Mathematics is essential to computer science and information technology in several ways: 1) Early tools like the abacus helped humans perform calculations, while analytical engines designed by Charles Babbage introduced the concept of the central processing unit that powers modern computers. 2) Computers understand binary language and use logic and arithmetic operations like addition, subtraction, multiplication and division to process data and perform comparisons. 3) Mathematical concepts like binary representation, IP addressing in decimal or hexadecimal, and cryptography techniques using permutations and combinations are crucial for data storage, transmission, and security.