[math-fun] Spiral of Fermat?

I ran across an article in The Humboldt Beacon (a newspaper published in Fortuna, CA) about a botanical garden that's being created at College of the Redwoods. Part of the garden is a double spiral walkway, in the shape of the Spiral of Fermat. (From a google search, I see that its polar equation is r^2 = theta.) The article has this paragraph, which I don't understand: Fermat first discussed his spiral equation in 1636, but he did not take the time to write the proof to it. The proof was developed over a number of years and finally confirmed in 2003. Does anyone know what this is about? What is there that needs to be proved about the spiral? Dean Hickerson dean@math.ucdavis.edu