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Could someone elaborate on why this is interesting? The linked page doesn't have much context.
Was featured on HN earlier: https://news.ycombinator.com/item?id=19492091
Lot of context there.
This is a great announcement; it reminds me of the legendary story of Frank Nelson Cole wordlessly announcing his factorization of 2^67 - 1: https://en.m.wikipedia.org/wiki/Frank_Nelson_Cole
In Python >>> (-80538738812075974)**3 + 80435758145817515**3 + 12602123297335631**3 42
scala> BigInt("-80538738812075974").pow(3) + BigInt("80435758145817515").pow(3) + BigInt("12602123297335631").pow(3)
res0: scala.math.BigInt = 42If I copy and paste this formula to Google, I get a different result
I must be missing something. Why is this significant?
Mathematicians are interested in which natural numbers k can be expressed as a sum of three cubes. Prior to this year, it had been established that this is possible for all k 33, 42, 114, 165, 390, 579, 627, 633, 732, 795, 906, 921, 975. Earlier this year a solution for k=33 was found [1], so 42 was the next unknown value. [1] Brooker, A., "CRACKING THE PROBLEM WITH 33", https://people.maths.bris.ac.uk/~maarb/papers/…
Why?
See also https://twitter.com/robinhouston/status/1169877007045296128 . I was prompted the twitter link has been submitted but wasn't able to find it. Edit: And apologies for using unicode ㊷ in the title, the ascii 42 was removed from the title after initial submission.
Could someone elaborate on why this is interesting? The linked page doesn't have much context.
It is an open question as to whether every integer not equal to 4 or 5 modulo 9 is the sum of three cubes, although it is suspected to be true. https://en.wikipedia.org/wiki/Sums_of_three_cubes#Computatio... 33 and 42 were known to be exceptions of all sums less than 100 for which solutions were found, until recently. 42 was the most recent to fall.
Why do we care if every integer not equal to 4 or 5 modulo 9 is the sum of three cubes? Just for fun?