Another Frenchman of the 17th Century, Pierre de Fermat, effectively invented modern number theory virtually single-handedly, despite being a small-town amateur mathematician. Stimulated and inspired by the “Arithmetica” of the Hellenistic mathematician Diophantus, he went on to discover several new patterns in numbers which had defeated mathematicians for centuries, and throughout his life he devised a wide range of conjectures and theorems. He is also given credit for early developments that led to modern calculus, and for early progress in probability theory.
Although he showed an early interest in mathematics, he went on study law and received the title of councillor at the High Court of Judicature in Toulouse in 1631, which he held for the rest of his life. He was fluent in Latin, Greek, Italian and Spanish, and was praised for his written verse in several languages, and eagerly sought for advice on the emendation of Greek texts.
Fermat's mathematical work was communicated mainly in letters to friends, often with little or no proof of his theorems. Although he himself claimed to have proved all his arithmetic theorems, few records of his proofs have survived, and many mathematicians have doubted some of his claims, especially given the difficulty of some of the problems and the limited mathematical tools available to Fermat.
One example of his many theorems is the Two Square Theorem, which shows that any prime number which, when divided by 4, leaves a remainder of 1 (i.e. can be written in the form 4n + 1), can always be re-written as the sum of two square numbers.
Fermat’s correspondence with his friend Pascal also helped mathematicians grasp a very important concept in basic probability which, although perhaps intuitive to us now, was revolutionary in 1654, namely the idea of equally probable outcomes and expected values.
To know what Fermat's Little Theorem is about, what numbers are watch a video below:
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