The Mystique of the Collatz Conjecture: An Unresolved Mathematical Puzzle

10 min readDec 9, 2023
Collatz Feather by MICHAEL SPILSBURY

Consider this your official warning: The mathematical puzzle I am about to plunge into, known as the Collatz Conjecture, holds a potent allure that can be overwhelmingly addictive. Much like the disclaimers you encounter at the start of a film, cautioning of flashing lights or intense action sequences, or the heart disease warnings that precede nail-biting soccer games, this notice serves the same purpose. The Collatz Conjecture, a seemingly simple premise, and yet maddeningly elusive solution, can draw you in with its seemingly straightforward premise. Proceed with caution.

Shizuo Kakutani, a renowned mathematician who began teaching at Yale University immediately after World War II, is a testament to the perplexing charm of the Collatz Conjecture. Known for his popularity among students, Kakutani was so captivated by the Collatz Conjecture that he introduced it to everyone around him, igniting a wave of intrigue that pulsated throughout the entire mathematics department at Yale. For an entire month, the math department was consumed by this confounding problem, with everyone immersed in vibrant discussions and attempts at resolution. Kakutani once commented on the experience:

For about a month everybody at Yale worked on it, with no result. A similar phenomenon happened when I mentioned it at the University of Chicago. A joke was made that this problem was part of a conspiracy to slow down mathematical research in the U.S.

Shizuo Kakutani was a Japanese-American mathematician, best known for his eponymous fixed-point theorem. | Source: The Royal Society

Indeed, the enchanting allure of the Collatz Conjecture was so potent that it stirred the imagination of the American public to the point of conspiracy theories. The pervasive obsession with the problem even led to the development of a popular theory that its very existence was a Soviet plot aimed at slowing down the progress of American science.

What is the Collatz Conjecture?

Lothat Collatz — From researchers and scholars. | Source: The University of Hamburg




Math Teacher. Content Curator. Soccer player. Maradona fan. Mostly write about the lectures I love to learn better.