42 is the new 33 - Numberphile

42 is the only remaining (eligible) number below 100 which has not been represented as the sum of three cubes... 33 was cracked by Andrew Booker from the University of Bristol. More links & stuff in full description below ↓↓↓ The original 33 video: https://youtu.be/wymmCdLdPvM The 74 cracked video: https://youtu.be/_-M_3oV75Lw Casting out nines: https://youtu.be/FlndIiQa20o Andrew Booker's webpage: http://www.bristol.ac.uk/maths/people/andrew-r-booker/overview.html Some of the papers we referenced... Undecidability in number theory: http://www-math.mit.edu/~poonen/papers/h10_notices.pdf The density of zeros of forms for which weak approximation fails: http://eprints.maths.ox.ac.uk/156/ Solutions of the Diophantine Equation: x^3+y^3+z^3=k: https://doi.org/10.1112/jlms/s1-30.1.101 Solutions of the Diophantine Equation x^3 + y^3 = z^3 - d: https://www.jstor.org/stable/2003763 Newer sums of three cubes: https://arxiv.org/abs/1604.07746 Early write-up of Booker's work: https://people.maths.bris.ac.uk/~maarb/papers/cubesv1.pdf Discuss this video on reddit: https://redd.it/b0ax2o Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. https://www.simonsfoundation.org/outreach/science-sandbox/ And support from Math For America - https://www.mathforamerica.org/ NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Videos by Brady Haran Patreon: http://www.patreon.com/numberphile Numberphile T-Shirts: https://teespring.com/stores/numberphile Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9