Presentation Type
Poster Presentation
Abstract
The Collatz conjecture was introduced in 1937, but, despite the efforts of many mathematicians, it has yet to be proven. It appears to have very little connection to other areas of mathematics, although some aspects of it allude to questions similar to those asked in studies of prime numbers and the Riemann Hypothesis. The nature of the Collatz sequence allows it to be useful in cryptography and semi-random number generation. Some, including Craig Alan Feinstein, believe a formal proof of the conjecture is not possible. Others believe mathematics has not been developed enough to resolve the issue. To enter into this dialogue, a discussion on Feinstein’s argument is offered. This paper provides an overview of significant findings on the Collatz conjecture, its provability, and its relative usefulness. Several questions are offered for further inquiry. The ultimate focus is on whether the conjecture is worth studying, particularly from a Christian standpoint.
Faculty Mentor
Dr. Gary Hall
Recommended Citation
Hayes, Morgan, "Discussion of the Collatz Conjecture" (2025). Student Scholar Symposium. 74.
https://digitalcollections.lipscomb.edu/student_scholars_symposium/2025/Full_schedule/74
Included in
Discussion of the Collatz Conjecture
The Collatz conjecture was introduced in 1937, but, despite the efforts of many mathematicians, it has yet to be proven. It appears to have very little connection to other areas of mathematics, although some aspects of it allude to questions similar to those asked in studies of prime numbers and the Riemann Hypothesis. The nature of the Collatz sequence allows it to be useful in cryptography and semi-random number generation. Some, including Craig Alan Feinstein, believe a formal proof of the conjecture is not possible. Others believe mathematics has not been developed enough to resolve the issue. To enter into this dialogue, a discussion on Feinstein’s argument is offered. This paper provides an overview of significant findings on the Collatz conjecture, its provability, and its relative usefulness. Several questions are offered for further inquiry. The ultimate focus is on whether the conjecture is worth studying, particularly from a Christian standpoint.