In 1900, at the second International Congress of Mathematicians, the German mathematician David Hilbert presented a list of twenty-three problems in Paris that had so far defied mathematicians. These challenges did indeed shape the course of 20th century mathematics. The seventeenth problem asked whether "every rational function that takes only positive values is a sum of squares of rational functions." To put it simply, for the purposes of this article, a rational function is a map from ? to ? that assigns to the variable x an expression involving only the "four elementary operations."
Thus, f (x) = (3x + 7 – 1) / (x 2– 3x + 1) is a rational function.
Hilbert's seventeenth problem was solved in 1927 by Emil Artin in the special case of "real closed fields." It subsequently gave rise to some surprising developments, including the Hasse–Minkowski theorem, often called the local–global principle. This principle seeks to reconstruct information about a global object from information about associated local objects, which is assumed to be easier to obtain.
And this is where self-driving cars come in…
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