Explore the mathematics of privacy in this 40-minute lecture by Cynthia Dwork, presented by the International Mathematical Union. Delve into fundamental concepts such as the Law of Information Reconstruction and Privacy Preserving Data Analysis. Examine the principles of Differential Privacy, including its properties, the Laplace Mechanism, and the Privacy Loss Random Variable. Investigate advanced topics like the Advanced Composition Theorem, Gaussian Mechanism, and Concentrated Differential Privacy. Learn about Privacy Amplification via Subsampling and optimized private gradient descent techniques. Engage with creative privacy accounting thought experiments and explore the concept of amplification by secrecy of the journey. Conclude by addressing challenges and crucial definitions in the field of privacy mathematics.