Fermat's Last Theorem Quotes

God exists since mathematics is consistent, and the Devil exists since we cannot prove it.

Carnal embrace is sexual congress, which is the insertion of the male genital organ into the female genital organ for purposes of procreation and pleasure. Fermat’s last theorem, by contrast, asserts that when x, y and z are whole numbers each raised to power of n, the sum of the first two can never equal the third when n is greater than 2.

Maths is one of the purest forms of thought, and to outsiders mathematicians may seem almost other-worldly.

There are lots of things I don't understand - say, the latest debates over whether neutrinos have mass or the way that Fermat's last theorem was (apparently) proven recently. But from 50 years in this game, I have learned two things: (1) I can ask friends who work in these areas to explain it to me at a level that I can understand, and they can do so, without particular difficulty; (2) if I'm interested, I can proceed to learn more so that I will come to understand it. Now Derrida, Lacan, Lyotard, Kristeva, etc. -- even Foucault, whom I knew and liked, and who was somewhat different from the rest -- write things that I also don't understand, but (1) and (2) don't hold: no one who says they do understand can explain it to me and I haven't a clue as to how to proceed to overcome my failures. That leaves one of two possibilities: (a) some new advance in intellectual life has been made, perhaps some sudden genetic mutation, which has created a form of "theory" that is beyond quantum theory, topology, etc., in depth and profundity; or (b) ... I won't spell it out.

Occasionally, I get a letter from someone who is in “contact” with extraterrestrials. I am invited to “ask them anything.” And so over the years I’ve prepared a little list of questions. The extraterrestrials are very advanced, remember. So I ask things like, “Please provide a short proof of Fermat’s Last Theorem.” Or the Goldbach Conjecture. And then I have to explain what these are, because extraterrestrials will not call it Fermat’s Last Theorem. So I write out the simple equation with the exponents. I never get an answer. On the other hand, if I ask something like “Should we be good?” I almost always get an answer.

I carried this problem around in my head basically the whole time. I would wake up with it first thing in the morning, I would be thinking about it all day, and I would be thinking about it when I went to sleep. Without distraction I would have the same thing going round and round in my mind. (Recalling the degree of focus and determination that eventually yielded the proof of Fermat's Last Theorem.)

Although this may seem a paradox, all exact science is dominated by the idea of approximation.

When people asked hilbert why he didn't prove Fermat's Last Theorem and win the Wolfskehl Prize, he said, "Why should I kill the goose that lays the golden egg?

Some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they're extremely hard to solve. There's no reason why these problems shouldn't be easy, and yet they turn out to be extremely intricate. [Fermat's] Last Theorem is the most beautiful example of this.

Scientific proof is inevitably fickle and shoddy. On the other hand mathematical proof is absolute and devoid of doubt.

Why does Alexander the Great never tell us about the exact location of his tomb, Fermat about his Last Theorem, John Wilkes Booth about the Lincoln assassination conspiracy, Hermann Göring about the Reichstag fire? Why don’t Sophocles, Democritus, and Aristarchus dictate their lost books?

Proof is what lies at the heart of maths, and is what marks it out from other sciences. Other sciences have hypotheses that are tested against experimental evidence until they fail, and are overtaken by new hypotheses. In maths, absolute proof is the goal, and once something is proved, it is proved forever, with no room for change.

Pascal was even convinced that he could use his theories to justify a belief in God. He stated that ‘the excitement that a gambler feels when making a bet is equal to the amount he might win multiplied by the probability of winning it’. He then argued that the possible prize of eternal happiness has an infinite value and that the probability of entering heaven by leading a virtuous life, no matter how small, is certainly finite. Therefore, according to Pascal’s definition, religion was a game of infinite excitement and one worth playing, because multiplying an infinite prize by a finite probability results in infinity.

An expert problem solver must be endowed with two incompatible qualities – a restless imagination and a patient pertinacity. Howard W. Eves

The Last Theorem is at the heart of an intriguing saga of courage, skulduggery, cunning, and tragedy, involving all the greatest heroes of mathematics.

The most famous Diophantine equation in history is the one known as Fermat's last Theorem, the celebrated statement by Pierre de Fermat (1601-55) that there are no whole number solutions to the equation x^n + y^n = z^n, where n is any number greater than 2. When n = 2, there are many solutions (in fact an infinite number). For instance, 3^2 + 4^2 = 5^2 (9 + 16 = 25); or 12^2 +5^2 = 13^2 (144 + 25 = 169). Miraculously, when we go from n = 2 to n = 3, there are no whole numbers x,y,z that satisfy x^3 + y^3 = z^3, and the same is true for any other value of n that is greater than 2. Appropriately, it was in the margin of the second book of Diophantus's Arithmetica, which Fermat was eagerly reading, that he wrote his extraordinary claim-one that took no fewer than 356 years to prove.

I looked at the food I had just finished preparing and then at my hands. Sautéed pork garnished with lemon, a salad, and a soft, yellow omelet. I studied the dishes, one by one. They were all perfectly ordinary, but they looked delicious—satisfying food at the end of a long day. I looked at my palms again, filled suddenly with an absurd sense of satisfaction, as though I has just solved Fermat's Last Theorem.

I looked at the food I had just finished preparing and then at my hands. Sautéed pork garnished with lemon, a salad, and a soft, yellow omelet. I studied the dishes, one by one. They were all perfectly ordinary, but they looked delicious—satisfying food at the end of a long day. I looked at my palms again, filled suddenly with an absurd sense of satisfaction, as though I has just solved Fermat's Last Theorem.

