Pascal - 17th Century Mathematics - The Story of Mathematics
Through his correspondence with Blaise Pascal he was a co-founder of the theory of Credit for changing this perception goes to Pierre de Fermat (– 65). 9 Council for Capital Formation, ) 1; D Bernheim, 'Financial illiteracy, amateur mathematician Pierre de Fermat and mathematician Blaise Pascal; 14 Ibid, at 7–10; eg, Giddens claimed that 'Trust is usually more of a continuous state . Winners and losers in the risk society' () 61 Human Relations , . Blaise Pascal was 17th century genius who invented the mechanical calculator. Pierre de Fermat is famous for a theorem that took three.
Beginning inhe was appointed exclusively deciphering the enemy's secret codes. His work was resumed, after his death, by the scientific adviser to the Pope, Christopher Clavius. Without doubt, he believed himself to be a kind of "King of Times" as the historian of mathematics, Dhombres, claimed.
He said that Clavius was very clever to explain the principles of mathematics, that he heard with great clarity what the authors had invented, and wrote various treatises compiling what had been written before him without quoting its references.
Pierre de Fermat - Wikipedia
So, his works were in a better order which was scattered and confused in early writings In March that same year, Adriaan van Roomen sought the resolution, by any of Europe's top mathematicians, to a polynomial equation of degree King Henri IV received a snub from the Dutch ambassador, who claimed that there was no mathematician in France.
He said it was simply because some Dutch mathematician, Adriaan van Roomen, had not asked any Frenchman to solve his problem. He resolved this at once, and said he was able to give at the same time actually the next day the solution to the other 22 problems to the ambassador.
Further, he sent a new problem back to Van Roomen, for resolution by Euclidean tools rule and compass of the lost answer to the problem first set by Apollonius of Perga. Van Roomen could not overcome that problem without resorting to a trick see detail below. Henry IV, however, charged him to end the revolt of the Notaries, whom the King had ordered to pay back their fees.
A few weeks before his death, he wrote a final thesis on issues of cryptography, whose memory made obsolete all encryption methods of the time. Jeanne, the eldest, died inhaving married Jean Gabriau, a councillor of the parliament of Brittany.
Suzanne died in January in Paris. The cause of Vieta's death is unknown.
Alexander Andersonstudent of Vieta and publisher of his scientific writings, speaks of a "praeceps et immaturum autoris fatum. At the time of Vieta, algebra therefore oscillated between arithmetic, which gave the appearance of a list of rules, and geometry which seemed more rigorous.
On the other hand, the German school of the Coss, the Welsh mathematician Robert Recorde and the Dutchman Simon Stevin brought an early algebraic notation, the use of decimals and exponents.
However, complex numbers remained at best a philosophical way of thinking and Descartesalmost a century after their invention, used them as imaginary numbers. Only positive solutions were considered and using geometrical proof was common. The task of the mathematicians was in fact twofold.
It was necessary to produce algebra in a more geometrical way, i. Vieta and Descartes solved this dual task in a double revolution.
François Viète - Wikipedia
Firstly, Vieta gave algebra a foundation as strong as in geometry. He then ended the algebra of procedures al-Jabr and Muqabalacreating the first symbolic algebra and claiming that with it, all problems could be solved nullum non problema solvere. Behold, the art which I present is new, but in truth so old, so spoiled and defiled by the barbarians, that I considered it necessary, in order to introduce an entirely new form into it, to think out and publish a new vocabulary, having gotten rid of all its pseudo-technical terms He took years in publishing his work, he was very meticulous and most importantly, he made a very specific choice to separate the unknown variables, using consonants for parameters and vowels for unknowns.
In this notation he perhaps followed some older contemporaries, such as Petrus Ramuswho designated the points in geometrical figures by vowels, making use of consonants, R, S, T, etc. Vieta also remained a prisoner of his time in several respects: First, he was heir of Ramus and did not address the lengths as numbers.
His writing kept track of homogeneity, which did not simplify their reading. He failed to recognize the complex numbers of Bombelli and needed to double-check his algebraic answers through geometrical construction. Although he was fully aware that his new algebra was sufficient to give a solution, this concession tainted his reputation.
- Pierre de Fermat
However, Vieta created many innovations: The curves determined by this equation are known as the parabolas or hyperbolas of Fermat according as n is positive or negative. 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. He also solved the related problem of finding the surface area of a segment of a paraboloid of revolution. Descartes had sought to justify the sine law through a premise that light travels more rapidly in the denser of the two media involved in the refraction.
Twenty years later Fermat noted that this appeared to be in conflict with the view espoused by Aristotelians that nature always chooses the shortest path. Through the mathematician and theologian Marin Mersennewho, as a friend of Descartes, often acted as an intermediary with other scholars, Fermat in maintained a controversy with Descartes on the validity of their respective methods for tangents to curves.
In he had enjoyed an exchange of letters with his fellow mathematician Blaise Pascal on problems in probability concerning games of chance, the results of which were extended and published by Huygens in his De Ratiociniis in Ludo Aleae Work on theory of numbers Fermat vainly sought to persuade Pascal to join him in research in number theory. Inspired by an edition in of the Arithmetic of Diophantusthe Greek mathematician of the 3rd century ad, Fermat had discovered new results in the so-called higher arithmetic, many of which concerned properties of prime numbers those positive integers that have no factors other than 1 and themselves.