# Step By Step Calculus » 2.0 - History and Applications

History and Applications
The discovery of irrational numbers is generally credited to Hippasus of Metapontum. He studied under Pythagoras, and showed that the square root of two is irrational. Unfortunately for him, his fellow Pythagoreans believed all numbers could be expressed as the ratio of two integers. According to legend, the discovery was made on a boat, and his fellows’ belief in the rationality of all numbers was so staunch that they threw him into the sea.
Euclid, aside from developing his algorithm for finding the greatest common divisor (GCD) of two numbers, wrote the Elements in 300 B.C., a series of thirteen books that helped lay the foundations for modern logic, mathematics and the sciences. In fact, the form of geometry most commonly taught is properly known as Euclidean Geometry, based on the content of the Elements.
People often view the study of numbers as studying a branch of pure mathematics. However, with the advent of computers, people are finding numbers in an increasing number of practical applications, such as in cryptography, random number generation, and coding theory.
Along with his work in logic and algebra, Augustus DeMorgan introduced the term mathematical induction in the mid 1800’s, and wrote a sixth of the articles in an encyclopedia called the Penny Cyclopedia. His birth year can be found by solving a problem that he himself proposed: “I was xx years old in the year x^2x^2”. This problem cannot be uniquely determined unless one accounts for the fact that he was born in the 19th-century. The solution to this problem is left as an exercise.