Diophantine Equations II

Diophantine Equation Theory is the branch of number theory that investigates the whole or rational solutions of polynomial equations, for example, 2x + 4y = 5, y² - x³ = -2 or x² + y² = z². The name Diophantine Equations is a tribute to one of the greatest algebraists of ancient Greece, Diophantus of Alexandria, who formulated and solved many of these equations. Diophantus's work served as a source of inspiration for many mathematicians, including the French mathematician Pierre de Fermat (1601-1665). I will use some passages from the MOST FAMOUS MATH STORY you find at

Pierre de Fermat was a Counselor of the Chamber of Requirements of Toulouse, France, 1631. His responsibility was linked to the conviction of people to death at the stake and therefore could not have many friendships. In his free time he devoted himself to mathematics and became known as the "Prince of Amateurs" for discovering the laws of probability, the foundations of differential calculus before Newton and Leibniz, developing analytic geometry before Descartes, and difficult and elegant theorems. about whole numbers. However Fermat became interested in the subject after reading the 1621 edition of Bachet's work: "Arithmetica de Diophantus", which consisted of material left over from Diophantus's work. Fermat began several areas of modern Number Theory, including Diophantine Analysis, and formulated the most famous problem of Number Theory and Mathematics that challenged generations of mathematicians. This battle lasted about 350 years and influenced virtually all of mathematics. Fermat simply stated that he had a demonstration for the following generalization of the Pythagorean Suits: if n≥3, the equation xⁿ + yⁿ = zⁿ does not allow nonzero integer solutions. But the demo “Didn't fit the margin of your copy of Diophantus's Arithmetica” where Fermat recorded this statement. Discovering the “Fermat demonstration” became the most famous math challenge and became known as the "Fermat's Last Theorem". It seemed so simple, but the great mathematicians of the last four centuries could not solve it before 1994.

Fermat was especially pleased to embarrass the mathematicians of his day, particularly the English. Fate wanted an Englishman, Andrew Wiles, to be chosen to put an end to such provocations. The most terrible of them, "Fermat's Last Theorem", was demonstrated in 1994 by the English mathematician Andrew Wiles. A leading mathematician, professor at Cambridge, England, named John Coates, who was the adviser to Andrew Wiles' doctoral thesis, compared this to the discovery that the atom is divisible and the discovery of the structure of DNA.

For Andrew Wiles, the problem has become an obsession since he was 10 when he first met Eric Temple Bell's book, "The Last Problem." Wiles thought it had to be him to solve it.

The story of the details of how Fermat's statement became the most terrible provocation is masterfully told by Simon Singh in his book "Fermat's Last Theorem" released by Record publisher here in Brazil. This book was the bestselling book in the world about "Fermat's Last Theorem" because it brilliantly recounts fun, dramatic and even tragic episodes of the history of mathematics to describe to the public the most famous achievement of mathematics.

In the next columns we will tell how the efforts and contributions of mathematicians from around the world were instrumental in Wiles's demonstration, and how chance, or chaos, has always been intensely present in the course of this mathematical epic.

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