Combinatorics Seminar 2018

Speaker: Jaume Llibre, Universitat Autònoma de Barcelona

Date: Fri, Nov 02, 2018

Time: 15:00 - 16:00

Venue: Large Meeting Room

Title: On the $3x+1$ conjecture and the limits of the mathematics


Consider the following operation on an arbitrary positive integer: If the number is even, divide it by two; If the number is odd, triple it and add one. Now form a sequence by performing this operation repeatedly, beginning with any positive integer, and taking the result at each step as the input at the next. The $3x+1$ conjecture is: In the sequence created by this process will appear the number 1, regardless of which positive integer is chosen initially. This conjecture goes back to 1930, it is due to the German mathematician Collatz. Today it remains as an unsolved problem in mathematics.

Paul Erdős said about the $3x+1$ conjecture: "Mathematics may not be ready for such problems." Jeffrey Lagarias in 2010 claimed that based only on known information about this problem, "this is an extraordinarily difficult problem, completely out of reach of present day mathematics."

The talk will be about what is known and what is unknown on this conjecture.