The famous bunkbed conjecture in probabilistic graph theory was disproven with a crazy counterexample with 7222 vertices!
Papers cited:
1) The main paper by Gladkov, Pak, and Zimin: https://arxiv.org/abs/2410.02545
2) The paper by Wagner documenting the machine learning algorithm: https://arxiv.org/abs/2104.14516
3) The paper by Hollom giving the counterexample in the hypergraph generalization: https://arxiv.org/pdf/2406.01790
4) Blog Post by Pak explaining the paper a bit more colloquially: https://igorpak.wordpress.com/2024/10/01/the-bunkbed-conjecture-is-false/
5) Blog Post by Pak on "what if they are all wrong", and the value of searching for counterexamples to conjectures: https://igorpak.wordpress.com/2020/12/10/what-if-they-are-all-wrong/
BECOME A MEMBER:
►Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join
MATH BOOKS I LOVE (affilliate link):
► https://www.amazon.com/shop/treforbazett
COURSE PLAYLISTS:
►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS
►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6
►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m
► CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n
►MULTIVARIABLE CALCULUS (Calc III): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd
►VECTOR CALCULUS (Calc IV) https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa
►DIFFERENTIAL EQUATIONS: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw
►LAPLACE TRANSFORM: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1
►GAME THEORY: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlX
OTHER PLAYLISTS:
► Learning Math Series
https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw
►Cool Math Series:
https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho
SOCIALS:
►X/Twitter: http://X.com/treforbazett
►TikTok: http://tiktok.com/@drtrefor
►Instagram (photography based): http://instagram.com/treforphotography