Mathematics is probably one of the most underestimated sciences. Everywhere in our lives, mathematics powers our computers, flies our planes, and protects our information. But for so much of our lives, very few people can say they know how it's done, how RSA encryption protects their email, or even that 21 squared is 441, without engaging in tedious calculations mental or look for their calculator. Contrary to popular belief, mathematics has a wide range of useful applications. Those who would ask when they would need algebra, linear algebra and calculus are widely used in programming and computer engineering. The fact is that mathematics is integrated into almost every profession and every aspect of your life. During World War II, number theory, a highly theoretical branch of mathematics focused on the properties of integers, found new applications in the field of cryptography. The Allies and Axis sent coded messages by air to which both sides had access. Obviously, they didn't want the other party to know what they were doing, so they both sent coded messages. Mathematics played a vital role in deciphering these codes, particularly the enigmatic code used primarily by Nazi Germany. The problem with a coded message, however, is that historically, a code had to be pre-established with some sort of decryption key, between the two parties wishing to communicate. This led to the field of public key cryptography. Imagine two people want to send messages through the postal service, but want to make sure no one reads them. Person A puts a padlock on their package, to which Person A and Person B both have the key. This allows person B to remove the bottom middle of the paper......known for his creation of the Mandelbrot set fractal, which is also shown in appendix a, he created the fractal at l using computer software. Fractals can be used to store images. The idea is to take a few colored pixels and create a fractal generating program that would produce the image. Storing a simple fractal generation program and a few pixels would be infinitely more efficient than storing an entire .JPG image. In conclusion, mathematics can and does have many applications outside of theory. Whether it's playing with probability by counting cards or analyzing a new road plan, mathematics has applications. Mathematics is also an integral part of daily life, it protects our data and enables the operation of electronics and computers that allow us to live our way of life. Whether we like it or not, mathematics is an integral part of our lives.