42 is the new 33 - Numberphile

Описание: 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:    • The Uncracked Problem with 33 - Numberphile  
The 74 cracked video:    • 74 is cracked - Numberphile  
Casting out nines:    • Casting Out Nines - Numberphile  

Andrew Booker's webpage: http://www.bristol.ac.uk/maths/people...

Some of the papers we referenced...
Undecidability in number theory: http://www-math.mit.edu/~poonen/paper...
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/~maar...

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/outr...

And support from Math For America - https://www.mathforamerica.org/

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