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. ‘Immortality’ may be a silly word, but probably a mathematician has the best chance of whatever it may mean. G.H. Hardy 23

The mathematician’s patterns, like the painter’s or the poet’s, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics. G.H. Hardy

The path, as the mystic poet Rumi writes, won’t appear until you start walking. William Herschel started walking, grinding mirrors, and reading astronomy-for-dummies books even though he had no idea he would discover Uranus. Andrew Wiles started walking when he picked up a book on Fermat’s last theorem as a teenager, not knowing where his curiosity might lead. Steve Squyres started walking in search of his blank canvas, even though he had no idea it would one day lead him to Mars. The secret is to start walking before you see a clear path. Start walking, even though there will be stuck wheels, broken drills, and exploding oxygen tanks ahead. Start walking because you can learn to walk backward if your wheel gets stuck or you can use duct tape to block catastrophe. Start walking, and as you become accustomed to walking, watch your fear of dark places disappear. Start walking because, as Newton’s first law goes, objects in motion tend to stay in motion—once you get going, you will keep going. Start walking because your small steps will eventually become giant leaps. Start walking, and if it helps, bring a bag of peanuts with you for good luck. Start walking, not because it’s easy, but because it’s hard. Start walking because it’s the only way forward.

What is the least number of weights that can be used on a set of scales to weigh any whole number of kilograms from 1 to 40?

prove that xn + yn = zn has no whole number solutions for n greater than 2.

The mathematical life of a mathematician is short. Work rarely improves after the age of twenty-five or thirty. If little has been accomplished by then, little will ever be accomplished.

It is the same with life. Some are influenced by the love of wealth while others are blindly led on by the mad fever for power and domination, but the finest type of man gives himself up to discovering the meaning and purpose of life itself. He seeks to uncover the secrets of nature. This is the man I call a philosopher for although no man is completely wise in all respects, he can love wisdom as the key to nature’s secrets.

Number theorists consider prime numbers to be the most important numbers of all because they are the atoms of mathematics. Prime numbers are the numerical building blocks because all other numbers can be created by multiplying combinations of the prime numbers.

On a fatal day, in the holy season of Lent, Hypatia was torn from her chariot, stripped naked, dragged to the church, and inhumanely butchered by the hands of Peter the Reader and a troop of savage and merciless fanatics; her flesh was scraped from her bones with sharp oyster-shells, and her quivering limbs were delivered to the flames.

Pascal was even convinced that he could use his theories to justify a belief in God. He stated that ‘the excitement that a gambler feels when making a bet is equal to the amount he might win multiplied by the probability of winning it’.

I am a liar!

Euclid discovered that perfect numbers are always the multiple of two numbers, one of which is a power of 2 and the other being the next power of 2 minus 1.

The product of mathematics is clarity and understanding. Not theorems, by themselves. Is there, for example any real reason that even such famous results as Fermat's Last Theorem, or the Poincaré conjecture, really matter? Their real importance is not in their specific statements, but their role in challenging our understanding, presenting challenges that led to mathematical developments that increased our understanding. The world does not suffer from an oversupply of clarity and understanding (to put it mildly). How and whether specific mathematics might lead to improving the world (whatever that means) is usually impossible to tease out, but mathematics collectively is extremely important.

Sophie Germain’s paper, ‘Recherches sur la théorie des surfaces élastiques’, written in 1815 and published in 1821, won her a prize of a kilogram of gold from the French Academy of Sciences in 1816. The paper contained some significant errors, but became the basis for work on the subject by Lagrange, Poisson, Kirchoff, Navier and others. Sophie Germain is probably better known for having made one of the first significant breakthroughs in the study of Fermat’s last theorem. She proved that if x, y and z are integers satisfying x5 + y5 = z5, then at least one of x, y and z has to be divisible by 5. More generally, she showed that the same was true when 5 is replaced by any prime p such that 2p + 1 is also a prime.

Choose a tough, world-class problem, one that requires only a sheet of paper and a pencil, like Goldbach’s Conjecture or Fermat’s Last Theorem, or a question in pure natural philosophy that doesn’t need pencil and paper at all, like the origin of the universe, and then throw yourself entirely into research. Think only of planting, not reaping, and as you concentrate, an entire lifetime will pass before you know it. That’s what people mean by settling down.

Fermat’s Last Theorem dates to 1637. The French mathematician and physicist Pierre de Fermat had scribbled it in the margins of a book, adding that he had discovered a marvelous proof but that the margins were too small to hold it.

Replying two weeks later he states his opinion of Fermat’s Last Theorem. “I am very much obliged for your news concerning the Paris prize. But I confess that Fermat’s Theorem as an isolated proposition has very little interest for me, because I could easily lay down a multitude of such propositions, which one could neither prove nor dispose of.

The problem looks so straightforward because it is based on the one piece of mathematics that everyone can remember – Pythagoras’ theorem: In a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides.

A problem worthy of attack Proves its worth by fighting back. Piet Hein

Life, Prince Leon, may well be compared with these public Games for in the vast crowd assembled here some are attracted by the acquisition of gain, others are led on by the hopes and ambitions of fame and glory. But among them there are a few who have come to observe and to understand all that passes here. It is the same with life. Some are influenced by the love of wealth while others are blindly led on by the mad fever for power and domination, but the finest type of man gives himself up to discovering the meaning and purpose of life itself. He seeks to uncover the secrets of nature. This is the man I call a philosopher for although no man is completely wise in all respects, he can love wisdom as the key to nature’s secrets.

Fermat’s last theorem,