Pierre de Fermat was born in in the first decade of the 17th century. He was an amateur mathematician, but one who became very famous for his “Last Theorem”: no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two. This deceptively simple theorem, eluded a formal proof from the most gifted mathematical geniuses for over three centuries. The theorem was not proven until September 1994, when Andrew Wiles finally achieved his lifelong ambition and proved it.
Once a mathematical theorem is proved, it becomes like a law of nature. Plants are green, the sun is yellow, the square of the hypotenuse of a right-angled triangle is the sum of the squares of its two sides, and so on. There is no mystery about it, it doesn’t engage our minds any longer because there is nothing to engage, only to learn. Once you study it sufficiently to learn it, there is nothing else left to learn. Fermat’s challenge to humanity lasted over three centuries, but it is a challenge no longer.
Wolfgang Amadeus Mozart was born in January 1756. He is world famous for many of his compositions. Over 250 years later, his compositions still continue to baffle listeners. We can study a composition and learn it, but it will continue to engage us and we will find there is yet more to learn. Our learning of great compositions is never complete.
Mathematical truths are eternal and timeless. But the genius mathematicians who discover them for the first time are distanced from that truth. The beauty of the truth does not belong to the discoverer, it belongs to the universe.
Musical compositions are eternal and timeless too. But the genius composer who creates them remains an integral part of them. The beauty of the truth in great compositions belongs as much to the composer as to the universe.
Mathematical beauty is innate to the Universe and gifted to mankind. Musical beauty is created by man and gifted to the Universe.