Abstract:
I will try to share a glimpse of this strange unification of many different ideas. This talk is aimed at a general audience, and no particular background will be assumed.

When we look carefully at nature, we can discover surprising coincidences, which suggest deeper underlying structure. The centrality of mathematics comes in part from the fact that seemingly unrelated ideas are often unified by some grand theory, which is far more powerful than the sum of its parts. Mathematics is most exciting when different ideas come together unexpectedly to give a new point of view. This is typified in algebraic geometry, and in the work of Deligne in particular, which brings together many themes in mathematics, including geometry, number, shape (topology), algebra, and more. This magic is the reason I became an algebraic geometer. For example, the theory of Pythagorean triples (such as ) connects geometry to the theory of numbers by way of algebra. This ancient example grows up to be the Weil conjectures, a wondrous prediction whose proof was finally completed by Deligne.

This lecture was given at The University of Oslo, May 22, 2013 and was part of the Abel Prize Lectures in connection with the Abel Prize Week celebrations.

Program for the Abel Lectures 2013
1. "Hidden symmetries of algebraic varieties" by Abel Laureate 2013, professor Pierre Deligne, Institute for Advanced Study, Princeton
2. "Life Over Finite Fields" by professor Nicholas Katz, Princeton University
3. "Mixed Hodge structures and the topology of algebraic varieties" by professor Claire Voisin, École Polytechnique and CNRS
4. "Algebraic geometry and the ongoing unification of mathematics", a science lecture by professor Ravi Vakil, Stanford University