Pierre de Fermat | Revolvy
Sophie Germain · Fermat Quiz Pierre de Fermat is one of the top ten greatest mathematicians in history. Alongside Blaise Pascal, he established the foundations of probability theory, which Number theory is the purest form of mathematics, concerned with the study of whole numbers, the relationships between them, and. All Quizzes Fresh Lists Trending Topics. Pierre de Fermat. Save. Pierre de Fermat (French:) (Between 31 October and 6 December  – 12 January . Through their correspondence in , Fermat and Blaise Pascal helped lay the  With his gift for number relations and his ability to find proofs for many of his. The Frenchman Blaise Pascal was a prominent 17th Century scientist, and correspondence with his French contemporary Pierre de Fermat and the Dutchman.
Pierre de Fermat - Wikipedia
Most kids with the idea that they're "good at math" do their best to avoid such problems altogether, because they automatically cause a crisis: Just as he harps on this relative evaluation of the two, he also harps on the fact that in the letter that frames the book, Pascal is visibly struggling to understand what Fermat is saying, and it is on this basis that Fermat is judged superior.
Devlin gives us to understand that Fermat probably solved the problem quickly and had no confusions about it, but humored Pascal's slow process of making sense of his elegant solution. Now, the primary sources Devlin provides us do not force this interpretation of the story, but more importantly, Devlin is implying to his readership that struggling with an idea makes you lesser.What is Financial Economics? - Definition of Financial Economics
In order to be truly great, we are being told, you have to solve the problem quickly, without struggle. A student fed on such ideas is doomed as a creator of original mathematics because no great idea was ever arrived at without struggle. There is a venerable history of hiding this fact, but the fact remains. I read elsewhere that the great Simon de Laplace used to write "it is easy to see" about conclusions that he would wrestle with for an hour.
What leaves me particluarly mad about this is that the story Devlin tells is clearly an opportunity for the opposite lesson. I was drawn to the book in the bookstore partly because of this. It has a sub-subtitle: It is the natural state of such an idea to be not entirely worked out, not yet cleaned up, still being struggled with.
Of course Pascal was struggling with Fermat's solution. I feel utterly certain that Fermat struggled with it too, even if by the time of the correspondence he had sorted things out for himself. My point is that this could have been a story that revealed the creation of original, groundbreaking, in fact world-changing mathematics to be a human activity that the reader can relate to.
That radical, exciting possibility is what this book could have been.
Pierre de Fermat
Diophantus was content to find a single solution to his equations, even if it were an undesired fractional one. Fermat was interested only in integer solutions to his Diophantine equationsand he looked for all possible general solutions. He often proved that certain equations had no solutionwhich usually baffled his contemporaries. Through their correspondence inFermat and Blaise Pascal helped lay the foundation for the theory of probability.
From this brief but productive collaboration on the problem of pointsthey are now regarded as joint founders of probability theory. In it, he was asked by a professional gambler why if he bet on rolling at least one six in four throws of a die he won in the long term, whereas betting on throwing at least one double-six in 24 throws of two dice resulted in his losing.
Fermat showed mathematically why this was the case. It says that, for the path of light reflecting from a mirror, the angle of incidence equals the angle of reflection. Hero of Alexandria later showed that this path gave the shortest length and the least time.
The terms Fermat's principle and Fermat functional were named in recognition of this role. Translation of the plaque: According to Peter L. Bernsteinin his book Against the Gods, Fermat "was a mathematician of rare power. He was an independent inventor of analytic geometryhe contributed to the early development of calculus, he did research on the weight of the earth, and he worked on light refraction and optics. In the course of what turned out to be an extended correspondence with Pascal, he made a significant contribution to the theory of probability.
Sometime before he became known as Pierre de Fermat, though the authority for this designation is uncertain. In he was named to the Criminal Court.
The curves determined by this equation are known as the parabolas or hyperbolas of Fermat according as n is positive or negative.
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These curves in turn directed him in the middle s to an algorithmor rule of mathematical procedure, that was equivalent to differentiation. This procedure enabled him to find equations of tangents to curves and to locate maximum, minimum, and inflection points of polynomial curves, which are graphs of linear combinations of powers of the independent variable. During the same years, he found formulas for areas bounded by these curves through a summation process that is equivalent to the formula now used for the same purpose in the integral calculus.
Such a formula is: It is not known whether or not Fermat noticed that differentiation of xn, leading to nan - 1, is the inverse of integrating xn. Through ingenious transformations he handled problems involving more general algebraic curves, and he applied his analysis of infinitesimal quantities to a variety of other problems, including the calculation of centres of gravity and finding the lengths of curves.