Data privacy and cryptography are critical components in the realm of information security, ensuring the protection of sensitive information from unauthorized access and breaches. This paper explores various mathematical approaches utilized in the field of data privacy and cryptography. It delves into classical and modern cryptographic techniques, including symmetric and asymmetric encryption, hash functions, and emerging methods such as homomorphic encryption and zero-knowledge proofs. The study also examines the role of mathematical frameworks like number theory, algebra, and combinatorics in developing robust cryptographic algorithms. Furthermore, the paper discusses the challenges and future directions in the application of mathematics to enhance data privacy and security.