Algebraic geometry and the ongoing unification of mathematics: explaining Deligne to a broad audience (Q389878)

At the Abel Prize award ceremony held at the University Aula in Oslo, there were several lectures including the author's ``Science Lecture'', which was intended for a broad audience. The present article is a short note where he explains what he talked in the lecture. He focuses on a viewpoint that ``an important aspect of the discovery of Mathematics is the dramatic unexpected connection,\dots'' First he takes up the issue of Pythagorean triples, which indicates the link between geometry and arithmetic, thereafter he proceeds to the Mordell Conjecture, which he explains as the statement that ``if there is more than one hole (of the corresponding Riemann surface), then there can only be a finite number of rational solutions.'' Finally he arrives at the Weil Conjectures, which say, in his own words, ``the holes of different dimensions have essentially exactly the same information as the solutions in finite extensions of \(\mathbb{Z}/p\),\dots'' He concludes the article by saying that ``The Weil Conjectures exemplify the unity of Mathematics and the call nature makes to us to understand Mathematics from a broad enough vantage point that we can see it as a single, highly interconnected subject.''