Diophantus Assignment 1. Little is known about the life of the Greek mathematician Diophantus. However, his work led to one of the greatest mathematical challenges of all time, Fermat's last theorem. He was born in Alexandria somewhere between 200 and 214 BC. Alexandria was the center of Greek culture and knowledge and Diophantus belonged to the ‘Silver Age’ of Alexandria. Altough little is known about his life, according to his riddle, he got married when he was 33, had a son who lived for 42 years and was 84 when he died. During his life, Diophantus wrote the Arithmetica, the Porismata, the Moriastica, and On Polygonal Numbers. Arithmetica originally had thirteen books, out of which we only have six. It is a collection of problems giving numerical solutions of both determinate and indeterminate equations. The information from these books tell us that Diophantus studied from Babylonian teachers. Porismata is a collection of lemmas, although the book is entirely lost. One such lemma is that the difference of the cubes of two rational numbers is equal to the sum of the cubes of two other rational numbers. The Moriastica is thought to have treated computation with fractions. Only fragments of Diophantus' books On Polygonal Numbers, a topic of great interest to Pythagoras and his followers, have survived. Diophantus is often called “the Father of Algebra" because he contributed greatly to number theory, mathematical notation, and because Arithmetica contains the earliest known use of syncopated notation. 2. Fermat’s solution was called his "Last Theorem”:
"If an integer n is greater than 2, then an + bn = cn has no solutions in non-zero integers a, b, and c. I have a truly marvelous proof of this proposition which this margin is too narrow to contain." 3. British mathematician Andrew J. Wiles was born April 11, 1953, in Cambridge, England, where his father was a professor of theology. In the Cambridge library, ten-year-old Wiles first came across Fermat's Last Theorem, and it intrigued him. He worked on it in his teens before realizing it was far more complex a challenge than he had originally assumed. After earning an undergraduate degree from Oxford University in 1974, Wiles went on to earn graduate degrees in math from Clare College, Cambridge, and specialized in elliptical curves. In 1982, two years after he earned his Ph.D., he began teaching at Princeton University in New Jersey. Starting in the summer of 1986 he realized a limited form of a theorem might be in reach. Wiles began conducting research in secrecy. In 1993, he presented his proof to the public for the first time at a conference in Cambridge. In August 1993 it turned out that the proof contained a gap. Wiles tried to fill in this gap, but found out that the error he had made was significant. The widely accepted version of the proof was released by Andrew Wiles in September 1994, and published in 1995.