on by an anonymous comment on his blog.
It’s something all of us can relate to: some challenges might stump us, but with persistence and by keeping an open mind, we might take a step or two closer to a solution.
I will be on leave for the rest of the year. Will spend some time trying to decipher Tao’s method. Also plan to catch up on my other readings, spend time with family, and perhaps go #jalanjalan (if the rain stays away). – LHL
Take any number, say the number 10. If it is even, halve it. If it is odd, multiply it by 3 and add 1. Repeat. Now 10 is even, so we halve it, yielding 5. 5 is odd, so multiply 5 by 3 and add 1: 3x5+1=16, which is also even. Halving it yields 8. Halve it again to yield 4, then 2, then 1. 1 is odd, so 3x1+1=4 again, and we are in an infinite loop 4, 2, 1, 4, 2, 1, … .
The Collatz conjecture says that this always happens. No matter what number we start with, we will eventually reach the repeating sequence 4, 2, 1, 4, 2, 1, … .
Using computers, this has been verified for all starting numbers up to at least 5x10^18 (i.e. 5 followed by 18 zeroes!). But nobody knows how to prove this. Mathematician Terence Tao has come the closest so far, spurred on by an anonymous comment on his blog.
It’s something all of us can relate to: some challenges might stump us, but with persistence and by keeping an open mind, we might take a step or two closer to a solution.
I will be on leave for the rest of the year. Will spend some time trying to decipher Tao’s method. Also plan to catch up on my other readings, spend time with family, and perhaps go #jalanjalan (if the rain stays away). – LHL
