The Oldest Unsolved Problem in Math

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Published 2024-03-07
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A massive thank you to Prof. Pace Nielsen for all his time and help with this video.

A big thank you to Dr. Asaf Karagila, Pascal Ochem, Prof. Tianxin Cai, and Prof. William Dunham for their expertise and help.

To try GIMPS out yourself: ve42.co/GIMPS

These sources were particularly helpful:
Perfect numbers via MacTutor - ve42.co/MTPerfect
Cai, T. (2022). Perfect numbers and fibonacci sequences. World Scientific. - ve42.co/Cai2022
Dunham, W. (2022). Euler: The master of us all (Vol. 22). American Mathematical Society. - ve42.co/Dunham2022

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References:
   • Perfect Numbers and Mersenne Primes -...  
   • Perfect Number Proof - Numberphile  
Dickson, L. E. (1919). History of the Theory of Numbers.. (Vol. 1). Carnegie Institution of Washington.
Knill, O. (2007). The oldest open problem in mathematics. NEU Math Circle, December2. - ve42.co/Knill2007
Perfect number via Wikipedia - ve42.co/WikiPerfect
Introduction to Arithmetic via HalthiTrust - ve42.co/IntroArithmetic
Nicomachus of Gerasa via MacTutor - ve42.co/MTNicomachus
Sonja, B. (1988). The First Perfect Numbers and Three Types of Amicable Numbers in a Manuscript on Elementary Number Theory by Ibn Fellûs. Erdem, c. IV, 11. - ve42.co/Sonja1988
Ibn Fallus via Wikipedia - ve42.co/WikiFallus
Mersenne prime via Wikipedia - ve42.co/WikiMP
List of Known Mersenne Prime Numbers - ve42.co/ListOfMP
Marin Mersenne via MacTutor - ve42.co/MTMersenne
Leonhard Euler via Wikipedia - ve42.co/WikiEuler
Frank Nelson Cole via Wikipedia - ve42.co/WikiFNCole
GIMPS History via Mersenne.org - ve42.co/GIMPSHistory
EFF Cooperative Computing Awards via EFF - ve42.co/EFFAwards
Jonathan Pace via Primewiki - ve42.co/PWikiPace
Book with just one number sells out in Japan via BastillePost - ve42.co/PrimeBook
Predicted distribution of Mersenne primes via John D. Cook - ve42.co/JDCookMP
Euler’s Odd Perfect Numbers Theorem via Cantor's Paradise - ve42.co/EulerOPN
A Perfect (Math) Mystery via Medium - ve42.co/Machado2024
Brent, R. P., Cohen, G. L., & te Riele, H. J. (1991). Improved techniques for lower bounds for odd perfect numbers. Mathematics of Computation, 57(196), 857-868. - ve42.co/Brent1991
Ochem, P., & Rao, M. (2012). Odd perfect numbers are greater than 10¹⁵⁰⁰. Mathematics of Computation, 81(279), 1869-1877. - ve42.co/Ochem2012
Mathematicians Open a New Front on an Ancient Number Problem via Quantamagazine - ve42.co/QuantaSpoofs
Descartes number via Wikipedia - ve42.co/WikiDescartesNumber
Andersen, N., Durham, S., Griffin, M. J., Hales, J., Jenkins, P., Keck, R., ... & Wu, D. (2022). Odd, spoof perfect factorizations. Journal of Number Theory, 234, 31-47. - ve42.co/Andersen2022
Pomerance’s Heuristic that Odd Perfect Numbers are Unlikely via OddPerfect.org - ve42.co/Heuristic

Images & Video:
Clip of Piergiorgio Odifreddi -    • Odifreddi da Gramellini: piccola lezi...  
Euclid’s Elements 1 via Claymath - ve42.co/CM1
Euclid’s Elements 2 via Claymath - ve42.co/CM2
Euclid’s Elements 3 via Claymath - ve42.co/CM3
Diophanti - ve42.co/Diophanti
Gauss book - ve42.co/GaussDis
Euler’s Archive 1 - ve42.co/Euler1
Euler’s Archive 2 - ve42.co/Euler2

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Directed by Casper Mebius
Written by Casper Mebius and Derek Muller
Edited by Peter Nelson
Illustrated by Jakub Misiek
Animated by Fabio Albertelli, Ivy Tello, David Szakaly, Alondra Vitae, Alex Drakoulis, and Leigh Williamson
Filmed 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 video/photos supplied by Getty Images and Pond5
Music from Epidemic Sound

All Comments (21)
  • @cupostuff9929
    >walks up to blackboard >multiplies 2 numbers >walks away >round of applause Frank Nelson Cole was unfathomably based
  • 13:25 "But Euler wasn't finished yet." I think this sentence appears in most histories of mathematical concepts.
  • Normal people would say “There’s no way” Some other people would say “The chance is low, but never zero” And then comes the mathematician: “The chance is never zero, but how low is it?”
  • @denverbeek
    I'd like to thank you for making me aware of GIMPS. I'm donating some of my cpu power overnight now.
  • @madjson1429
    When Euler says "it's most difficult", it's gotta be impossible.
  • 4:03 "Euclid was actually thinking along similar lines" Euclid: calculates perfect numbers with actual lines
  • @BoolFalse
    i'm becoming more respectful to my teachers, when i realize i can now understand and enjoy these kind of videos.. even 15 years later after the school..
  • Me: > starts watching video > gets engrossed > gets the motivation to find the odd perfect number > forgets what a perfect number is > refuses to elaborate > leaves
  • @deanrinehart
    Watching a math related video strictly out of curiosity and having your general math professor Bill Dunham from 25 years ago pop up is a surprise…and finding out he’s now a well respected mathematics historian and not just some guy who endlessly suffered non-math students struggles with train problems is absolutely fantastic. Go Mules!
  • I'm an English major, and I just subscribed to Veritasium because I enjoyed this so much. Thank you! I can't wait to chase down every last video!
  • @logician1234
    There is something so bizarre about Euclid and Euler having a collaboration. If the history of mathematics was a book of fiction, I would call this a fan service 😂
  • @ZenZooZoo
    Not me watching thinking I’m gonna try to solve this while eating hot cheetos
  • @LoBoToM81
    This channel is absolutely THE BEST science channel. Not only on YT but in general. I'm a primary school teacher from Poland and the amount of facts and curiosities I get from here and transfer into teaching physics, chemistry and even English is astonishing. Thank you.
  • @Amor_24
    I had a fun watch, definitely amazing to think about! I've been fascinated with numbers and problems since grade school and has been thinking about problems with patterns like this ever since. Not that I am any good at it nor am I sure when trying to come up with formulas based on these patterns. And sometimes, I tend to simplify these kind of problems based on what they look at. With that, I also think there is no odd perfect number for the fact that these perfect numbers we currently have all have the factor "2" which obviously makes it divisible by 2.
  • Finding perfect numbers is one of the first algorithm assignments you get in a computer Science degree. I never knew it was such an old idea.
  • @VintageBlacklist
    I have a research project due tomorrow and I was really looking for something distracting. My procrastination thanks you.
  • Congrats on making such a topic so enjoyable and interesting throughout the whole video. Wow!
  • @Wunba
    They lowkey tricked me with the outro at 16:25 I was so disappointed for a second 😂