A Historical Note on the Pythagorean Theorem, Part 1

(Editorial Note: The following entry continues JPedia's Music Week with a note on maths, the universal music.)

“Striking Cuba with 100% effectiveness would have been like planning to disprove Fermat’s Last Theorem.”

-John F. Kennedy

Pierre de Fermat wrote in his “Arithmetica of Diophantus” that it was unfeasible to break any powered number into the sum of two like-powered integers (i.e., a^x +b^x can never equal c^x). This proof by converse inflection remains one of the most potent statements ever made in the mathematical world. Like Galileo, Fermat dared the greatest minds of the ancient world not to prove him correct, but to prove him incorrect. Just as it took Christopher Columbus a thousand years after the death of Galileo to prove him wrong, it took the birth of Pythagoras of Samos to prove Fermat a fool.

Born in 580 B.C.E. in the eastern Aegean, Pythagoras was the Einstein of his day, teaching himself to read Greek and mastering its numerical system by age five. Traveling from Greece to Egypt to modern-day Spain, he earned a following known as Pythagoreanists and was the first recorded “philosopher.” During these itinerant years, an unnamed student presented him with Fermat’s Last Theorem. At age 15, Pythagoras dedicated his life to proving this theory wrong. Within a week, using the simple equations a⁰ + b⁰ =c⁰ and a¹ + b¹ =c¹, he presented his accomplishment to the public square in mockery of Fermat, but mathematicians instead laughed at Pythagoras for making such an oblivious, childish statement. He hypothesized that there were more and that he just needed time. Shamed into seclusion, Pythagoras was discovered in a temple 20 years later reciting triples and saying “δεν υπάρχουν πιο” (“there are no more”). In just two short years, he had allegedly proven so many 3-number combinations that he had gone mad. Moving on to the next local integer, 3, he spent the latter 18 years falling deeper and deeper into madness. . .