Number theory
The rest of the post goes into much more detail, but to summarize: all integers were able to be plotted onto the tree (self-explanatory), and by ‘going down the tree’ and ‘across different branches’, every odd input becomes even, and then halves repeatedly, eventually decreasing distance to 1.
Yet as I completed further research, I realized that numerous similar proofs had been published, just to be brutally dismantled by critics. The proof above suffered in similar ways. The author did not provide sufficiently vigorous proof that the 1-2-4 loop was the only one present in the tree; lots of ideas and explanations were based purely on assumption; and worst of all, the post was littered with scornful remarks for the readers. It seemed to me it was unfortunately another unsuccessful attempt to prove the conjecture. And yet, this is what makes the Collatz Conjecture so fascinating. Its rules are so simple that a child could test them with pencil and paper, but its behaviour is so complicated that the world’s greatest mathematicians avoid it.
Conclusion
Where Fermat’s Last Theorem was eventually solved through the development of new mathematical frameworks, the Collatz problem stands as a symbol of mathematics’ current limits. A bittersweet ending to the most famous unsolved mystery in modern day number theory, and in turn it holds so much weight in the future of mathematics.
Bibliography
Anonymous (2024) The Unofficial Proof of the Collatz Conjecture. https://www.reddit.com/r/Collatz/comments/1b2vrhi/the_unofficial_proof_of_the_collatz_conjecture. Date consulted: 24/8/25 Cambridge University Faculty of Mathematics (n.d.) https://www.maths.cam.ac.uk/features/fermats-last-theorem-history-new-mathematics. Date consulted: 23/8/25 J. J. O'Connor and E F Robertson (2002) Pierre de Fermat. https://mathshistory.st-andrews.ac.uk/Biographies/Fermat. Date consulted: 23/8/25 Numberphile and S L Singh (2013) Fermat's Last Theorem – Numberphile. https://www.youtube.com/watch?v=qiNcEguuFSA. Date consulted: 23/8/25 Veritasium (2021) The simplest math problem no one can solve - Collatz Conjecture. https://www.youtube.com/watch?v=094y1Z2wpJg. Date consulted: 24/8/25
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