Definition:Hilbert 23/17

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Hilbert $23$: Problem $17$

Definite Rational Function as Quotient of Sums of Squares

Expression of definite rational function as quotient of sums of squares.

Definite Rational Function as Quotient of Sums of Squares

Historical Note

The Hilbert 23 were delivered by David Hilbert in a famous address at Paris in $1900$.

He considered them to be the oustanding challenges to mathematicians in the future.


There was originally going to be a $24$th problem, on a criterion for simplicity and general methods in proof theory, but Hilbert decided not to include it, as it was (like numbers $4$, $6$, $16$ and $23$) too vague to ever be described as "solved".