Algebraic Geometry might solve the P vs. NP challenge

When i first read the cover article in the September Communications of the ACM, I had the feeling that this article was not ordinary and would raise much attention among computer science specialists and even the curious average reader. The subject of the article was very amazing and the reader could not resist the tempting Idea to wonder about this beautiful -Still Not Found- World of P=NP.
The article did Indeed took its promise and more than 10 times the usual number of readers downloaded this popular article. This success was also quoted by NY Times science and technology reporter John Markoff who highlights the allure of the P vs. NP challenge. He reports that if this grand challenge for theoretical computer science and complexity theory is proven, some of the hardest computing challenges may collapse, leading to burst of new economic and technological productivity.
Another reaction to the article was by Communications Editor in Chief Moshe Vardi. He predicts that to investigate the P vs. NP problem, computer scientists may have to start learning a very difficult mathematical field known as algebraic geometry, which offers some hope for proving or disproving the problem.