video thumbnail 13:39
42 is the new 33 - Numberphile

2019-03-12

[public] 666K views, 17.8K likes, 179 dislikes audio only

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: /youtube/video/wymmCdLdPvM

The 74 cracked video: /youtube/video/_-M_3oV75Lw

Casting out nines: /youtube/video/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


The Uncracked Problem with 33 - Numberphile by Numberphile
/youtube/video/wymmCdLdPvM
74 is cracked - Numberphile by Numberphile
/youtube/video/_-M_3oV75Lw
74 is cracked - Numberphile 512,322 views
/youtube/video/_-M_3oV75Lw
The Uncracked Problem with 33 - Numberphile 1,873,577 views
/youtube/video/wymmCdLdPvM