24 years ago today Andrew Wiles announced “I think I’ll stop here” and the rest, as they say, dear mathematicians, is history:
...Links for math buffs and number-luvin' laymen
“The joke about the mathematics professor who gave a test consisting of four problems is apt. The first three problems required proofs of theorems and the last one was a statement prefaced with the directions ‘prove or disprove.’ One student toiled for a while and then came up to the professor’s desk and asked, ‘On that last problem, do you want me to prove it or disprove it?’ The professor responded, ‘Whichever is the right thing to do.’ ‘Oh,’ replied the student, ‘I can do either one. I was just asking which one you preferred.’ The interchange, of course, would not be a joke if the subject were history or literature.”
"Mathematicians are finite, flawed beings who spend their lives trying to understand the infinite and perfect. That kind of thing is bound to result in problems and misunderstandings. Trends and fashion, politics and pig-headedness all affect the lurching progress of mathematical knowledge. None of them, however, affect the validity of mathematical knowledge. 'There are many ways,' [Edward] Rothstein writes, 'to show that the ratio between the circumference of any any circle and its diameter is always the same, a number known as pi. The priests, farmers, and builders who first used that ratio may have had various intentions and goals. And the ratio may be given names like pi or zed or Milwaukee, for that matter. But the number and its meaning are unaffected by cultural apparatus and influence.'"
“The day when the light dawned… I suddenly understood epsilons and limits, it was all clear, it was all beautiful, it was all exciting… It all clicked and fell into place. I still had everything in the world to learn, but nothing was going to stop me from learning it. I just knew I could. I had become a mathematician.”
“Education has made all the difference for me. Mathematics taught me to reason logically and to understand numbers, tables, charts, and calculations as second nature. Physics, chemistry, astronomy, and biology revealed the wonders of the world, and showed me how to build models and theories to describe and to predict. This paid off for me in both gambling and investing.
“Education builds software for your brain. When you’re born, think of yourself as a computer with a basic operating system and not much else. Learning is like adding programs, big and small, to this computer, from drawing a face to riding a bicycle to reading to mastering calculus. You will use these programs to make your way in the world. Much of what I’ve learned came from schools and teachers. Even more valuable, I learned at an early age to teach myself. This paid off later on because there weren’t any courses in how to beat blackjack, build a computer for roulette. or launch a market-neutral hedge fund.”
“The importance of the unattained destination is illustrated by the strange reaction many mathematicians have when a great theorem is finally proved. Just as there is a sense of sadness when you finish a great novel, the closure of a mathematical quest can have its own sense of melancholy. I think we were enjoying the challenge of Fermat’s equations so much that there was a sense of depression mixed with the elation that greeted Andrew Wiles’s solution of this 350-year-old enigma.”
“To [Joel] Spencer and many other mathematicians, Erdös was a modern version of a medieval mendicant monk. Erdös is frequently called without a trace of irony, a saint. Indeed, there was something saintly in Erdös’s generosity, in his honesty and his support of the rights of the individual. But the essence of the saintliness his friends speak of was his total devotion to the mathematical pursuit of pure beauty. Erdös often said that ‘property is a nuisance.’ In fact, to Erdös all aspects of life — jobs, money, property, and intimate personal attachments — that interfered with his devotion to mathematics were a nuisance to be avoided. While few people would choose to emulate him, Erdös’s life was an example cherished by many.”
“Numbers are fine and useful things, I would say in that alternate universe, but we must be careful not to be smitten with them. ‘Not everything that counts can be counted,’ goes a famous saying, ‘and not everything that can be counted counts.’ In this era of computers and algorithms, some social scientists have forgotten that. As the cultural critic Leon Wieseltier put it in the New York Times, ‘There are ‘metrics’ for phenomena that cannot be metrically measured. Numerical values are assigned to things that cannot be captured by numbers.’ This naive positivism is running rampant, taking over domains it has no business being in. As Wieseltier poetically put it, ‘Where wisdom once was, quantification will now be.’”