ON FERMAT'S LAST THEOREM
We live in an age in which the depressing dimensions of the human condition in their myriad manifestations are reflected day in and day our in the media. Newspapers and magazines are filled with reports of crime and war, of cheating and hatred, of drug and disease. The TV screen, whether for entertainment or as news, often offers us violent, tragic, or obscene images. Such are the impressions of the human race formed in the impressionable minds of our young. In their professed commitment to presenting the news and inspired by blatant greed, media manipulators blow up the gruesome and the gory, the sleazy and the sordid, for these seem to sell more. They are indifferent the impact of parading such truths on the emerging generation.
An item like the discovery of a new elementary particle or the proof of a mathematical theorem cannot have the same claim for headline on the first page as deception in a fund-raising campaign, a verdict of guilt in a murder trial, or the career-transition in the life of a midnight buffoon. So it was good to see in bold-faced heading -even if it was only on the second page- a report on a major ripple in the world of mathematics. We need to be reminded now and again that while the world goes wild with its atrocities, sick with its fanaticism, and helpless with its countless problems, there are men and women who still compose music and write poetry, explore the universe and do mathematics for the sheer joy of it all.
Seeing the prominence given to the report that Fermat's Last theorem had finally been proved, an economist friend of mine called me up to ask what the fuss was all about. After listening to my spirited discourse on the significance of the achievement in the world of mathematics, he sighed plaintively, unconvinced that an abstruse proof about some puzzling property of numbers deserved all that attention.
I asked him if he thought that the split between Charles and Di, or the honeymoon of Naruhito and Masako should demand our attention more than the conquest by the human mind of a challenge that has taunted the greatest of mathematicians for more than three and a half centuries. "But this is not as interesting," he replied. Ruskin talked about books of the hour and books of the ages. Likewise, there are also news of the hour and news of the ages. While the former is what we are inundated with, the latter is seldom given much prominence.
Yes, scientific discoveries, artistic achievements, literary creations, and selfless acts do find a place in Sunday magazines. But I have often wondered how we would perceive the world if these were the headlines in our papers, while bank robberies and briberies, political scandals and wasteful wars were relegated to small prints in later pages. Would the public be any less informed as a result? Perhaps not, and it is even possible that the thoughts and interests of people, young and old, will be more attuned to the nobler elements of the human potential.
This is not the place to discuss Fermat's Last Theorem, but the mere story of how it arose could fascinate and inspire the young. Suffice it to say that Pierre de Fermat (1601-1665) was not even a professional mathematician. He wrote poetry in French and Spanish, was a scholar in Greek and Latin, and served as councilor to the King of France. Yet, he is remembered as one of the creators of the mathematical theory of probability and the proponent of a fundamental principle governing the physical universe, and as a curious contributor to the theory of numbers. It was in this last context that he scribbled in the margins of a book that he had discovered a truly marvelous demonstration of an apparently simple property of numbers (integers). But generations of the most prolific creators in mathematics have been baffled by the result, unable to prove it with rigor. [The interested reader with only minimum familiarity with arithmetic can find out about the theorem from a book in the local library.]
And now, if the report be true, the theorem has been proved to be correct. Not that anybody doubted its veracity, but proof in mathematics is like tasting in kitchen-creations: by looking at an elegantly served platter, we may be convinced that it is delicious, but we need to taste it before we can be absolutely certain.
So, to recall my friend's question, "why all this fuss about the proof?", I say that proving Fermat's Last Theorem is the equivalent of the hoisting a flag on the peak of a mountain defiant thus far. Not all of us may reach the mountain top, but we can all share in the excitement. It is a triumph of the human spirit, and we can all rejoice in the achievement. Problems and politicians come and go, fights and frustrations arise and abate, but the positive landmarks left by human minds and efforts, from the Vedas and the Pyramids to sublime symphonies and the unveiling of the secrets of the physical world and of the magic of numbers: these and the like will remain as our lofty legacies for as long as our species treads this planet. These too deserve frequent and prominent mention in the media.