# Blaise pascal and pierre de fermat relationship

### Pierre Fermat ()

The Frenchman Blaise Pascal was a prominent 17th Century scientist, and correspondence with his French contemporary Pierre de Fermat and the Dutchman. Mathematician Blaise Pascal was born on June 19, , theory with Pierre de Fermat and published the theological work Les Provinciales. Pierre de Fermat is one of the top ten greatest mathematicians in history. Alongside Blaise Pascal, he established the foundations of probability theory, which concerned with the study of whole numbers, the relationships between them, and.

With his method, he was able to reduce this evaluation to the sum of geometric series. It was while researching perfect numbers that he discovered Fermat's little theorem. Fermat developed the two-square theoremand the polygonal number theoremwhich states that each number is a sum of three triangular numbersfour square numbersfive pentagonal numbersand so on.

Although Fermat claimed to have proven all his arithmetic theorems, few records of his proofs have survived. Many mathematicians, including Gaussdoubted several of his claims, especially given the difficulty of some of the problems and the limited mathematical methods available to Fermat.

### Pierre de Fermat | Biography & Facts | rhein-main-verzeichnis.info

His famous Last Theorem was first discovered by his son in the margin in his father's copy of an edition of Diophantusand included the statement that the margin was too small to include the proof. It seems that he had not written to Marin Mersenne about it.

It was first proven inby Sir Andrew Wilesusing techniques unavailable to Fermat. Although he carefully studied and drew inspiration from Diophantus, Fermat began a different tradition.

### Pascal - 17th Century Mathematics - The Story of Mathematics

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. From this brief but productive collaboration on the problem of pointsthey are now regarded as joint founders of probability theory. But, if the game is interrupted at the point where Fermatsay, is winning 8 points to 7, how is the franc pot to divided?

Fermat claimed that, as he needed only two more points to win the game, and Pascal needed three, the game would have been over after four more tosses of the coin because, if Pascal did not get the necessary 3 points for your victory over the four tosses, then Fermat must have gained the necessary 2 points for his victory, and vice versa. Pascal then looked for a way of generalizing the problem that would avoid the tedious listing of possibilities, and realized that he could use rows from his triangle of coefficients to generate the numbers, no matter how many tosses of the coin remained.

Pascal and Fermat had grasped through their correspondence a very important concept that, though perhaps intuitive to us today, was all but revolutionary in This was the idea of equally probable outcomes, that the probability of something occurring could be computed by enumerating the number of equally likely ways it could occur, and dividing this by the total number of possible outcomes of the given situation.

This allowed the use of fractions and ratios in the calculation of the likelhood of events, and the operation of multiplication and addition on these fractional probabilities. Later in life, Pascal and his sister Jacqueline strongly identified with the extreme Catholic religious movement of Jansenism.

Following the death of his father and a "mystical experience" in latehe had his "second conversion" and abandoned his scientific work completely, devoting himself to philosophy and theology.

Fermat met Carcavi in a professional capacity since both were councillors in Toulouse but they both shared a love of mathematics and Fermat told Carcavi about his mathematical discoveries.

In Carcavi went to Paris as royal librarian and made contact with Mersenne and his group. Mersenne 's interest was aroused by Carcavi 's descriptions of Fermat's discoveries on falling bodies, and he wrote to Fermat. Fermat replied on 26 April and, in addition to telling Mersenne about errors which he believed that Galileo had made in his description of free fall, he also told Mersenne about his work on spirals and his restoration of Apollonius 's Plane loci.

His work on spirals had been motivated by considering the path of free falling bodies and he had used methods generalised from Archimedes ' work On spirals to compute areas under the spirals.

In addition Fermat wrote: I will share all of this with you whenever you wish and do so without any ambition, from which I am more exempt and more distant than any man in the world. It is somewhat ironical that this initial contact with Fermat and the scientific community came through his study of free fall since Fermat had little interest in physical applications of mathematics.

Even with his results on free fall he was much more interested in proving geometrical theorems than in their relation to the real world. This first letter did however contain two problems on maxima which Fermat asked Mersenne to pass on to the Paris mathematicians and this was to be the typical style of Fermat's letters, he would challenge others to find results which he had already obtained.

Roberval and Mersenne found that Fermat's problems in this first, and subsequent, letters were extremely difficult and usually not soluble using current techniques. They asked him to divulge his methods and Fermat sent Method for determining Maxima and Minima and Tangents to Curved Lines, his restored text of Apollonius 's Plane loci and his algebraic approach to geometry Introduction to Plane and Solid Loci to the Paris mathematicians. His reputation as one of the leading mathematicians in the world came quickly but attempts to get his work published failed mainly because Fermat never really wanted to put his work into a polished form.

## What was the relationship between Pascal and Fermat...?

The widening correspondence between Fermat and other mathematicians did not find universal praise. Frenicle de Bessy became annoyed at Fermat's problems which to him were impossible. He wrote angrily to Fermat but although Fermat gave more details in his reply, Frenicle de Bessy felt that Fermat was almost teasing him.

• Pierre de Fermat
• Blaise Pascal

However Fermat soon became engaged in a controversy with a more major mathematician than Frenicle de Bessy. He claimed that Descartes had not correctly deduced his law of refraction since it was inherent in his assumptions.

To say that Descartes was not pleased is an understatement. Descartes attacked Fermat's method of maxima, minima and tangents. Fermat proved correct and eventually Descartes admitted this writing: Did this end the matter and increase Fermat's standing? Not at all since Descartes tried to damage Fermat's reputation. For example, although he wrote to Fermat praising his work on determining the tangent to a cycloid which is indeed correctDescartes wrote to Mersenne claiming that it was incorrect and saying that Fermat was inadequate as a mathematician and a thinker.

Descartes was important and respected and thus was able to severely damage Fermat's reputation.

Pierre de Fermat: Biography of a Great Thinker

The period from to was one when Fermat was out of touch with his scientific colleagues in Paris. There are a number of reasons for this.