(E) Named after German mathematician Lothar Collatz who introduced it in 1937, the Collatz conjecture is one of those fun math problems that are simple to explain but very difficult to solve.

The conjecture is defined as follows:  “start with any positive integer n. Then each term is obtained from the previous term as follows: if the previous term is even, the next term is one half of the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1. The conjecture is that no matter what value of n, the sequence will always reach 1.“

Professor Lawrence Tao from UCLA proved that “almost all Collatz orbits attain almost bounded values“.

Now, computational scientists Emre Yolcu, Scott Aaronson, and Marijn J.H. Heule are trying to investigate it with sophisticated computer programs:”An Automated Approach to the Collatz Conjecture“.

Following is nice video on the Collatz conjecture:

References:

• Quanta Magazine: “Computer Scientists Attempt to Corner the Collatz Conjecture“
• MIT Technology Review: “Are computers ready to solve this notoriously unwieldy math problem?“

Note: The picture above is from the YouTube video above.

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