Explore a comprehensive lecture on Jean Bourgain's groundbreaking mathematical contributions, delivered by renowned mathematicians Peter Sarnak and Avi Wigderson. Delve into key topics such as the Vinogradov Mean Value Theorem, Fractal Uncertainty Principle, and Schrödinger Equation. Gain insights into Bourgain's innovative approaches to the Uniqueness Theorem, Montgomery's conjecture, and the Sum product theorem. Discover the impact of his work on randomness extraction and the relationship between points and lines in mathematics. Honor Bourgain's enduring legacy and his profound influence on various mathematical fields through this in-depth presentation.