Hilbert-Waring Theorem/Particular Cases/2/Mistake

Source Work

1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.):

Waring's problem


Mistake

Thus, if $n = 2$ then $N = 4$; i.e. any positive integer can be expressed by a sum of up to four squared terms -- a result proved by Euler.


Correction

While it is true that Euler did indeed publish such a proof (in $1780$, having written it in $1772$), the fact is that Joseph Louis Lagrange got there first with his own proof in $1770$.


These errors had both been corrected by the time of the publication of the $4$th edition.


Sources

  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Waring's problem
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