Deceptive puzzle may be solved after 74 years

A long-standing and apparently simple puzzle that has left mathematicians stumped for nearly three-quarters of a century may finally be solved.
The Collatz conjecture was proposed by Lothar Collatz in 1937. It is also known as the "3n + 1 problem" because of its deceptively-simple definition.
Now mathematician Gerhard Opfer of the University of Hamburg, who was a student of Collatz, says he has proved the conjecture true.

The problem starts by choosing any whole number, n. If n is even, divide it by 2. If n is odd, multiply it by 3 and add 1 to get 3n + 1. Collatz believed that if you keep repeating these operations on the resulting numbers, no matter what your starting number, the result will always reach the number 1 eventually.

This has been verified for numbers up to 5.76 x 10¹⁸ (nearly 6 billion billion), but without a proper mathematical proof there is always the possibility that an incredibly large number could violate Collatz's rule.
Opfer claims to have achieved this proof, which is set out in a paper on the University of Hamburg's preprint server - but the result has yet to be peer-reviewed and could prove incorrect. The paper has been submitted to the journal Mathematics of Computation for review.

Prolific Hungarian mathematician Paul Erdős once said of the Collatz conjecture that "Mathematics is not yet ready for such problems" and offered a $500 reward for its solution.
In our 2011 preview, we found that 50 per cent of long-standing mathematical problems are solved after 53 years. Perhaps mathematics is finally ready to provide an answer to the Collatz conjecture.