By Leen Veirman, Ine Weyn and Sophie Verhaert

 

 

Pierre de Fermat

 

 

 

 

 

 

 

 

 

Born : 17 August 1601

Died : 12 January 1665

 

 

 

 

 

 

 

 

"I have discovered a truly remarkable proof

which this margin is too small to contain."

 

 

 

Pierre de Fermat was born on August 17, 1601 in Beaumont-de-Lomagne near Toulouse in France. His father had a prosperous leather business and his mother was member of a famous family who practiced law. At the beginning Fermat took lessons at home, later he received a classical secondary education, beginning at the convent of the Cordeliers in Beaumont (run by the Fransiscans). Afterwards he studied with the Jesuits and later he attended the University of Toulouse.He obtained the degree of Bachelor of Civil Laws from the University of Orleans in 1631.On May 14, 1631, he registered as a lawyer in Toulouse and so he became entitled to change his name from Pierre Fermat to Pierre de Fermat. He was very humble and dutiful.To protect himself against corruption, he lived a pull backed live. So he had lots of time to practice his hobbies: classical languages and pure maths. He got married on the first of June1631 and had five children. He was a true catholic and so were his children. That ‘s why two of them went to the convent.


When a book called: "Diophantus’Arithmetica" was published in 1621, it interested Fermat very much. There was a question in the Arithmetica : assuming that x, y, z and n are positive integers, when does xn + yn = zn have a solution?

Fermat claimed : "I have discovered a truly remarkable proof, that it is impossible to separate any power above the second into powers of the same degree, but this margin is too narrow to contain it". The marginal notes only became known after Fermat's dead, when his son Samuel published an edition of Bachet's translation of Diophantus's Arithmetica with his father's notes in 1670.

It took mathematicians more than 300 years to figure out the proof of Fermat’s Last Theorem. The British mathematician Andrew Wiles, professor of Princeton, proved Fermat's assertion in June 1993 but Wiles withdrew the claim when problems emerged later in 1993. In November 1994 Wiles again claimed to have a correct proof. Be that as it may, a proof of such enormous complexity, requiring some 1000 pages to present, will need to be checked and rechecked in every detail by the few mathematicians capable of doing so. Prof. Van Geel and Cornelissen from the R.U.G. called the proof "Fermat -Wiles" which confirms that there can be no counter-example to Fermat's Last Theorem.

In 1634 Fermat rose to the position of Conseiller aux Enquêtes. On January 16, 1638 he was appointed to a higher Chamber of the Parliament.

When Descartes published a book called "La Géometrie" in 1637, it seems that Fermat was already studying analytic geometry for seven years. After Fermat had corrected a mistake in Descartes’ book, Descartes considered Fermat as his enemy.

 In 1642, Fermat entered the highest Council of the Parliament, the Criminal Court and the Grand Chambre. He also served as president of the Chambre de l’Edit.

 In 1648 Pierre de Fermat became Councillor of king Louis XIV in the Parliament of Toulouse.

Fermat died on January 12, 1665, at the age of 64 in Castres(France).

Fermat's contribution to mathematics

Although Fermat did not publish his findings, he communicated with nearly every great mathematician of his day on a variety of mathematical topics, including analytical geometry, number theory, geometry, differential calculus and trigonometry. He proposed problems, offered solutions, and presented statements of fact that he had proven, challenging others to do so as well. Dubbed "Prince of the Amateurs" for his achievements in maths, he is considered the last great mathematician to pursue maths as simply a recreation and not a vocation. It appears that Fermat visualized analytical geometry before René Descartes (1596-1650) and had much of notion of differential calculus in hand years before Isaac Newton (1642-1727) invented it. By writing letters to his friends, among them to Blaise Pascale(1623-1662) ... an other great French mathematician, originated the study of the calculation of probability and the least time principle which states that light will travel through an optical system in such a way as to pass from starting to ending point in the least amount of time.

There can be little doubt that Fermat's favourite mathematical recreation was to explore the properties of the natural numbers. Pierre de Fermat will be best remembered for his work in number theory, in particular for his Last Theorem which has been (and will be ?) the source of mystery and discussion since the publishing(1670) of his marginal notes.

 Least time principle

Although primarily a 'pure mathematician', Fermat was always ready to apply his mind to physical problems. In two letters written in 1657 and 1662 he enunciated his 'principle of least time'. This states that a ray of light travelling from a point A to another point B, and being reflected and refracted in any manner in the course, of its journey, will take the quickest path from A to B. The figure above illustrates a single reflection. Clearly the shortest - and hence fastest - path from A to B via the reflecting surface (i.e. AP + PB) requires P to ber so positioned that the marked angles are equal. Any other path (e.g. AQ + QB) is obviously longer.

Fermat's point : historical problem, proposed also to Evangelista Torricelli (1608-1647)

For a while, Fermat was the clearinghouse for all mathematical progress in Europe. In response to a problem he received, he determined the location of a minimum point in a triangle : i.e. the point that is located at a minimum total distance from all three vertices of an acute triangle. In the figure below, FA + FB +FC is at the minimum when point F is Fermat's point or, in mathematical terms, known as the isogonic point.

Fermat's solution uses the construction of equilateral triangles on sides AB,AC,BC. The intersection of the segments QC,RA, SB gives you Fermat's point. Torricelli found the same point but by a slightly different construction. Using the same three equilateral triangles as constructed by Fermat, draw circumscribed circles about each one of them. The circumstribed circles will intersect in the same minimum distance point.

 

Sources :

Fermat eindelijk overwonnen : "De Standaard" van 1 april 1995

"Fermat, Pierre de" Microsoft(R) Encarta(R) 96 Encyclopedia. (c) 1993-1995

Makers of mathematics : Stuart Hollingdale

Classic Math, History Topics for the Classroom : Art Johnson

internet:

http://www.es.rice.edu/ES/humsa/Galileo/Catalog/Files/Fermat.html

http://www.astro.virginia.edu/ewwbr/bios/Fermat.html

http://www.studww.rug.ac.be/hvernaev/Fermat.html

http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Fermat.html

 

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