Today's Google doodle is apparently too small to contain the proof of Fermat's Last Theorem
Joyeux anniversaire, Pierre de Fermat! Today is the French mathematician's 410th birthday.
Fermat is best known as the originator or Fermat's Last Theorem, which consists of a deceptively simple-looking formula famously scrawled in a book's margin, where he claimed the proof was too large to fit. The theorem's fame grew because – despite the efforts of countless mathematicians – four centuries would pass before the publication of a successful proof in 1995 by Sir Andrew Wiles, a Royal Society Research Professor at Oxford.
Fermat's birthday is marked today with a Google doodle, and in a wry reference to the mathematician's original margin note, if you hover your mouse over the doodle the alt text is "I have discovered a truly marvelous proof of this theorem, which this doodle is too small to contain."
According to the theorem, for any integer n greater than two, there are no positive integers a, b, and c that can satisfy the equation:
an + bn = cn
You may recognise from your school days the simple case when n = 2 as Pythagoras' Theorem.
Perhaps Fermat would have preferred to be remembered for something other than a small comment in the margin of a book? Here are some of the things that you may not know about Pierre de Fermat.
• Pierre de Fermat is not Pierre de Fermat. He studied to be a lawyer at the University of Orleans, and went on to be the councillor at the High Court of Judicature in Toulouse. Here he became entitled to change his name from Pierre Fermat to Pierre de Fermat.
• Fermat has his own number. Fermat numbers have been found to be good at generating sequences of random numbers that are ideal for data encryption on computers, keeping all your banking and personal files safe.
• Fermat also has a little theorem. Fermat's Little Theorem is used in something called Fermat's Primality Test. The test tells us whether a whole number is a probable prime. Whereas a prime number is strictly a number only divisible by one and itself, a probable prime has similar properties but may be easier to generate. These numbers are very important in cryptography and internet security.
• Fermat is one of the founders of probability theory. Through his close relationship with Blaise Pascal, a mathematician and philosopher, he studied how chance behaves in games with dice. An exchange of letters between the two mathematicians developed a general formulation of probability theory – work which still provides the basic principles of how sporting odds are calculated today from horse racing to football.
It is a measure of Fermat's influence that many of his results are used today in computing and cryptography. However, he is well known for not giving rigorous mathematical proofs with his work. For example, the proof of Fermat's Little Theorem was first given not by Fermat but by Gottfried Leibniz.
This reticence has intrigued and frustrated mathematicians for centuries. On the plus side, there's still some of Fermat's work yet to be proven. So, given the inclination, you can try your hand at solving them.
Pierre de Fermat
Pierre de Fermat
Born August 17, 1601
Beaumont-de-Lomagne, France Died January 12, 1665 (aged 63)
Castres, France Residence France Nationality French Fields Mathematics and Law Known for Number theory
Analytic geometry
Fermat's principle
Probability
Fermat's Last Theorem Influences François Viète
Life and work
Fermat was born in Beaumont-de-Lomagne, Tarn-et-Garonne, France; the late 15th century mansion where Fermat was born is now a museum. He was of Basque origin. Fermat's father was a wealthy leather merchant and second consul of Beaumont-de-Lomagne. Pierre had a brother and two sisters and was almost certainly brought up in the town of his birth. There is little evidence concerning his school education, but it may have been at the local Franciscan monastery.
He attended the University of Toulouse before moving to Bordeaux in the second half of the 1620s. In Bordeaux he began his first serious mathematical researches and in 1629 he gave a copy of his restoration of Apollonius's De Locis Planis to one of the mathematicians there. Certainly in Bordeaux he was in contact with Beaugrand and during this time he produced important work on maxima and minima which he gave to Étienne d'Espagnet who clearly shared mathematical interests with Fermat. There he became much influenced by the work of François Viète.
From Bordeaux, Fermat went to Orléans where he studied law at the University. He received a degree in civil law before, in 1631, receiving the title of councillor at the High Court of Judicature in Toulouse, which he held for the rest of his life. Due to the office he now held he became entitled to change his name from Pierre Fermat to Pierre de Fermat. Fluent in Latin, Basque,classical Greek, Italian, and Spanish, Fermat was praised for his written verse in several languages, and his advice was eagerly sought regarding the emendation of Greek texts.
He communicated most of his work in letters to friends, often with little or no proof of his theorems. This allowed him to preserve his status as an "amateur" while gaining the recognition he desired. This naturally led to priority disputes with fellow contemporaries such as Descartes and Wallis. He developed a close relationship with Blaise Pascal.
Anders Hald writes that, "The basis of Fermat's mathematics was the classical Greek treatises combined with Vieta's new algebraic methods."
Holografikus kép Pierre de Fermat 1660. március 4 írt végrendeletéről – Departmental Archives,Haute-Garonne, Toulouse.
Pierre de Fermat's Last Theorem celebrated in a cheeky Google doodle
- Wednesday, August 17, 2011
- By Sourabh Banerjee
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