I'm self-learning about Model Theory and I just got to the proof of Hilbert's 17th Problem via Model Theory of Real Closed Fields. The 17th problem asks to show that a non-negative rational function must be the sum of squares of rational functions.
It seems to me that I lack a strong enough understanding of the context of the problem to understand its significance. Why did Hilbert think it was important enough to include it as one of his 23 problems?