One of the great mathematicians of the seventeenth century, he was a
jurist and parliamentary counsellor of the king
in the French town of Toulouse. He discovered a method for drawing
tangents to curves and for finding maxima and minima (the elements
of the Differential Calculus). In 1924 a letter written by Isaac
Newton was discovered wherein Newton acknowledged that his own early
ideas came from Fermat's work. Jointly with Pascal, Fermat established
the basics of the theory of probability and, with Descartes, he was
the founder of analytic geometry. One of the most famous problems in mathematics is Fermat's Last Theorem:
For integer values on n > 2, the equation xn + yn = zn has no positive integer solutions for x, y, z.
Of this theorem Fermat wrote in the margin of a book:
I have found
a truly wonderful proof which this margin is too narrow to contain.
Although many great mathematicians tried hard, it remained
unsolved until just recently.
(See Wiles and PBS/NOVA/proof but, most especially, the inspiring story of Math's Hidden Woman, Sophie Germain.)