Fermat's Last Theorem
We often wonder what it is about humans that sets us apart from every other species of life on Earth. We can communicate with each other in languages more complex than any other life form; we can invent tools and machines that make life for us longer and easier. We have the stunning ability to prove the truth with our minds—and we do this through reason. The 18th-century Age of Enlightenment sealed the deal for reason, establishing it as the highest source of authority for mankind. If there is any one trait that sets us apart from all other life on Earth, it has to be our impeccable ability to reason: the ability to conclude that if all humans are mortal, and Mr. Stroh is a human, then Mr. Stroh must be mortal. The foundations for reasoning are the rules of logic—and so too are the foundations for mathematics.
Fermat’s Last Theorem states that equation
Fermat’s Last Theorem itself may not have any tangible effects on human life, but it is noteworthy because it is beautiful, because it epitomizes what humans can do, exemplifying the power of the human mind. A truly beautiful mathematical proof is one that uses the rules of logic to reason the truth of an assertion. We spend endless hours of our time on Earth in humble pursuit of the truth—in science, when we design experiments to theorize the causes of natural phenomena; in court, when we hold a trial to decide whether an accused individual is guilty of a crime. But only in mathematics, can the truth be unequivocally known through reason alone. Once we have proven something in mathematics, we know it to be the truth. In this sense, mathematics is not only supported by reason—mathematics is reason, mathematics is rationality. It is using the human mind alone to ascertain the truth beyond all doubt.
Fermat’s Last Theorem states that equation
xn + yn = znwill have no whole number solutions when n > 2. The theorem was proposed by French mathematician Pierre de Fermat in 1637, who stated in the margin of his copy of Arithmetica that he had a “marvelous proof” for the theorem, but would not share it because the margin was too small to fit it. Unfortunately, he died before he could write it down. Countless mathematicians following Fermat tried to rediscover his proof. Decades passed, then centuries. Finally, in the last decade of the 20th century, after over three centuries since Fermat first proposed his Last Theorem, British mathematician Andrew Wiles successfully proved it.
Fermat’s Last Theorem itself may not have any tangible effects on human life, but it is noteworthy because it is beautiful, because it epitomizes what humans can do, exemplifying the power of the human mind. A truly beautiful mathematical proof is one that uses the rules of logic to reason the truth of an assertion. We spend endless hours of our time on Earth in humble pursuit of the truth—in science, when we design experiments to theorize the causes of natural phenomena; in court, when we hold a trial to decide whether an accused individual is guilty of a crime. But only in mathematics, can the truth be unequivocally known through reason alone. Once we have proven something in mathematics, we know it to be the truth. In this sense, mathematics is not only supported by reason—mathematics is reason, mathematics is rationality. It is using the human mind alone to ascertain the truth beyond all doubt.