While searching for more references for the new Wikipedia article (https://en.wikipedia.org/wiki/Sums_of_three_cubes) I found a horrible mistake related to this problem in Wolfram's _A New Kind of Science_, p. 789 (https://www.wolframscience.com/nks/p789--implications-for-mathematics-and-its-foundations/). Wolfram says that the smallest solution to \(x^3+y^3+z^3=2\) is the known sporadic one,
But the parametric solution has many that are smaller: \((1,1,0)\), \((7,-5,-6)\), \((49,-47,-24)\), etc.
@11011110 also z is not negative according to Wolfram there. A typo of course but still.
A Mastodon instance for maths people. The kind of people who make \(\pi z^2 \times a\) jokes.
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