Il mistero matematico irrisolto più antico di sempre

Are there odd perfect numbers? Go to https://brilliant.org/veritasium to start your 30-day free trial, and the first 200 people will receive 20% off a premium annual subscription. A special thank you to our supporters on Patreon! Join this list to help us keep our videos free, forever: https://ve42.co/PatreonDEB A huge thank you to Prof. Pace Nielsen for all his time and help with this video. A big thank you also to Dr. Asaf Karagila, Pascal Ochem, Prof. Tianxin Cai, and Prof. William Dunham for their expertise and support. To try GIMPS for yourself: https://ve42.co/GIMPS These sources were especially helpful: Perfect numbers via MacTutor - https://ve42.co/MTPerfect Cai, T. (2022). Perfect numbers and fibonacci sequences. World Scientific. - https://ve42.co/Cai2022 Dunham, W. (2022). Euler: The master of us all (Vol. 22). American Mathematical Society. - https://ve42.co/Dunham2022 Directed by Casper Mebius Written by Casper Mebius and Derek Muller Edited by Peter Nelson Illustrations by Jakub Misiek Animations by Fabio Albertelli, Ivy Tello, David Szakaly, Alondra Vitae, Alex Drakoulis, and Leigh Williamson Film by Derek Muller, Raquel Nuno, and Peter Nelson Additional research by Aaron Santos, Camilla Machado, and Gregor Čavlović Produced by Casper Mebius, Gregor Čavlović, Han Evans, and Derek Muller Thumbnail by Ren Hurley Additional videos/photos provided by Getty Images and Pond5 Music by Epidemic Sound 👉 This channel is created in collaboration with @veritasium and localized into your language by www.linguana.com 0:00 - Introduction to the Perfect Numbers Problem 0:51 - What are the perfect numbers 2:27 - Euclid's model and the first conjectures 7:02 - History and refutation of the conjectures 10:01 - Euler's contributions and the sigma function 1:33 - Modern progress and the calculation of perfect numbers 18:59 - Contemporary research and limits of odd perfect numbers 23:13 - Modern discussion, applications, and conclusions